preface - universitas brawijaya...13.00 - 13.30 invited a/prof. dann mallet investigating chlamydia...

The Third Basic Science International Conference - 2013 i

Preface

All praises are due to Allah, God Almighty, Who made this annual event of successful. The “3rd

Annual Basic Science International Conference (BaSIC-2013)” is an annual scientific event organized

by the Faculty of Mathematics and Natural Sciences, Brawijaya University. As a basic science conference,

it covered a wide range of topics on basic science: physics, biology, chemistry, mathematics and statistics.

In 2013, the conference took a theme of “Basic Science Advances in Energy, Health and Environment”

as those three aspects of life are hot issues.

The conference in 2013 was the continuation of the preceding conferences initiated in 2011 as the

International Conference on Basic Science (ICBS), where it was a transformation from the similar

national events the faculty had organized since 2004. What also changed in year 2013 was the use of the

ISSN for the conference proceedings book, instead of an ISBN used in previous proceedings books. The

change was based on the fact that BaSIC is an annual event, and, therefore, the use of ISSN is more

appropriate. The proceedings book was also divided into four books: Physics, Biology, Chemistry and

Mathematics, each with a different ISSN. The proceedings were also published in electronic forms that can

be accessed from BaSIC website. I am glad that for the first time both types of publication can be realized.

This event is aimed to promote scientific research activities by Indonesian scientists, especially

those of Brawijaya University, in a hope that they may interact and build up networks and collaborations

with fellow overseas counterparts who participated in the conference. This is in line with university vision

as a World Class Entrepreneurial University.

I am grateful to all the members of the program committee who contributed for the success in

framing the program. I also thank all the delegates who contributed to the success of this conference by

accepting our invitation and submitting articles for presentation in the scientific program. I am also

indebted to PT Semen Gresik and PT PLN (Persero) for their support in sponsoring this event.

I wish for all of us a grand success in our scientific life. And I do hope that the coming conferences

will pick up similar success, and even better.

Malang, April 2013

Johan Noor, Ph.D.

Conference Chairperson

The Third Basic Science International Conference - 2013 ii

Foreword by the Rector of Brawijaya University

First of all I would like to congratulate the Organizing Committee for the success in organizing this

amazing event. I believe all dedicated time and efforts will contribute to the advancement of our beloved

university.

I would like to welcome all participants, domestic and overseas, especially the distinguished invited

speakers, to Malang, to the conference. An international conference is a good means to establish and build

relationships and collaborations among participants. So, I hope this conference will facilitate all of you, the

academicians and scientists, to setup a network of mutual and beneficial collaboration. As a university with

a vision to be “A World Class Entrepreneurial University”, Brawijaya University will support all efforts to

realize that dream.

Finally, I do hope that the conference will run smoothly and nicely and is not the last one. I would

like to thank all parties who have lent their hands in making this conference happened.

Malang, April 2013

Prof. Dr. Yogi Sugito

Rector, Brawijaya University

The Third Basic Science International Conference - 2013 iii

Table of Contents

Preface .............................................................................................................................................................. i

Foreword by the Rector of Brawijaya University ........................................................................................... ii

Table of Contents ........................................................................................................................................... iii

Program Committee ......................................................................................................................................... v

Scientific Program ........................................................................................................................................ viii

Scientific Papers

Invited Papers

Cluster Dynamics by Ultra-Fast Shape Recognition Technique.................................................... I01

Nanotechnology Development Strategy for Supporting National Industry in Indonesia .............. I02

Role of Atomic Scale Computational Research in the Nanoscale Materials ................................. I03

Paeonilorin(PF) Strongly Effects Immuno System ........................................................................ I04

Investigating Chlamydia trachomatis using mathematical and computational .............................. I05

Recent Trends in Liquid Chromatography for Bioanalysis ........................................................... I06

Submitted Papers

Input-Output Decoupling Problem for Descriptor System: Transfer Function Matrix ApproachM01

A cellular automata model to investigate immune cell-tumour cell interactions in growing tumours

in two spatial dimensions ............................................................................................................. M02

On The Structural Properties of Latin Square in Max-Plus Algebra ........................................... M03

On Uniform Convergence of Trigonometric Series Under p-Supremum Bounded Variation

Condition ...................................................................................................................................... M04

Generalized Dedekind Modules ................................................................................................... M05

Application Random Utility Method for Economic Valuation on Change of Tourism Quality (Case

Study : Gedong Songo Temple & Muncul, Central Java Province) ............................................ M11

The Third Basic Science International Conference - 2013 iv

Application of Statistic Non Parametric-Friedmen Test In Taste Testing Snack ........................ M13

Exploring the Metacognitive Skills of Secondary School Students' Use During Problem Posing

...................................................................................................................................................... M15

Role of Teacher and Mathematical Concept to Build Student's Character by Using 'Everyone is

Teacher' Method ........................................................................................................................... M16

Object Representation on Geometry Learning using Augmented Reality Approach .................. M17

Higest Posterior Density for Identifying Differences in Gene Expression Microarray Experiments

...................................................................................................................................................... M18

Estimation in Measurement Error Models on Cases of Malnutrition in the Province of East Java

...................................................................................................................................................... M21

Non-Trend Fourier Series Estimator in Heteroscedastic Nonparametric Regression .................. M22

On the Confidence Band of Local Likelihood Estimates in Generalized Poisson Regression Model

...................................................................................................................................................... M23

Prediction of Hourly Rainfall using Bayesian Neural Network with Adjusting Procedure ........ M24

Vector Auto-Regressive Control Chart and Its Application in Industry ...................................... M25

Application of the Peak Over Threshold Method for Extreme Rainfalls Modeling in Malang

Regency ........................................................................................................................................ M26

Bayesian Confidence Interval for Smoothing Spline in Nonparametric Multivariable Regression

Model ........................................................................................................................................... M28

Full Conditional Distribution Investigation of Bayesian Poisson Lognormal 2-Level

Spatiotemporal for Analyzing DHF Risk ..................................................................................... M29

On the View of the Modeling Interregional Migration in East Java: Selected Models ............... M30

Generalized Linear Model for Estimating AIDS Cases in Indonesia .......................................... M31

Determining Teaching Quality of Lecturer Based on Questioner Using Multinomial Distribution &

Objective Bayesian....................................................................................................................... M33

Spatial Interpolation Comparison in Estimating A Coal Deposit in Kabupaten Hulu Sungai Utara,

South Kalimantan, Indonesia ................................................................................................... PSM14

Author List ............................................................................................................................................... AU-1

Acknowledgement .................................................................................................................................. ACK-1

The Third Basic Science International Conference - 2013 v

Program Committee Patrons

Rector, Universitas Brawijaya

Dean, Faculty of Mathematics and Natural Sciences, Universitas Brawijaya

Advisory Boards

Associate Deans 1, 2 and 3, Faculty of Mathematics and Natural Sciences, Universitas Brawijaya

Chairperson

Johan A.E. Noor, Ph.D.

Deputy-Chair

Dr. Suharjono

Secretary

Agus Naba, Ph.D.

Treasurers

Mrs. Sri Purworini

Mrs. Rustika Adiningrum

Mr. Surakhman

Secretariat & Registration

Dr. Masruroh

dr. Kusharto

Mr. Sugeng Rianto

Mr. Gancang Saroja

Conference Web

Agus Naba, Ph.D.

Publication & Proceedings

Arinto Y.P. Wardoyo, Ph.D.

Mr. Wasis

Public Relations & Sponsorship

Chomsin S. Widodo, Ph.D.

Mr. Moch. Djamil

Mrs. Firdy Yuana

Venue

Mr. Ahmad Hidayat

Dr. Ahmad Nadhir

Mr. Sunariyadi

Mr. Purnomo

Mr. Karyadi Eka Putra

Accommodation & Hospitality

Ms. Siti J. Iswarin

Mrs. Lailatin Nuriyah

The Third Basic Science International Conference - 2013 vi

Mrs. Nur Azizah

Mr. Robi A. Indrajit

Mrs. Trivira Meirany

Master of Ceremony

Himafis

Transportation, Excursion & Social Events

Djoko Santjojo, Ph.D.

Dr. Sukir Maryanto

Mr. Wahyudi

Mrs. Arnawati

Workshop, Poster & Scientific Exhibitions

Hari Arief Dharmawan, Ph.D.

Mr. Pudji Santoso

Mr. Sahri

Mr. Murti Adi Widodo

Documentation

Mauludi A. Pamungkas, Ph.D.

Mr. Susilo Purwanto

General Supports

Himafis

Scientific Program

Dr. rer.nat. M. Nurhuda

Dr. Sunaryo

Mr. Agus Prasmono

Local Scientific Committees (Reviewers & Editors)

Physics

Dr. rer.nat. Abdurrouf

Adi Susilo, Ph.D.

Mr. Unggul P. Juswono

Dr.-Ing. Setyawan P. Sakti

Biology

Dr. Moch. Sasmito Djati

Dr. Muhaimin Rifai

Dr. Catur Retnaningdyah

Chemistry

Dr. Masruri

Dr. Ahmad Sabarudin

Dr. Lukman Hakim

Mathematics

Dr. Agus Suryanto

Dr. Wuryansari M.K.

Dr. Rahma Fitriani

Dr. Solimun

The Third Basic Science International Conference - 2013 vii

International Scientific Committee and Editors

A/Prof. Lilibeth dlC. Coo, University of the Philippines, the Philippines

Prof. Dr. Gereon Elbers, FH Aachen, Germany

Prof. S.K. Lai, National Central University, Taiwan

Prof. Kwang-Ryeol Lee, Korean Institute of Science and Technology, Korea

A/Prof. Dann Mallet, Queensland University of Technology, Australia

Prof. Lidia Morawska, Queensland University of Technology, Australia

Prof.Dr. Petr Solich, Charles University, Czech Republic

Dr. Michitaka Suzuki, Nagoya University, Japan

Prof. Hideo Tsuboi, Nagoya University, Japan

Prof. Jia-Lin Wang, National Central University, Taiwan

The Third Basic Science International Conference - 2013 viii

Scientific Program

Time Day One – 16 April 2013 Day Two – 17 April 2013

07.30 – 08.00 Registration

08.00 – 08.30 Inaugural Session, Welcome Remarks and

Opening Ceremony Poster Preparation

08.30 – 09.00 Coffee Break

Poster Session (08.30-09.30)

(Majapahit Hall)

09.00 – 09.45

Invited Speaker 1

Prof. Lidia Morawska, Queensland University

of Technology, Australia

Title: “Emissions to the Air: from

Multidisciplinary Science to Applications”

Coffee Break (09.30 – 10.00)

09.45 – 10.30

Invited Speaker 2

Dr. rer. nat. M. Nurhuda, Universitas

Brawijaya

Title: “Towards Energy Security for the Poor”

Parallel Session (start at 10.00)

10.30 – 11.15

Invited Speaker 3

Prof. S.K. Lai, National Central Univ., Taiwan

Title: “Cluster Dynamics by Ultra-Fast Shape

Recognition Technique”

11.15 – 12.00

Invited Speaker 4

Dr. Nurul Taufiqurrochman*, Indonesian

Nanotech Society

Title:”Nanotechnology Development Strategy

for Supporting National Industry in

Indonesia”

12.00 – 13.00 Lunch Break

13.00 – 15.00

Parallel Session Parallel Session

15.00 – 16.30

16.30 – 17.00 Closing Ceremony

17.00 – 19.00 Free Time

19.00 – 22.00 Conference Gala Dinner

The Third Basic Science International Conference - 2013 ix

Parallel Session Day One - 16 April 2013

Room 3: Mathematics

Time Paper

ID Author Title Moderator

13.00 -

13.30 Invited A/Prof. Dann Mallet

Investigating Chlamydia trachomatis

using Mathematical and

Computational Models

13.30 -

14.30

M01 Trisilowati, Scott

McCue, Dann Mallet

A cellular automata model to

investigate immune cell-tumour cell

interactions in growing tumours in two

spatial dimensions.

Edi

Cahyono

M02 Muhammad Syifa'ul

Mufid, Subiono

On the structural properties of Latin

squares in Max-Plus Algebra

M03

Moch. Aruman

Imron, Ch. Rini

Indrati, and Widodo

On Uniform Convergence of

Trigonometric series Under p-

Supremum Bounded Variation

Condition

M04

Erma Suwastika and

Intan Muchtadi-

Alamsyah

Generalized Dedekind Modules

M05 Nelly Oktavia A, S.Si,

MT

Object Representation on Geometry

Learning using Augmented Reality

Approach

Discussion/Questions/Answers

14.30 -

15.20

M06 Edi Cahyono

Temporal Data, Candle Stick

Representation and Temporal

Probability Density Function

Trisilowati

M07

Pasrun Adam, La

Gubu, and Edi

Cahyono

Statistical Characteristics of the

Dynamics of Jakarta Composite Index (JCI) Based on Short Term Data

Represented in Candle Sticks

M08

La Gubu, Jony Puspa

Kusuma, and Edi

Cahyono

Temporal Probability Density

Function of the Dynamics of United

States Dollar Relative to Indonesia

Rupiah

M09

La Ode Saidi, Rasas

Raya, and Edi

Cahyono

A temporal-probability density

function based on candle stick

representation data: The case of the

dynamics of Japan yen relative to

Indonesia rupiah


The Third Basic Science International Conference - 2013 x

15.20 -

16.10

M11 Sri Subanti

An Application of Random Utility

Method for Economic Valuation on

Change of Tourism Quality (Case

Study : Gedong Songo Temple &

Muncul, Semarang Regency, Central

Java Province)

Mukhsar

M13 Lisa Nesti

APPLICATION OF STATISTIC

NON PARAMETRIC-FRIEDMEN

TEST IN TASTE TESTING OF

SNACK PRODUK

M15 Tony Karnain

Exploring the Metacognitive Skills of

Secondary School Students' Use

During Problem Posing

M16 Muhammad Rifki

Taufik

Role of Teacher and Mathematical

Concept to Build Student's Character

by Using 'Everyone is Teacher'

Method

M17 Nelly Oktavia

Adiwijaya

Object Representation on Geometry

Learning using Augmented Reality

Approach


The Third Basic Science International Conference - 2013 xi

Parallel Session Day Two - 17 April 2013

Room 3: Mathematics

Time Paper

ID Author Title Moderator

10.00 -

11.00

M18

Ani Budi Astuti, Nur

Iriawan, Irhamah,

Heri Kuswanto

Higest Posterior Density for

Identifying Differences in Gene

Expression Microarray Experiments

Rita Diana

M19 Mukhsar, N. Iriawan,

B.S.S. Ulama, Sutikno

Full Conditional Distribution

Investigation of Bayesian Poisson-

Lognormal 2-Level Spatiotemporal for

Analysing DHF Case

M20

Preatin, Nur Iriawan,

Ismaini Zain, Wendy

Hartanto

Modelling interregional migration in

East Java : Selected Models

M21

Ida Mariati Hutabarat,

Asep Saefuddin,

Hardinsyah, Anik

Djuraidah

Estimation in measurement error

models on Cases of Malnutrition in

the Province of East Java

M22 I Nyoman Budiantara

and Rahmawati Pane

Non Trend Fourier Series Estimator In

Heteroscedastic Nonparametric

Regression


11.00 -

12.00

M23 I Nyoman Budiantara,

Sony Sunaryo,

Mohamad Dokhi

On the Confidence Band of Local

Likelihood Estimates in Generalized

Poisson Regression Model

Ani Budi

Astuti

M24

K. Fithriasari, N.

Iriawan, B.S.S.

Ulama, Sutikno, H.

Kuswanto

Prediction of Hourly Rainfall using

Bayesian Neural Network with

Adjusting Procedure

M25 J.K. Wororomi, M.

Mashuri, Irhamah and

A. Z. Arifin

Vector Auto-Regressive Control Chart

and Its Application in Industry

M26

Rita Diana, I. Nyoman

Budiantara, Purhadi

and Satwiko Darmesto

Bayesian Confidence Interval for

Smoothing Spline in Nonparametric

Multivariable Regression Model

M31 Herlina Hanum Generalized Linear Model For

Estimating Aids Cases In Indonesia


Scientific Papers

Invited Papers

The Third Basic Science International Conference - 2013 I01

S.K. Lai1,2

and P.J. Hsu1,2

1Complex Liquids Laboratory, Department of Physics, National Central University, Chungli 320, Taiwan

2Molecular Science and Technology Program

Taiwan International Graduate Program, Academia Sinica,

Taipei 115, Taiwan

The time development of the molecular shapes (configurations) of macromolecules may be generated by

the molecular dynamics simulation and used to calculate for each molecular shape its structural similarity

(with respect to a reference configuration) with the ultra-fast shape recognition technique. This idea of

using the ultra-fast shape recognition technique [1] to track down the motion of atoms stems from our

observation that there are fundamental differences in the dynamics of atoms between a bulk system and a

finite system such as a macromolecule. For concreteness, we test the generality of the technique by

studying disparate metallic clusters. In broad sense, we look upon the metallic clusters as

“macromolecules”. To gain deeper insight into the cluster dynamics, our calculations are carried out in

three steps: pin down firstly individual atoms of the cluster and compute from their instantaneous

configuration a distribution of atomic distances, calculate a shape similarity index parameter, and finally

construct the temperature dependent contours of a probability shape similarity index function. The physical

content of the contours of the latter function presents a new perspective in interpreting the temporal change

of microstates and the bearings they have in revealing microscopic panoramas of pre-melting and melting

transition. Specifically, we found a correlation between the temperature variation of the probability shape

similarity function and the change in cluster dynamics, and hence gaining a more precise picture of

melting-like scenarios. Perhaps most importantly is that the ultra-fast shape recognition technique can be

implemented for understanding the sub-structures of clusters whose characteristic features present the kind

of discernment that proves difficult to extract in laboratory and computer-simulation experiments.

Reference:

[1] P.J. Ballester and W.G. Richards, Proc Roy Soc A Math. Phys. Eng. Sci. 463, 1307 (2007).

Cluster Dynamics by Ultra-Fast Shape Recognition

Technique


Nurul Taufiqu Rochman*

Research Center for Metallurgy, Indonesian Institute of Sciences

*Chairman, Indonesian Society for Nano

Kawasan PUSPIPTEK Serpong, Tangerang 15314 Indonesia

E-mail: [email protected]

It is believed that nanotechnology will become the next industrial revolution. Indonesia, a country with

abundant of natural resources (minerals, biodiversities) and 4th

largest in population, has to take advantage

for development of nanotechnology. This required appropriate strategy regarding to Indonesia’s potential

and capability in advancing technology. This study overviews a current status on development and

implementation of nanotechnology in Indonesia. First, a brief story about nanotechnology initiation in

Indonesia is described. National activities including policy, program and funding are then reported and

followed by explanation of several activities in each ministry (Ministry of Research and Technology,

Ministry of National Education, Ministry of Industry, and Ministry of Agriculture). Pictures of

nanotechnology human resources, R & D programs and facilities, and application of nanotechnology in

national industry are also explained in brief. Several research results on nanotechnology at our group are

also highlighted. Finally, activities on standardization, commercialization and building public awareness

are mentioned. In addition, potential areas of cross-country R&D cooperation and collaboration in the field

of nanotechnology also are described. As recommendation, good synergy between academic-

business/industry-government and networking development within regional research institution will

accelerate nanotechnology progress in Indonesia.

Keywords: nanotechnology development strategy, national industry, natural resources

Nanotechnology Development Strategy for Supporting

National Industry in Indonesia


Kwang-Ryeol Lee, Ph.D ([email protected])

Director-general, Institute for Multiscale Convergence of Matter,

Korea Institute of Science and Technology, Seoul, Korea

Computational research has been of increasing importance in wide spectrum of modern science and

technology. However, nowhere more so than in nano-bio science where molecular or atomic level

understandings of its structure, dynamics and properties are essential. Center for Computational Science

at KIST is focusing on the computational research in nano and bio technology. We are also

emphasizing the collaboration with experimental research for the synergic effect between experiments

and calculations. In this presentation, I will discuss the most up-to-date research activities of CSC-KIST

with specific examples of the nano-scale surface phenomena in both bulk and low-dimensional

materials, the multi-scale investigation of CNT reinforced composite materials, and the efforts for the

development of nano-TCAD environment.

Role of Atomic Scale Computational Research in the

Nanoscale Materials Science

mailto:[email protected]


Hideo Tsuboi

Nagoya University, Japan

Abstract

Paeony root (Paeoniae radix; Shakuyaku in Japanese) is one of the most well-known herbs in China, Korea

and Japan and has been used as a medicine for more than 1200 years. Paeoniflorin (PF), a glucoside, is

known to be one of the principle bioactive components of paeony root. PF has been reported to have

immunoregulatory, anti-allergic, anti-inflammatory, cognition-enhancing, neuromuscular-blocking, anti-

convulsant, anti-hyperglycemic, anti-coagulant, and sedative effects. However, the effect to innerceller

signal transduction or the bioactivity in molecular level is still not investigated at all. I have been interested

especially in the effect of PF to our immuno system and its working mechanism. Today, I introduce PF as a

herbal medicine and it's bioactivity from immunological stand point.

Paeonilorin(PF) Strongly Effects Immuno System


A/Prof. Dann Mallet

Mathematical Sciences, Queensland University of Technology, Brisbane, Australia

Abstract

Chlamydia trachomatis is the most common sexually transmitted pathogen of humans, with over 90 million

new adult cases occurring worldwide each year. Left untreated, chlamydial infection may result in severe

detrimental effects on reproductive health, especially in women. Infection becomes problematic and

persistent when it progresses from the lower to the upper genital tract, but despite intensive research there

is still debate over the mechanisms by which this progression occurs. This has led to the development of

mathematical models of the spatial changes and dynamics involved in the infection process. Here we

present a brief discussion of C. trachomatis before illustrating the progress to date in mathematical

modeling of the pathogen.

Investigating Chlamydia trachomatis using mathematical

and computational models


Petr Solich

Department of Analytical Chemistry, Charles University, Faculty of Pharmacy, Hradec Kralove, Czech

Republic

Abstract

Analytical chemistry – as a part of chemistry - is playing critical roles in the understanding of basic science

to a variety of practical applications, such as biomedical applications, environmental monitoring, quality

control of industrial manufacturing, food analysis, etc. One of the major challenges facing the medicine

today is developing of new therapies that improve human health. To help address these challenges the

utilization of enormous modern analytical technologies and high-throughput automated platforms has been

employed in the last decade, in order to perform more and more experiments in a shorter time frame with

increased data quality.

Liquid chromatography – and chromatography in general as well - is without any doubts the most

important analytical methodology, combining both qualitative and quantitative analysis in one step. In the

last decade various analytical strategies have been established to enhance separation speed and efficiency in

liquid chromatography applications. Current trends in fast liquid chromatographic separations involve

monolith technologies, fused-core columns, high-temperature liquid chromatography (HTLC) and ultra-

high performance liquid chromatography (UHPLC). The high specificity in combination with high

sensitivity makes it an attractive complementary method to traditional methodology used for routine

applications.

Introduction of ultra-high performance liquid chromatography (UHPLC) in 2006 has brought a new

challenge and attract more and more scientists for development of new applications using liquid

chromatography. Together with this new instrumentation, a huge expansion of new stationary phases was

registered during the last decade. Several different technologies in stationary phases - with different

characteristics were introduced into the market. Introduction of sub-2-micro particles brought a new

challenge into laboratories. Extensive decrease of time of analysis and excellent separation efficiency

attracted manufacturers and scientists to look for new applications. Monolithic technology is based on a

unique sorbent material allowing good quality of separations in a minimal time. The main advantages of

monoliths, apart from short analysis time, are long lifetime and immense robustness, in most cases far

exceeding those of particulate columns. This new type of monoliths have at higher efficiency, better peak

symmetry and longer lifetime compared with particulate columns. Core-shell technology using porous shell

and solid core particles broke into market during last 5 years. These columns can be used in common

HPLC instruments as well as in UHPLC systems. This technology promises to increase of resolution and

maximizes throughput, and result in solvent saving and easier method transfer.

Application of UHPLC and various new stationary phases to the mainly bioanalytical analysis, but also to

environmental and pharmaceutical analysis will be discussed and examples of application to analysis of

real samples will be shown.

Recent Trends in Liquid Chromatography for Bioanalysis

Scientific Papers

Submitted Papers

The Third Basic Science International Conference - 2013

M01-1

Abstract—In practical system analysis and control system design,

many system models may be established in the form of the general

descriptor (singular) system, while they cannot be described by the

standard normal system form. Descriptor systems appear in many fields, such as electrical networks, power systems, aerospace

engineering, chemical processes, social economic systems, and so on.

The problem of input-output decoupling is one of the major control

design problems, since it aims to reduce a multi-input/multi-outputsystem to a set of single-input/single-output systems, thus

greatly facilitating the control strategy. In this paper, we study the

problem of the input-output decoupling for descriptor system. The

problem is handled in transfer function matrix setting. The necessary and sufficient conditions for a solution of the decoupling problem are

established and an algorithm for calculation of feedback gains is

presented. Finally, a structural interpretation is also given for

decoupled systems.

Keywords—Descriptor system, input-output decoupling,

transfer function matrix

I. INTRODUCTION

he study of decoupling linear time-invariant multivariable

systems has received considerable attentions in both

control theory and industrial practice for several decades.

It is well known that within a multivariable control systems,

every input affects several outputs resulting in a complicated

input-output relationship. Decoupling control strategies have

been developed for the transformation of coupled input-output

system to equivalent decoupled systems. System decoupling

or noninteracting control is one of the major problems in

multivariable system theory and has been extensively

discussed in a number of papers on linear regular systems[l-

5].Some literature has also appeared on the decoupling of the

descriptor systems [6-9].In this paper, we study the problem of

the input-output decoupling for descriptor system. The

problem is handled in transfer function matrix setting. The

necessary and sufficient conditions for a solution of the

decoupling problem are established and an algorithm for

calculation of feedback gains is presented. Finally, a structural

interpretation is also given for decoupled systems.

Consider the descriptor system defined by

(1)

where , and are the state vector, the

input vector and the output vector, respectively ; ;

; , E is singular. It is well known that the

existence and uniqueness of (classical) solutions to (1) are

guaranteed if (E,A) is regular, i.e., for some

. The system (1) is said to have index at most one

if the dimension of the largest nilpotent block in the

Kronecker canonical form of (E,A) is at most one [10].

Descriptor systems that are regular and of index at most one

can be separated into purely dynamical and purely algebraic

parts (fast and slow modes). If the index is larger than 1, then

impulses can arise in the response of the system if the control

is not sufficiently smooth [9, 10]. Therefore, in the design of

feedback control, one should ensure that the closed-loop

system is regular and of index at most one.

II. FORMULASION OF THE PROBLEM

In this study, an approach for the input-output decoupling

of descriptor system of the form is

presented. Here transfer function matrix approach is used. For

the existence of a solution to system (1), we assume that

, where s is the complex variable associated

with the Laplace Transformation, i.e., is assumed to

be a regular pencil matrix.

Let the transfer function matrix of system (1) be defined

as follows:

(2)

Here, we assume that , i.e., the system has an equal

number of inputs and outputs. Then, it is called single input-

single output decoupled if and only if is diagonal and

nonsingular.

Many feedback laws have been used in the regular system

case in order to achieve decoupling systems. Most commonly

used is the static state feedback law. If we apply state

feedback of the form

(3)

to the descriptor system (1), then the closed-loop system

becomes

(4)

The problem of decoupling the descriptor system (1) by

feedback (3) is to determine a state feedback matrix

and a nonsingular input transformation matrix

such that the pencil (E, A + BF) is regular and of

index at most one, and the closed-loop transfer function matrix

(5)

is nonsingular and diagonal.

III. BASIC CONCEPT

Before studying the input-output decoupling problem for

the descriptor system (1), we summarize the main results on

the input-output decoupling available in the some literature:

The input-output decoupling problem for linear time-invariant

systems of the form

(6)

Input-Output Decoupling Problem for Descriptor System:

Transfer Function Matrix Approach

Arman, Ari Suparwanto, and Salmah

T


M01-2

with ; ; and nonsingular

has been investigated extensively over the last three decades

and is still attracting continuing interests [2, 3, 4, 5, 6, 9,

10,21]. In particular, because system (6) is equivalent to

we have the following theorem

Theorem 1(see [11]).

Given system (5) with E nonsingular, let be the ith row of C.

If

for some nonnegative integer j, then set.

j is integer satisfyin

};

Otherwise, set . Define

;

.

Then the input-output decoupling for system (6) is solvable if

and only if the matrix is nonsingular.

In this case, a solution pair ( , ) is given by

The following two lemmas are basic results for matrix pencils

and will be needed in the development to be given in the next

section.

Lemma 2. (See [12, 13])

Given , , and

withn nonsingular

(i). if and only if

, ;

(ii). assume

, .

Then

if and only if

, .

Lemma 3.

Given , , and

(i). ;

(ii). if and are of full row rank, then

The next lemma provides necessary and sufficient conditions

for a matrix pencilto be regular and of index at most one.

Lemma 4. (See [9, 10])

Let . The following statements are equivalent.

(i). is regular and of index at most one.

(ii). , where denotes a matrix

with orthogonal columns spanning the right nullspace of

matrix E.

(iii). .

IV. MAIN RESULTS

The purpose of this section is to present necessary and

sufficient solvability conditions as well as a numerically

reliable algorithm for the input-output decoupling of

descriptor system (1). For this purpose, first we transform the

input-output decoupling problem for descriptor system (1) into

the input-output decoupling problem for a linear time-

invariant system using orthogonal transformations.

Theorem 5. Given system (1), there exist nonnegative

integers and and ortogonal matrices

, and with

(7)

Such that , is

nonsingular, and

(8)

where and are nonsingular, and is of full

column rank for any .

In the following, we give a system interpretation of the form

(8). With respect to the coordinate transformations in the form

(8), the system (1) can be expressed as

(9)

where represents the transformed state vector and the

transformed input.

Let

, (10)


M01-3

Then system (9) is equivalent to

(11)

Because is of full column rank for any ,

according to [22], we know

that:

, .

Consequently, is a redundant subsystem

(associated with constrained to be zero). As the redundant

subsystem has a zero trajectory = 0, we can delete this part.

Therefore, (1) is reduced to

• a regular subsystem (with nonsingular )

(12)

• an algebraic subsystem (associated with )

. (13)

The algebraic part of the system results in the algebraic

condition (13), which must be satisfied. This can be taken as

an algebraic constraint on the feasibility of the system (1).

Since is nonsingular, we can always find an input to

ensure that the descriptor system (1) is consistent. If we

consider

as a new input and choose , then

the regular subsystem (12) becomes

(14)

and the algebraic constraint (14) is satisfied.

The following lemma shows that the form (8) can be used to

characterize the existence of a feedback matrix F such that the

pencil (E, A + BF) is regular and of index at most one.

Lemma 6.Given a descriptor system of the form (1), there

exists a matrix F such that the pencil (E, A + BF)is regular and

of index at most one if and only if

, , . (15)

Proof: (see Delin Chu, 2006).

In the next result it will be shown that the input-output

decoupling problem for descriptor system (1) can be reduced

to the input-output decoupling problem for the linear time-

invariant system (14).

Theorem 7.Given a descriptor system (1), the input-output

decoupling problem for system (1) is solvable if and only if

the condition (15) holds and, furthermore, the input-output

decoupling problem for system (15) is solvable; i.e., there

exist matrices Fand Hwith Hnonsingular such that

is nonsingular and diagonal.

Proof. (see Delin Chu, 2006).

We obtain the following result, which presents explicit and

numerically verifiable necessary and sufficient solvability

conditions for the RRDP of system (1).

Theorem 8.Given a descriptor system (1) and assuming that

the forms (8) has been determined, then the following

statements are equivalent:

(i) The input-output decoupling problem for descriptor

system (1) is solvable.

(ii) (a). , , ,

(b). , is nonsingular,

and the input-output decoupling problem for linear

time-invariant system

(16)

is solvable.

(iii) The conditions in (a) and (b) above hold and

where is defined as follows.Let be the i-th row of . If

.

for some nonnegative integer j; then set

is integer satisfying

}

otherwise, set .. Define

. (17)

Theorems 7 and 8 can be used as a basis for devising a

numerically reliable algorithm for solving the RRDP for the

descriptor system (1) as follows.

Algorithm 1.

Input: Matrices E, A,B, and C of the system (1) with E

singular.

Output: Solution (F,H) of the input-output decoupling

problem for system (1) if the solution exists.

Step 1. Compute the form (8); check conditions in (a) of

Theorem 8(ii). If these


M01-4

conditions are satisfied, go to Step 2; otherwise, conclude that

―The input-output decoupling problem is not solvable‖ and

stop.

Step 2. Compute the form (32); check condition in (b) of

Theorem 8(ii). If these

conditions are satisfied, go to Step 3; otherwise, conclude that

―The input-output decoupling problem is not solvable‖ and

stop.

Step 3. Verify the solvability conditions of the input-output

decoupling problem for the linear time-invariant system (16)

and compute a solution ( .

Step 4. Solve the 4 linear equations in (59) and (31) to get

(F,H). Output (F,H)and stop.

V. CONCLUSION

The decoupling problem for the descriptor systems by means

of state feedback has been studied using transfer function

matrix approach. The necessary and sufficient conditions for a

solution of the decoupling problem are established and an

algorithm for calculation of feedback gains is given.

REFERENCES

[1] Falb, P.L., and Wolovich, W.A.: ―Decoupling in the

designand synthesis of multivariable control

systems‖,IEEE Trans., 1967,AC-12, pp. 651-659

[2] Gilbert, E.G.: ―The decoupling of multivariable systems

by stateFeedback‖, SIAM J. Control, 1969, I, pp. 5&63

[3] Wonham, W.M., and Morse, A.S.: ―Decoupling and pole

assignment in lineare systems: a geometric approach‖,

SIAM J.Control, 1970.8, pp. 1-18

[4] Silverman, L.M., and Payne, H.J.: ―Input-output

structure oflinear systems with application to the

decoupling problem‖, SIAM J .Control, 1971, 9, pp.

199-233

[5] Paul, C.R.: ―Pole specification in decoupled systems‖,

Int. J .Control, 1972, 15, pp. 651-664

[6] Armentano, V.A. : ―Eigenvalue placement for

generalized linearSystems‖, Systems Control Lett., 1984,

4, pp. 199-202

[7] Christodoulou, M.A.: ―Decoupling in the design and

synthesisof singular systems‖, Automatica, 1986, 22, pp.

245-249

[8] Zhou, Z., Shayman, M.A., and Tarn, T.J.: ―Singular

systems:A new approach in the time domain‖, IEEE

Trans., 1987, AC-32, pp.42-50

[9] Dai, L.: ―Singular control systems - Lecture notes in

control andinformation sciences, 118‖ (Springer-Verlag,

1989)

[10] Bunse-Gerstner, A., . Mehrmann, V, and Nichols, N. K.

―Regularization of descriptor systems by derivative and

proportional state feedback‖, SIAM J. Matrix Anal.

Appl., 13 (1992),

[11] Chen, C.T., Linear System Theory and Design, Holt,

Rinehart and Winston, New York, 1984.

[12] Chu, D and Mehrmann, V., ―Disturbance decoupling

for descriptor systems by state feedback”, SIAM J.

Control Optim., 38 (2000), pp. 1830–1858.

[13] Chu, D and. Tan, R.,―Numerically reliable computing for

row by row decoupling problem with stability‖, SIAM J.

Matrix Anal. Appl., 23 (2002), pp. 1143–1170.

[14] Chu, D and. Hung, Y.S., ―A matrix pencil approach to

the row by row decoupling problem for descriptor

systems‖, SIAM J. Matrix Anal. Appl., 28 (2006), pp.

682–702.

Arman,

Ph.D student, Mathematics Department, Gadjah Mada University,

Yogyakarta, Indonesia.

Mathematics Department, Haluoleo University, Kendari, Indonesia

Ari Suparwanto

Mathematics Department, Gadjah Mada University, Yogyakarta, Indonesia

Salmah

Mathematics Department, Gadjah Mada University, Yogyakarta, Indonesia

The Third Basic Science International Conference - 2013 M02-1

Trisilowati, Scott McCue, Dann Mallet

Abstract- Cancer is still the leading cause of death worldwide. There is strong evidence in the literature for

the hypothesis that tumour growth is directly influenced by the cellular immune system of the human host

and this hypothesis is now generally accepted. For example, immune cells such as cytotoxic T

lymphocytes, natural killers and dendritic cells can identify and kill tumour cells. In this paper, a hybrid

cellular automata (HCA) model of the interactions between a growing tumour and the host immune system

is developed. While individual cells are modelled using a discrete, cellular automata description, the effect

of chemokines is introduced using a continuous partial differential equation (PDE) to describe the

concentration of chemokines secreted by the tumour. The numerical solution of the PDE model is

combined with a number of biologically motivated automata rules to form the hybrid model. We simulate

the growing tumour using this model in a number of in silico 'cancer patients' and present the results in

various ways including Kaplan-Meier survival-like curves.

A cellular automata model to investigate immune cell-

tumour cell interactions in growing tumours in two spatial

dimensions.


Abstract— Matrices L of size n × n are called Latin square if

every column and every row of L contain n different numbers.

And, Max-Plus Algebra is algebraic system using two operations,

max and plus. In this paper, we derive some properties of a Latin

square in Max-Plus Algebra and their eigenvalues and

corresponding eigenvector.

Index Terms— Latin square, Max-Plus Algebra, Eigenvalue,

Eigenvector.

I. INTRODUCTION

A Latin square of order n is square matrix of size n × n such

that every row and every column has n distinct numbers. For

convenience, we use n = {1,2,…,n}. The notion of Latin

square is firstly introduced by Leonhard Euler. A Latin square

is in reduced form if first row is [1, 2, 3, …, n] and first

column is [1, 2, 3, …, n]T. If numbers in both diagonals also

distinct then we called it by Latin square-X. An example of

Latin square and reduced Latin square is given below

321

213

132

213

132

321

The study of Latin square is mainly about discrete

mathematics aspect especially enumeration of Latin square.

Until now, the exact number of Latin square is known only for

1 ≤ n ≤ 11. The result of enumeration Latin square-X is can be

found in [1]. The number of Latin square of order 5 and 6 is

960 and 92160 respectively, and for order 7 the number of

Latin square is increasing sharply, that is 862848000.

Accordance with its name, Max-Plus Algebra is algebra that

using two operations, max and plus. In Max-Plus algebra

defined algebraic structure ),,( R where is set of

extended real numbers, i.e. }{ RR. In this paper, we

denoted infinite element, i.e. Operation max denoted

by and defined by },max{ baba , and operation plus

denoted by and denoted by baba for every a, b

inR . For example, 3}2,3max{23 and

46262 .

It is easy to show that both operations , are

commutative in max-plus algebra. Because all Rx satisfy

xxx and xxx 00 , then the zero and

unit element in max-plus algebra is and 0 , respectively.

The set of all mn matrices in max-plus algebra is denoted

by mnR

, and for 1m we denoted the set of all 1n vectors

by nR . Let mnRA

, the entry of A in ith row and j

th column

is denoted by jia ,and sometimes we write

jiA ,][ . The ith row

and jth column of A is denoted by

,][ iA and jA ,][

respectively. For mnRBA , BA is defined by

},max{][ ,,,,, jijijijiji babaBA

and for pmpn RBRA , , BA is defined by

)}(),...,(),max{(][ ,,1,22,,11,, jppjijiji bababaBA

For example,

320

41

211

A ,

21

150

13

B

We get

320

410

213

BA ,

513

663

404

BA

In max-plus algebra, we defined AAA 2 or

generally kk AAA 1 for ,...2,1k

Let nnε

RA , a digraph (directed graph) of A is denoted

as G(A). Graph G(A) has n vertices and there is an edge from

vertex i to vertex j if ija ,and this edge is denoted by (i, j).

Weight of edge (i, j) is denoted by ),( jiw and equal toija ,.

Sequence of edges ),(),...,,(),,( 13221 kk jjjjjj is called by

a path and if all vertices1321 ,...,,, kjjjj are different then

called by elementary path. Circuit is an elementary close path,

i.e. ).,(),...,,(),,( 113221 jjjjjj kCircuit that consisting of

single edge, from a vertex to itself, is called by looping.

Weight of a path ),(),...,,(),,( 13221 kk jjjjjjp is

denoted by wp || and equal to the sum of weight each edge.

Length of path p is denoted by lp || and equal to the number of

edges in p. Average weight of p is defined by

l

w

p

p

||

|| .

Any circuit with maximum average weight is called by

critical circuit. Graph G(A) is called strongly connected if

there is path for any vertex i to any vertex j in G(A). If graph

G(A) is strongly connected, then matrix A is irreducible. From

On The Structural Properties of Latin Square in Max-Plus

Algebra

Muhammad Syifa’ul Mufid, Subiono


matrix A, ji

kA ,][ is equal to the maximal weight of a path

with length k from vertex i to vertex j.

II. LATIN SQUARE IN MAX-PLUS ALGEBRA

Because the discussion is in max-plus algebra, it is allowed

to use infinite element as number/element of Latin

square. In this paper we define two types of Latin square:

a. Latin square without infinite element, the numbers that

used are in }...,2,1{ nn

b. Latin square with infinite element, the numbers that

used are in }1...,2,1,{ nn

The set of all Latin squares of order n without infinite element

is denoted by nLS and the set of all Latin squares of order n

with infinite element is denoted by nLS. Example of two types

of Latin square is given below.

We can infer that 4

1 LSL and 4

2 LSL .

III. PROPERTIES OF LATIN SQUARE IN MAX-PLUS

ALGEBRA

Properties of Latin square in max-plus algebra that will be

derived are:

a. Irreducible. Are all Latin squares in max-plus algebra

irreducible?

b. Close under operation . Are all Latin squares closed

under operation ?

c. Close under operation . Are all Latin squares closed

under operation ?

A. Property of Irreducibility

Lemma 1. All Latin squares are irreducible matrix.

Proof.

Let L be Latin square. If nLSL then all numbers of L are

finite. Therefore, in graph G(L) there is a path with length 1

from vertex i to vertex j for all nji , . Then we can conclude

that G(L) is strongly connected and consequently L is

irreducible.

If nLSL we consider matrix LLL 2 . Because there

is only one in every row and every column of L then

jiL ,

2 ][ is finite for all nji , . Therefore in graph G(L) there

are some paths with length at least 2 from vertex i to vertex j

for all nji , . Then we can conclude that G(L) is strongly

connected and consequently L is irreducible.

B. Property of closed under operation

We say that Latin squares are closed under operation if

for all Latin squares A and B, BA is Latin square.

Lemma 2. Let both A and B are in nLS or in nLS. BA is

Latin square if and only if BA .

Proof.

Let nLSBA , and BAC . Because nBA jiji ,, ][,][

then nBAC jijiji ,,, ][][][ . If C is Latin square then

nLSC . To prove A = B we only need considering first

column. See the illustration below

1,1,

1,21,2

1,11,1

1,

1,2

1,1

.

.

.

.

nnn ba

ba

ba

c

c

c

Let nxa 1,1, if xb 1,1

then x can appear more than one

or not appear in left side matrix. Therefore we get

1,11,1 ba and by same way we get 1,11,21,2 ,..., nn baba or

generally1,1, ii ba for all ni . Consequently, the first column

of A and B is equal or generally ii BA ,, ][][ for all ni , in

other word BA .

Conversely, if BA then

jijijijijijijiji aaaaabac ,,,,,,,, },max{

Consequently, AAABAC andC is Latin square.

For nLSBA , it can be proved by similar way.

By Lemma 2 we can conclude that Latin square is not closed

under operation

Example:

123

231

312

,

213

132

321

BA

We get

231

312

123

231

,

3241

1324

2413

4132

21 LL


223

232

322

BA

and BA is not Latin square.

C. Property of closed under operation

We say that Latin squares are closed under operation if

for all Latin square A and B, BA is Latin square. In other

word, there is Latin square C and natural number p such

that CpBA .

Lemma 3. If three Latin squares nLSCBA ,, satisfy

CpBA then np .

Proof. Let DBA , and D is Latin square, then

)}(),...,(),max{(][ ,,1,22,,11,, jnnjijiji bababaD

Because maximum value both kia , and jka , for all

nk are n , then maximum value of jiD ,][ is n2 . Next, we

determine the minimum value ofjiD ,][ .

Let kjkki dba ,,

then },...,,max{][ 21, nji dddD and

we know that

n

k

k nnd1

)1( . It is easy to find that the

minimum value of jiD ,][ occur when

1...21 nddd n,

then 1}1,...,1,1max{][ , nnnnD ji. If there are

some k such that 1 nd kthen there are some l such

that 1 nd l and consequently 1][ , nD ji

. So, it is clear

that minimum value of jiD ,][ is 1n .

Because D is Latin square of order n

and nDn ji 2][1 , , then we can conclude that

}|{}2,12,...,2,1{][ , nkknnnnnD ji

So, if CpD , we get np .

From Lemma 3, one of requirement for BA producing

Latin square is for all ni there is nj such that

]11..11[][][ ,, nnnnBA ji

So we can conclude that Latin square is not closed under

operation .

Example:

321

213

132

,

213

132

321

BA

We get

556

565

655

BA

and BA is not Latin square.

IV. EIGENPROBLEM OF LATIN SQUARE IN MAX-PLUS

ALGEBRA

Matrix L of order n has eigenvalue R and

corresponding eigenvector nnRv if both of them satisfy

vvL

In this paper we denoted )(A be eigenvalue of matrix A.

From [2,3], there is algorithm to find eigenvalue corresponding

eigenvector that called by Power Algorithm. If L is irreducible

matrix, then eigenproblem is equivalent to problem to find

critical circuit in G(L), where eigenvalue is equal to weight of

that critical circuit.

We define LL )( and

nLLLLL ...32

It can be proved thatjL ,][

is eigenvector of L if

0][ ,

jjL[3].

A. Eigenvalue of Latin square in Max-Plus Algebra

From Lemma 1, all Latin squares are irreducible matrix.

Therefore, to find eigenvalue of L we need to find the weight

of critical circuit in G(L).

If nLSL then },...,2,1{][ , nL jj and it is clear that

nL ji }]max{[ ,. Let

),(),,(),...,,(),,( 113221 jjjjjjjjp kkk

be critical circuit with length k with nk in G(L), then

knjjwjjwjjwp kkw ),(...),(),(|| 13221

and average weight of p is equal to

nk

kn

p

p

l

w ||

||

Because n occurs exactly one in every row and column of L,

we can ensure that average weight of critical circuit p is equal

to n. Therefore, eigenvalue of L is equal to n, in other word

n .

By the same method, we get eigenvalue of nLSL , that is

1 n .

B. Eigenvector of Latin square in Max-Plus Algebra

Let nLSA and nLSB . From the definition we get

AnA )(and AnB )1(

. It is clear that

average weight of critical circuit both in G(A) and and G(B) is

0.

From [3], if p is critical circuit of G(L) then for all vertices

in p satisfy 0][ ,

L . But in this case,


for nLSA and nLSB , the average weight of A and B is

equal to maximum value of matrix A and B, i.e

nAA ji }]max{[)( ,

and

1}]max{[)( , nBB ji .

Moreover, n occurs exactly one in every row and column of

A and 1n occurs exactly one in every row and column

of B . Consequently, there is always critical circuit in A such

that the initial vertex is i. The same condition is for matrix B .

Therefore, for all n in satisfy

0][ , A and 0][ , B

or in other word, all diagonal entries of both A and B are equal

to 0. So we can conclude that all columns of

A is

eigenvector of A and all columns of

B is eigenvector of B

Example.

4213

3124

1342

2431

A

We get 4)( A and

0231

1320

3102

2013

A

0121

1010

2101

1010

A

from

A we get three different columns and we can check that

all of them are eigenvector of A

1

0

1

0

4

3

4

3

4

1

0

1

0

A ,

2

1

0

1

4

2

3

4

3

2

1

0

1

A

0

1

2

1

4

4

3

2

3

0

1

2

1

A

V. CONCLUSION

In this paper we can conclude that Latin squares have

properties in Max-Plus Algebra, that is

1. All Latin squares are irreducible matrix

2. Latin squares are not closed under operation

3. Latin squares are not closed under operation

Moreover, eigenvalue of Latin squares L are equal to

maximum value of L and all columns of

L are eigenvector of

L.

REFERENCES [1] Mufid, M.S., 2012, Kajian Teori Permutasi and Its Application to

Enumeration of Latin Square-X and Sudoku-X (In Indonesian), Bachelor

Thesis, Mathematics and Natural Science Faculty, Institut Teknologi

Sepuluh Nopember, Surabaya.

[2] Subiono and van der Woude, J.W., Power Algorithm for (max, +)- and

Bipartite (Min, Max,+)-system, Discrete Event Dynamic Systems:

Theory and Application 10, pp. 369-389, 2000.

[3] Subiono, 2012, Aljabar Max-Plus dan Terapannya, Buku Ajar Mata

Kuliah Pilihan Pasca Sarjana Matematika, Institut Teknologi Sepuluh

Nopember, Surabaya.


M04-1

Abstract

Let be trigonometric series for

. It is well known that if the nonnegative sequences

{an} is decreasing and , then

if and only if

We weaken the monotone condition in this classical result to the

so called p-supremum bounded variation condition and shows

the similar conclusion for uniform convergence of certain

trigometric series still holds.

Index Terms— p-supremum bounded variation,

trigonometric series , uniform convergence

I. INTRODUCTION

It is well known that there are several interesting

classical theorems in Fourier analysis having

assumptions determined by certain monotonicity of

the coefficients. The following classical convergence

result can be found in some monograph such as in

[1, 10].

Theorem 1.1. Suppose that is nonincreasingly

tending to zero. A necessary and sufficient condition for the

uniform convergence of the series

is

Tikhonov [8] introduced a class of General Motonotone

Sequences (GMS) as follows: A sequence

is said to be GMS if there exists such that the relation

holds for . He used a class of GMS to weaken the

monotonicity condition of coefficient (1.1) as stated in

Theorem 1.2.

Theorem 1.2. Let be non negative sequence

satisfying and . A necessary and

sufficient condition for the uniform convergence of the series

(1.1) is

The class of GMS was further generalized by Zhou

[9] to class of Mean Value Bounded Variation

Sequences (MVBVS) . A sequence is

said to be MVBVS if there exist and such that

holds for , where the greatest integer that a

less then or equal to x. He proved that Theorem 1.2 also

valid when the condition is replaced by

.

1 Mathematics, FMIPA, UB and Student Graduade School FMIPA, UGM 2 Mathematics, FMIPA, UGM 3 Mathematics, FMIPA, UGM

Further, in [6, 7] Liflyand and Tikhonov defined the

class of p-General Monotone Sequences . Let

and be two sequences of complex and

positive numbers, respectively, a couple if

there exist such that the relation

holds for and . Then Dyachenko and

Tikhonov [2] proved the following Theorem:

Therem 1.3. If and and.

Then necessary condition for the uniform convergence of the

series (1.1) is

For , if and only if [8].

As corollary, more general then GMS.

Futhermore, Imron, et al [3, 4] generalized MVBVS and

SBVS to (p-Mean Value Bounded Variation

sequences) and (Supremum Bounded variation

Sequences). Let and be two sequences of

complex and positive numbers, respectively, a couple

if there exist and such that

for p, and if there exist

and such that

for p, A little modification of definition of

is class .The couple is p-

Supremum Bounded Variation Sequences Second Type ,

written if there exist and

tending monotonically to infinity depending

only on such that

holds for p, .

Imron, et al [ 4] have shown that

. In the present paper, we

investigate the uniform convergence of trigonometric series

under p-Supremum Bounded Variation Condition.

On Uniform Convergence of Trigonometric Series Under

p-Supremum Bounded Variation Condition

Moch. Aruman Imron1, Ch. Rini Indrati

2, and Widodo

3


M04-2

II . SOME PROPERTIES OF p-SUPREMUM BOUNDED

VARIATION SEQUENCES SECOND TYPE

In this section, we study some properties and

relation between and

Theorem 2.1. If and

decreasing monotone then

holds for p, .

Proof. We denote

for every . Given then we write

Theorem 2.2. If and

tending to zero then is

bounded variation.

Proof. Let and we

denote

Given then For every , there exists

such that for

Given and from proof Theorem 2.1. we

obtained

Thus

therefore is bounded variation.

Theorem 2.3. If , then

.

Proof. By Theorem 3.5 and Theorem 3.8 in [4],

. Now, we will show that

Let , there exists a

positive constant C such that

for , therefore . Thus

.

III. UNIFORM CONVERGENCE OF TRIGONOMETRIC

SERIES

In this section we investigate the uniform convergence of

trigonometric series under condition of class of .

We consider the series

and

where is a given null sequence of complex numbers,

i.e., as We define by f(x) and g(x) the sums of

series (4.1) and (4.2) respectively at the point where the series

converge.

Theorem 4.1. Let . If

,fo ,

then series (3.2) converges uniformly on .

Proof. We denote

Given then For every , there exists

such that for . Let be

nonincreasing null sequence such that , so

there exists such that for . Let

, by proof Theorem 2.2 we write

Let us now estimate , where

. By Abel’s transformation, we get

where and ,

.

By (3.3)

To estimate A, for any we can find such

that . Since

, if , then

and (3.3) imply

If , then we decompose A as

. Similar to (3.1) we

get

Further


M04-3

where and

.

Since

then

From , we obtain

From (3.3), (3.4) and (3.5) we get

Thus, if given there exists such

that for

Series (3.2) converges uniformly on .

ii. For x = 0 , and from i , then (3.2)

converges uniformly on . The proof is complete.

Theorem 3.2. Let , if

, for , then series

(3.1) converges uniformly on .

Proof. The proof is similar to proof of Theorem 3.1. for

.

Corollary 3.3. Let . If

for and

, then series (3.2) converges uniformly on .


for and ,

then series (3.2) converges uniformly on .


for , then series (3.2) converges uniformly on

.

IV. CONCLUSION.

Under p-Supremum Bounded Variation Condition, the

sufficient condition of uniform convergence of trigometric

series is , for .

ACKNOWLEDGEMENTS

The authors gratefully acknowledge the support of the

Department of Mathematics FMIPA UB and the Graduate

School Department of Mathematics FMIPA UGM .

REFERENCES

[1] Chaundy, T.W. and Jollife, A.E., 1916, The Uniform

Convergence of certain class trigonometric

series, Proc. London, Soc. 15, 214-116.

[2] Dyachenko, M. and Tikhonov, S., General monotone

sequences and convergence of trigonometric

series, in: Topics in Classical Analysis and

Applications in Honor of Daniel Waterman

(World Scientific, Hakensack, NJ, 2008), pp.

88-101.

[3] Imron, M.A., Indrati, Ch.R.and Widodo, Sifat-sifat

Barisan dan fungsi dasri klas p-mean Value

Bounded variation, Konferensi Nasional

Matematika 16, Unpad , Bandung, 2012

[4] ] Imron, M.A., Indrati, Ch.R.and Widodo, Relasi Inklusi

pada Klas Barisan p-Supremum Bounded

variation, Jurnal Natural A ,No 1, Vol 1,

FMIPA, UB, Malang (Appear 2013).

[5] Korus,P., Remark On the uniform And L1-Convergence

Of Trigonometric Series, Acta Math. Hungar,

128(4), 2010.

[6] Liflyand,E. and Tikhonov,S., The Fourier Transforms of

General Monotone Functions, Analysis and

Mathematical Physics, Trends in Mathematics

(Birchauser, 2009).

[7] Liflyand, E. and Tikhonov, S., A concept of general

monotonicity and applications, Math Nachr,

284, No. 8-9, 2011.

[8] Tikhonov,S., Best approximation and moduli of

Smoothness computation and Equivalence

Theorems, Journal of Approximation Theory,

153 (19-39), 2008.

[9] Zhou, S.P., Zhou, P. and Yu, D.S., Ultimate generalization

to monotonicity for Uniform Convergence of

Trigonometric Series, http://arxiv.org/ abs/

math/0611805v1.

[10] Zygmund, A., Trigonometric Series, Vol I, II, Second ed,

Cambridge Univ. Press, 1959.


M05-1

Abstract—Zafrullah defined generalized Dedekind domain and

Akalan defined generalized Dedekind prime ring to get a

polynomial ring that has same structure as its base ring.

Meanwhile the concept of Dedekind modules was defined by

Naoum and Al-Alwan by adapting the property of the ideals of a

Dedekind domain to submodules. In this paper we define the

concept of generalized Dedekind modules by adapting the

property of ideals of a generalized Dedekind domain to

submodules. We also show that and integral domain R is a

generalized Dedekind domain if and only if every torsionless R -

module is a generalized Dedekind module.

I. INTRODUCTION

HE structure of a ring may not be preserved on its

polynomial ring. For example, a polynomial ring over a

Dedekind domain is not always a Dedekind domain. Also a

polynomial ring over a Dedekind prime ring is not always a

Dedekind prime ring. To obtain a polynomial ring which has

the same structure as its base ring, the property of Dedekind

domain is weaken to a ring which is called a generalized

Dedekind domain (G-Dedekind domain, see [11]). Moreover,

one also generalize Dedekind prime ring into generalized

Dedekind prime ring (G-Dedekind prime ring, see [1]).

Akalan [2] has proved that if R is a G-Dedekind prime ring

with an automorphism of finite order, then ;R x is G-

Dedekind prime. In [10] we have shown the converse: that if

;R x is G-Dedekind prime then R is -G-Dedekind

prime, i.e., all reflexive -ideals are invertible. In [6] these

results have been generalized to generalized Asano prime rine

(G-Asano prime ring) where a G-Asano prime ring is a non-

Noetherian G-Dedekind prime ring.

Meanwhile the concept of Dedekind modules was

introduced by Naoum and Al-Alwan [7] as a generalization of

Dedekind prime rings. Following this introduction, the

structure and properties of this class modules have been

investigated in [8], [3], [9], and [5]. In [7] Naoum and Al-

Alwan have shown that for a faithful projective R -module

M , if M is a Dedekind module then M is finitely generated

and R is a Dedekind domain.

In this paper we introduce the concept of generalized

Dedekind modules (G-Dedekind modules). We call M a G-

Dedekind module if every reflexive submodule of M is

invertible. We also obtain the relation between G-Dedekind

domain and torsionless G-Dedekind modules as follows: a

maximal order R is a G-Dedekind domain if and only if every

torsionless R -module is a G-Dedekind module. A key result is

the relation between reflexive ideals of R and reflexive

submodules.

1 Erma Suwastika and Intan Muchtadi-Alamsyah is with Algebra Research

Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi

Bandung

II. BASIC DEFINITION

Let R be an integral domain with field of fractions Q . For

any R -ideal A , we define

1A q Q qA R q Q Aq R

and * ,RA Hom A R . By [4] we can identify 1A and *A .

We define

1

1 1A q Q qA R

and ** *,RA Hom A R .

Once again we identify 1

1A

and **A . It is clear that

1

** 1A A A

.

An R -ideal A is reflexive if 1

** 1A A A

and it is

invertible if 1 1A A AA R . A ring R is a G-Dedekind

domain if R is an integral domain which every reflexive ideal

is invertible.

Now we generalized the above concept to modules. To begin

with, let M be an R module. Let S be a set of regular

elements of R , then 1RS be the total quotient ring and

0 for some implies 0T t S tm m M m . It is clear

that T is multiplicative subset of S . Hence we have the

quotient ring 1RT . We denote 1RT by Q . For any R -

submodule N of M , we define 1N q Q qN M . Then

1N is an R -submodule of Q satisfying 1R N and

1N N M . The R -submodule N is called invertible if 1N N M . According to Naoum and Al-Alwan [7], an R -

module M is called a Dedekind module if every submodule

of M is invertible.

For any R -module M we define * ,RM Hom M R and

** *,RM Hom M R . Any R -module M is called torsionless

if M can be identified as submodule of **M and it is reflrxive

if **M M .

We define G-Dedekind modules as follows.

Definition 1. Let R be an integral domain with field of

fractions Q defined as above and M be an R -module. We

say M a G-Dedekind module if every reflexive R -submodule

of M is invertible.

It is clear that every Dedekind module is a G-Dedekind

module.

Generalized Dedekind Modules

Erma Suwastika and Intan Muchtadi-Alamsyah1

T


M05-2

III. MAIN THEOREM

If R is an integral domain, then we have ** *B A AB for

any R -ideal A and B . The following lemma shows that a

similar property holds.

Lemma 2. Let L be an R -module and A an ideal of R .

Then

1) ** *A L LA .

2) *

** ** * *L A A L .

Proof.

1) Let * * 1 *g A L A L . Then

1

n

i i

i

g q f

, where 1

iq A ,

*

if L , and n . Hence ,i i Rq f Hom L Q for all

1,2,...,i n . We will show that ,i i Rq f Hom LA R .

Let

1

k

j j

j

l a LA

where k . Then for all 1,2,...,i n ,

1 1 1

k k k

i i j j i i j j i i j j

j j j

q f l a q f l a q f l a R

, because

i j jf l a A . Hence *

i iq f LA and *

g LA .

2) Let ** **h L A . Then

1

n

i i

i

h b s

, where **

ib L ,

1

** 1

is A A

, and n . We will show that

* * ,i i Rb s Hom A L R for all 1,2,...,i n .

Let * * 1 *

1

k

j j

j

g q f A L A L

, where k . Then for

all 1,2,...,i n , 1 1

k k

i i j j i i j j

j j

b s q f b s q f R

,

because i js q R and ,i j j Rs q f Hom L R where

i j j j i js q f x f xs q for all x L . Hence

*

* *

i ib s A L and *

* *h A L . ▪

Lemma 3. Let M be a torsionless R -module and N be a

reflexive submodule of M . Then there exists a reflexive ideal

T such that MT N

Proof. Define T r R Mr N . By definition, MT N .

It is clear that /RT Ann M N , hence T is an ideal of R .

We will show that T is reflexive.

It is enough to show that **T T . First, as R is reflexive,

then ** **T R R .

Let **q T and m M . Then

** * **** ** ** * * **mq MT M T T M MT MT N N

since N is reflexive. We conclude that q T . ▪

The main theorem below shows that every torsionless

module over G-Dedekind prime ring is G-Dedekind module.

Theorem 4. Let R be an integral domain. The following

are equivalent:

1) R is a G-Dedekind domain.

2) Every torsionless R -module is a G-Dedekind module.

Proof. It is clear that (2) implies (1) since every reflexive

ideal of R can be considered as right submodule of RR , and

hence invertible.

Now we assume that R is a G-Dedekind domain. Let M

be a torsionless R -module. We will show that M is a G-

Dedekind module.

Let N be a reflexive submodule of M . It is clear that 1NN M . By Lemma 3, there exists a reflexive ideal T of

R such that MT N . Since R is G-Dedekind domain, then 1R TT . Since 1R M , we have

11 1 1 1 1 1M MRM M TT M MT T M N MT NN

. We conclude that N is invertible. ▪

For further research, it is interesting to see if we can also

define G-Asano modules and G-HNP modules.

ACKNOWLEDGMENT

The authors would like to thank Hanni Garminia for various

discussion on Dedekind modules.

REFERENCES

[1] E. Akalan, “On Generalized Dedekind Prime Rings”, Journal of

Algebra, 320 (2008), 2907-2916.

[2] E. Akalan, “Ore Extensions over pi G-Dedekind Prime Rings”,

Communications in Algebra, 39 (2011),594-600.

[3] M. Alkan, B. Sarac, and Y. Tiras, “Dedekind Modules”,

Communications in Algebra, 33 (5) (2005), 1617-1625.

[4] D. Eisenbud and J.C. Robson, “Modules over Dedekind Prime Rings”,

Journal of Algebra, 16 (1970), 67-85.

[5] H. Garminia, P. Astuti, and Irawati, “A Note on Dedekind Modules”,

International Journal of Algebra, vol. 5 no. 10 (2011), 491-498.

[6] H. Marubayashi, I. Muchtadi-Alamsyah, and A. Ueda, “Skew

Polynomial Rings which Are Generalized Asano Prime Rings”, preprint.

[7] A. G. Naoum and F. H. Al-Alwan, “Dedekind Modules”,


[8] A. G. Naoum and F. H. Al-Alwan, “Dense Submodules of

Multiplication Modules”, Communications in Algebra, 24 (2) (1996),

413-424.

[9] B. Sarac, P. F. Smith. And Y. Tiras, “On Dedekind Modules”,


[10] E. Suwastika, I. Muchtadi-Alamsyah, and Irawati, “Polynomials over G-

Dedekind Prime Rings”, Far East Journal of Mathematical Sciences,

vol. 58 issue 2 (2011), 173-178.

[11] M. Zafrullah, “On Generalized Dedekind Domains”, Mathematika, 33

(1986), 285-295.

.


M11-1

Abstract— This study aims to determine the profit (loss)

earned economic actors tourism activities if the tourism quality

of Gedong Songo Temple and Muncul will be improved

(deteriorated). Change of tourism quality can be seen by

traveling expenses, natural environment, Javanese cultural

performances, and traditional markets. The method used to

measure changes in the economic benefits or economic loss with

random utility method. For Gedong Songo Temple, the study

found that traveling expenses, natural environment, and

traditional markets have significant factors about respondent

preferences to choose the change of tourism quality. For Muncul,

the study found that Javanese cultural performances have

significant factors about respondent preferences to choose the

change of tourism quality. Value of compensation received by

visitors as a result of changes in conditions improved by 2,482

billion Rupiah for Gedong Songo and 1,641 billion Rupiah for

Muncul. While the change in the condition deteriorated by 1,864

billion Rupiah for Gedong Songo and 1,352 billion Rupiah for

Muncul. Recommendation of this study for local government

should consider tourism quality factors in the formulation of

tourism development. Gedong Songo Temple (natural

environmental and traditional markets) and Muncul (Javanese

cultural performances).

Index Terms— economic valuation, gedong songo temple,

muncul, random utility method

I. INTRODUCTION

edong Songo Temple and Muncul are located in

Rawapening Area. They are administratively located in

Semarang Regency, Central Java Province, Indonesia.

Gedong Songo Temple located in district of Ambarawa.

Muncul located in district of Banyubiru. We can show the

location of Gedong Songo Temple and Muncul in figure 1.

Gedong Songo Temple and Muncul as a part of

Rawapening area will be developed Central Tourism in

Central Java especially on natural and history tourism

development for regional and national scale. Development of

Gedong Songo Temple and Muncul should have paid attention

from visitors preferences. It is important because changes of

tourism quality can provide multiple benefits, both tourism

actor (visitors) and tourism management (local government).

This study analyzed changes occurring conditions associated

changes of tourism quality.

It could be expected to affect the preferences of visitors

and potential visitors went to tourism object. The combination

of tourism quality called as attributes. From discussion group

and literature, we found four attributes to formulate changes of

quality in Gedong Songo Temple and Muncul.

Four attributes are: (a)travelling expenses, (b)natural

environment; (c) Javanese cultural arts performances, and (d)

traditional market. Four attribute were the basis to

accommodate hypothetical changes in Gedong Songo Temple

and Muncul. Thus, the hypothetical changes can be detected

gains or losses are received by the tourism actors in Gedong

Songo Temple and Muncul.

Based on this background, this study aims to determine the

profit (loss) earned economic actors tourism activities if the

tourism quality of Gedong Songo Temple and Muncul will be

improved (deteriorated).

II. METHODOLOGY

A. Method and Survey Instruments

In this study, the survey concentrated on the visitors in

Gedong Songo Temple and Muncul. We choose head of

household for interview. Respondents defined who use

tourism object for recreation and they must have paid the

entrance fee.

Interviewer were two undergraduate student. They have

trained to undertake the survey. Each of the trained

interviewers was responsible for one location where he/she

distributed the questionnaire to respondents, offered

explanations, and assistance in completing the questionnaire.

In total, 100 copies of the questionnaire were prepared and

distributed by interviewers. 86 questionnaires returned. It

could be used for analysis. From 86 questionnaires returned,

60 questionnaires for Gedong Songo Temple and 26

questionnaires for Muncul.

The questionnaire consisted of five sections, covering (1)

background and purpose of study, (2) motivations, desires, and

activities of the respondent in Gedong Songo Temple and

Application Random Utility Method for Economic Valuation on Change

of Tourism Quality (Case Study : Gedong Songo Temple & Muncul,

Central Java Province)

Sri Subanti(1)

, Rara Sugiarti(2)

, Endang Widiyastuti(3)

, and Arif Rahman Hakim(4)

G

Fig. 1. Location of Tourism Object : Gedong Songo Temple and Muncul,

Semarang Regency, Central Java Province.


M11-2

Muncul, (3) respondent rating for visiting experience to

Gedong Songo Temple and Muncul, (4) demographic

information from respondents, (5) respondents rating for

attributes in Gedong Songo Temple and Muncul.

Questionnaire consisted of multiple choice questions,

dichotomous questions about current condition or hyphotetical

condition, and rank-ordered response. In addition there is also

an open question that is useful to provide further explanation

and to give support information from respondent.

B. Random Utility Method

Random utility method is a method of decomposing the

overall utility into two components, namely, deterministic

(observed utility) and random (utilities are not observed).

Utilities were not observed in the form of attributes that are

not observed, unobservable taste variation, error and imperfect

information, and the instrumental variables (McFadden, 1973

in Martha, 2008; Patunru, 2004).

Random utility model is used to overcome the

disadvantages of Contingency Valuation Method (Contingent

Valuation Method) which based on hypothetical behavior

directly. In the contingency valuation method, willingnes to

pay (WTP) or willingnes to accept (WTA) asked directly so it

is very possible that more assessment (overvalued) or even

less (undervalued). This can happen because the respondents

could not correctly convert their judgment in monetary units.

Therefore the WTP or WTA should be estimated, not

observed. Random utility models is one way to measure the

WTP and WTA indirectly (Patunru, 2004).

If known, there is a group of individuals n: i = 1, ..., i, ..., n.

For every opportunity to recreation, such individuals may

choose an alternative m which is part of a group of AP : j = 1,

..., j, ..., m.

Each individual has income (Mi) vectors and

socioeconomic characteristics (Si). Each AP has an attribute

environmental quality (Qj). Individual travel costs is Cji. In

this study, j and k represent alternative development (changing

conditions) in Rawapening. For individual i who chooses APj,

utilities can be formulated as follows:

Uji = Vji(Mi - Cji , Qj , Si) + ε ji ……................................…(2.1)

where, εji is the unobservable component of utility and

assumed to be random. Price of goods or services market

(other consumption) omitted to simplify notation. The model

can be formulated as mathematical function follows :

Chji=f(ASCji,TEji,NATENVji,JAVACULji,TRDMRKTji)..(2.2)

where, Ch is choice of respondent preference for hyphotetical

scenario (improved/deteriorated and current condition). ASC

is alternative spesific constant that used to divide choive

alternative i.e 1 represent change condition vice versa 0

represent current condition. TE is travel expense. NATENV is

natural environment. JAVACUL is javanese cultural

performance art. TRDMRKT is traditional market.

III. RESULTS

A. Demographic Profile of Respondents

Table I, for Gedong Songo Temple, the proportion of male

respondents (63.33%) than female respondents (36.67%). The

marital status of respondents with single status represent

66.67%. It’s greater than married status and not answer

represent 31.67% & 1.67%. Groups by age, majority

respondent between 21 – 30 years old represent 68.33%, for

respondent between 41 – 50 years old only 5%. Majority

respondents have attended senior high school represent

63.33%, eventhough many respondents have attended

university represent 25%. Respondents that have attended

junior high school or less represent 5%, whereas 6.67% of the

respondents had master degree.

From job sides, majority of respondents work as private

staff represent 53.33%. Based from respondent origin,

majority respondents cames from semarang regency with

66.67% and from others with 33.33%. Persons with a monthly

household income of 1.51 – 2.25 million rupiah and 2.25 – 3

million rupiah accounted for 23.33% and 1.67%. Majority

respondents with incomes less than 1.5 million rupiah

represented 75.00%.

Table II, for Muncul, the proportion of male respondents

(88.46%) than female respondents (11.54%). The marital

status of respondents with married status represent 65.38%.

It’s greater than single status represent 34.62%. Groups by age

divided into two, there are age groups between 21 – 30 years

old represent 69.23%, and between 31 – 40 years old represent

30.77%. Majority respondents have attended senior high

school represent 76.92% than attended university represent

23.08%.

From job sides, majority of respondents work as private

staff (50%), government staff (23.08%), and pension (26.92).

Based from respondent origin, majority respondents cames

from semarang regency with 84.62% and from others with

15.38%. Persons with a monthly household income of 1.51 –

2.25 million rupiah and 2.25 – 3 million rupiah accounted for

26.92% and 15.38%. Majority respondents with incomes less

than 1.5 million rupiah represented 57.69%.


M11-3

B. Estimation Results

Based on Table III, for Gedong Songo Temple, the

attributes that affect the choice of respondents are travel

expense, natural environment, and traditional markets. For

Muncul, the attributes that affect the choice of respondents are

Javanese cultural performance art.

ASC variable indicates the average individual utility when

other variables unchanged. ASC value is positive for Gedong

Songo suggests the possibility of respondents would vote for a

new scenario (scenario improved) higher than the scenario

worse. This finding is somewhat different for the sub-region

appears likely scenario new respondents received lower. For

Muncul, respondents hope for a change in policy governance

of new attractions better. Both in terms of natural

environment, Javanese cultural performances, and traditional

markets.

Variable travel expense has a negative value and

significant in Gedong Songo Temple. Negative values indicate

a change scenarios selected respondent will decline as rising

travel cost incurred by the respondent. Travel expenses such

as admission price, consumption while in tourist attractions,

souvenir, hand pieces, travel place transformation, and other

costs (including toilets and parking). Different findings for

Muncul, because it is positive, the change of the selected

scenarios respondents tended to increase in line with rising

travel expense.

Natural environment variable is positive and significant in

Gedong Songo Temple. For Muncul is positive and not

significant. This value indicates the possibility of change

scenarios selected respondents will increase along with the

improvement of natural environment not only Gedong Songo

but also Muncul. Respondents appear increasingly aware of

the importance of natural environment when they are

conducting activities traveled.

Javanese cultural art performance is positive and

significant in Muncul. This value indicates the possibility of

change scenarios selected respondents will increase along with

the rise of Javanese cultural art performances held in Gedong

Songo Temple.

Traditional market variables is negative and significant in

Gedong Songo Temple. Different with this finding, for

Muncul is negative and not significant. This value indicates

the possibility of change in the selected scenarios of

respondents would decline with traditional market located in

Gedong Songo Temple. Based on these findings, the

respondents did not pay much attention souvenir or handmade.

Visitors choose a tourist attraction that has a beautiful natural

environment, can interact with the local community, Javanese

TABLE I

DEMOGRAPHIC PROFILE OF RESPONDENTS

IN GEDONG SONGO TEMPLE

Characteristics Freq. Percentage

Sex

Male 38 63.33

Female 22 36.67

Age

18 - 20 10 16.67

21 - 30 41 68.33

31 - 40 6 10.00

41 - 50 3 5.00

Marital Status

Single 40 66.67

Married 19 31.67

Not Answer 1 1.67

Monthly Household Income

(in Rupiah) 1US$ = Rp 9730

<= 1,5 million 45 75.00

1,51 - 2,25 million 14 23.33

2,25 - 3 million 1 1.67

Respondent Origin

Semarang Regency 40 66.67

Others 20 33.33

Education

Junior High School or Less 3 5.00

Senior High School 38 63.33

Graduate 15 25.00

Master 4 6.67

Occupation

Student 2 3.33

Government Staff 13 21.67

Private Staff 32 53.33

Entrepreneur 13 21.67

TABLE II

DEMOGRAPHIC PROFILE OF RESPONDENTS

IN MUNCUL

Characteristics Freq. Percentage

Sex

Male 23 88.46

Female 3 11.54

Age

21 - 30 18 69.23

31 - 40 8 30.77

Marital Status

Single 9 34.62

Married 17 65.38

Monthly Household Income

(in Rupiah) 1US$ = Rp 9730

<= 1,5 million 15 57.69

1,51 - 2,25 million 7 26.92

2,25 - 3 million 4 15.38

Respondent Origin

Semarang Regency 22 84.62

Others 4 15.38

Education

Senior High School 20 76.92

Graduate 6 23.08

Occupation

Government Staff 6 23.08

Private Staff 13 50.00

Pension 7 26.92


M11-4

cultural art performance, and affordable with income

respondents.

Calculation of compensating surplus obtained by the

attributes used in the study (the natural environment, Javanese

cultural art performances, and traditional markets). Attributes

are determined by comparing the change in the conditions of

new scenarios to the status quo scenario. New scenario is

defined as a scenario, while improving the status quo scenario

is defined as the scenario gets worse or no change.

Compensating surplus received visitors at Gedong Songo

Temple amounted to Rp 2.482 billion for improved scenario

compared with worsened scenario Rp 1.864 billion. For

Muncul, the compensating surplus received visitors amounted

to Rp 1.641 billion for improved scenario than worsened

scenario amounted to Rp 1.352 billion.

IV. CONCLUSION & RECOMMENDATION

A. Conclusion

First, only three attributes affect the preferences of

respondents in choosing the changing conditions in Gedong

Songo Temple. There are travel expense, natural environment,

and traditional markets. For Muncul, only Javanese cultural

performance art.

Second, the compensation surplus received visitors due to

changing scenario of the region improved Rawapening higher

than the scenario worse. Value scenarios improved

compensation amounted of Rp 2.482 billion for Gedong

Songo Temple and Rp 1.641 billion for Muncul. While the

worsening scenario amounted of Rp 1.854 billion for Gedong

Songo Temple and Rp 1.352 billion for Muncul.

B. Recommendation

First, the government needs to reformulate development

policies in Gedong Songo Temple and Muncul. Natural

environment and traditional market as the main visitor

preference needs to be improved in Gedong Songo Temple.

For Muncul, Javanese cultural performance art needs to be

improved.

Second, the development of cultural tourism and natural

tourism can be applied for development of Gedong Songo

Temple and Muncul. Development of natural environment

combined with an increased frequency of Javanese cultural

performances earned positive response. It can be good

combination to increase rates for visitors and prospective

visitors in future.

ACKNOWLEDGMENT

Authors thanks to Local Government of Semarang Regency

and Surveyor Team for support this study.

REFERENCES

[1] Ben-Akiva, Moshe and Steve R Lerman. Discrete Choice Analysis :

Theory and Application to Travel Demand. MIT Press, 1985.

[2] Fauzi, Akhmad. Natural Resources and Enviromental Economics :

Theory and Aplication (in Bahasa). Jakarta. Gramedia, 2004.

[3] Freeman III, A. Myrick. The Measurement of Environmental and

Resources Values: Theory and Methods. Washington 1993..

[4] Gujarati, Damodar. Basic Econometrics 5th Edition. New York.

Macmillan Publising Company, 2009.

[5] Hakim, Arif Rahman, Sri Subanti, dan Mangara Tambunan. Economic

Valuation of Nature Based Tourism Object in Rawapening, Indonesia :

An Application of Travel Cost and Contingent Valuation Method.

Journal of Sustainable Development. Vol 4 No 2, April 2011. [Online].

Available: http://www.jsd.com

[6] Martha, Luhur Fadjar & Arianto A Patunru, (2007). “Measuring

Economic Value of Change of Tourism Environment in Tanjung Pinang

: An Application of Random Utility Model (Presented Conference Paper

Style)”, presented at Economic End Year Simposium, Depok, Indonesia,

December 13, 2007., Indonesia.

[7] Patunru, Arianto A. “Three Essays on Choice Based Estimations of The

Economic Benefits of Contamined Site Cleanup”. PhD Dissertation,

Dept. of Agricultural and Consumer Economics, University of Illinois,

Urbana-Champaign, United States, 2004.

TABLE III

ESTIMATION RESULTS WITH RANDOM UTILITY METHOD

Variable

Muncul Gedong Songo

n=26 n=60

ASC

-1.6368 * 0.6474

-0.9056 -0.6047

TC

0.0501

-0.8708 ***

-0.2256 -0.1537

NATENV

0.2433

0.8732 ***

-0.2283 -0.1576

JAVACUL

0.4582 ** 0.1652

-0.2265 -0.1527

TRDMRKT

-0.0733

-0.3792 ***

-0.1872 -0.1288

LR chi2 7.7300

83.1100

Prob > chi2 0.1720

0.0000

Pseudo R2 0.0130 0.0570

( ) : standard error

*** : sign α = 1% ** : sign α = 5%

* : sign α = 10

http://www.jsd.com/


M13-1

Lisa Nesti, Akademi Teknologi Industri Padang

Abstract. Snack food industry in West Sumatra is

currently facing various problems. Quoted in the Daily

Express Padang (Wednesday, 11/05/2011) that according

to the Governor of West Sumatra, West Sumatra opening

Food and Craft Fair IV, on the first floor of Industry

Ministry building on Tuesday (10/5) snack food industry

production of West Sumatra are still limited the market

share of traditional and not been able to get in modern

markets. This is because the packaging has not been so

good, the quality has not been homogenized to a certain

standard, and less varied types of products, as well as a

limited production capacity. Therefore, the author is very

interested in the theme of Innovation Taste diversified

products with a case study Emping Malinjo Pariaman by

using statistical non-parametric Friedman test. Friedman

test is one of the nonparametric tests using the k-related

samples (K-related sample), the method is based on the

data pairs k sampled at least ordinal, is used to test the

null hypothesis that the samples were drawn from the

same population. Friedmen test this, the data generated

into a two-way table with N rows and k columns where

rows represent different subject pairs and columns

represent a wide range of conditions. This test data is

ranking, the scores in each row are ranked separately. The

hypothesis used is: H0: There is no difference in taste

preference level for the four different flavors crackers and

H1: At least there is one kind of flavor chips that have a

different level of preference.

Test of love for the four different flavors crackers

(original flavor, spicy sweetness, flavor and taste of

chocolate butter paprica) using 7 hedonic scale. By

processing SPSS statistical values obtained Friedman

(Chi-Square observation) of 14.139. By setting the real

-square table so

that the null hypothesis is rejected 11.3 (r2 observation

X2,t-1 table) and conclusion at least there are one kind

of flavor chips that have a different level of preference.

chips taste is preferred by respondents paprica

Keywords: organoleptic, non-parametric statistics, Test

Friedmen

I. INTRODUCTION

1.1.Background

Development and empowerment of small businesses in order

to restore national ekomoni plays a fairly important, it can be

seen from the overall number of small businesses in

Indonesia by 40 million to the workforce and contribute 88%

to the national Gross Domestic Product of 38.9% ( Dep.

Industry). Nonetheless, small business development,

empowerment in order to increase the product selling many

constraints, the constraints due to several factors including:

limited capital, limited qualified human resources and lack of

capacity in science and

technology in processing and designing high value products.

Especially for snacks industry in West Sumatra is currently

facing various problems. Quoted in the Daily Express

Padang (Wednesday, 11/05/2011) that according to the

Governor of West Sumatra, West Sumatra opening Food and

Craft Fair IV, on the first floor of Industry Ministry building

on Tuesday (10/5) snack food industry production of West

Sumatra are still limited the market share of traditional and

not been able to get in modern markets. This is because the

packaging has not been so good, the quality has not been

homogenized to a certain standard, and less varied types of

products, as well as a limited production_capacity.

Although small businesses face obstacles in the competition,

but small business is quite a lot of advantages, one of which

is the ability of small businesses to the potential advantages

as an object to generate revenue. Lodging in West Sumatra

(Sumatra), the small business sector of the economy

kerupakan highest and best interests of the people of West

Sumatra, namely 99% of the total number of small

businesses that exist in West Sumatra (Sumatra Industrial

Service). On this basis the Government of West Sumatra

with local governments conducting training and small

business development through excellent products in each

region. Flagship program draws on the advantages of each

region in terms of geography, climate and culture.

In this study, researchers conducted a study with the object

of research Pariaman Emping Malinjo. According to sources

from the Ministry of Industry, West Sumatra in 2002 that

there were 658 SMEs (Small Medium Enterprises) in

Kab.Padang Pariaman with flagship product is the Small

Business Emping Malinjo. Efforts in Pariaman malinjo chips

are quite well known in West Sumatra due around this area

grow quite a lot of rods malinjo fruitful seasonally and

fruitful enough to motivate people to make a light meal, but

progress in the sense that can not be eaten immediately and

packaged potluck. Therefore encourage investigators to the

theme of research on diversification Taste Product

Innovation with case studies Emping Malinjo Pariaman

using statistical non-parametric Friedman test.

1.2.Limitation Problem

In this study, four different flavors using only the original

flavor chips, spicy sweetness, flavor and taste of chocolate

Application of Statistic Non Parametric-

Friedmen Test In Taste Testing Snack


M13-2

butter paprica using hedonic scale 7 is: It does not like, do

not like, kinda do not like, neutral, somewhat like, like, very

like

1.3.Problems

The problem of this research is to know the four

different flavors of chips that taste is the most preferred by

consumers. By using hypothesis:

H0: There is no difference in taste preference level for the

four different flavors crackers


different level of preference.

II. LITERATURE REVIEW

2.1. Organoleptic Test

Organoleptic Test is also known as assessment of sensory or

sensory assessment is a subjective assessment of the oldest

ways is very commonly used to measure the quality

attributes of a commodity by using humans as a

measurement tool based on the ability penginderaannya the

eyes, nose, tongue, skin, ears (BN Polli, 2007). Organoleptic

assessment in research applications are numerous, including:

assessment of the shelf, matching products, mapping

products, product specifications, product formulation, testing

irregularities potential odor and appearance of foreign odors

and determine keterterimaan products. In the food industry,

measurement characteristics of food quality is essential as

the basis of food quality control program development.

Foodstuffs or food received by humans on the basis of

certain characteristics that describe the taste, feeling and

perception resulting from the factors of physical appearance,

kinestetika and flavor. Included in the physical appearance

factor adlah color, size, shape and physical damage. Factors

kinestetika go round texture, viscosity, consistency, feeling

and touching the mouth with a finger. While the flavor factor

is the combination of smell and taste sensations.

2.2.Test-hedonic

Hedonic properties of a further psychological reactions of a

panel after he recognized that the arrest of the sensory

properties of food products that are served by declaring the

form of a personal response like: like it or not, accept it or

not accept, for better or worse, good or bad. ( Irma and

Cahyo, 2007). Besides, they also noted the level of likes and

dislikes so-called hedonic scale as in the case of love,

hedonic scale can have such profound love, love, a little

love. Conversely responses do not like to have such hedonic

scale: rather do not like, do not like, very unhappy and very

very unhappy. Hedonic scale can be stretched or reduced

according to the desired scale. In the analysis of hedonic

scale was transformed into a numerical scale with the

number rising by level of preference. The number penelis

used for hedonic test was sebayak 20-25 people to panelists

somewhat trained while using untrained panelists sebayak 80

people or more. (Soekarto,1992).

2.3. Nonparametric Statistical Data Analysis for

Organoleptic Test: Test Friedman

Statistics known as nonparametric statistical distribution of

free, does not need the assumption that the population is

normal spreads or other assumptions about the distribution of

the population. Nonparametric statistics is very well used for

data categorical (qualitative) or ranking (discrete) with a

simpler calculation. Friedman's analysis is one of the

nonparametric tests using the k-related samples (K-related

sample), the method is based on the data pairs k sampled at

least ordinal, is used to test the null hypothesis that the

samples were drawn from the same population. Friedmen

test this, the data generated into a two-way table with N rows

and k columns where rows represent different subject pairs

and columns represent a wide range of conditions. This test

data is ranking, the scores in each row are ranked separately.

The hypothesis used is:

H0: Each rank of treatments in the same group.

H1: At least one treatment that is different from others

Statistical_formulation:

r2 observation = (12/Nk (k-1)) (Rj)

2 – 3 N (k +1)

Description: r2 observation = Statistics Friedman, N =

many lines, k = Lots of columns,

Q = number of ranking of the i-th treatment

DecisionRule:

H0 is rejected if: r2 observation X

2,t-1 table , that tells us

there at least one treatment that is different from others H0 is

accepted if: r2 observation < X

2,t-1 table which means the

ranking of treatments in each group is thesame .

III. RESULTS AND DISCUSSION

Introduction to Descriptive Statistics Taste Typical Emping

Of the four kinds of flavor chips are tested to 80 panelists

consisting of original flavor chips, chocolate chips butter,

crackers and chips taste sweet spicy flavor paprica results

obtained 96.3% stated that the original chips (not supplied

various flavors) there is a sense of a typical empingnya, only

3.8% expressed no distinctive flavor chips. This suggests that

the original chips were just fried without being offered a

variety of flavors characteristic flavor was very subtle

empingnya.

For chips that have been given chocolate butter, only 32% of

the panelists said it was no distinctive flavor chips, while

67.5% said there was no longer distinctive flavor empingnya.

This suggests that the cocoa butter flavor given has given

them a distinctive flavor chips dominant than themselves.

Given chips spicy sweeness, as much as 37.5% of the

panelists said it was no distinctive flavor chips, while 62.5%

said there was no longer distinctive flavor empingnya. This

suggests that the taste of brown sugar and chili had given

impart a distinctive flavor chips dominant than themselves.

While Emping given a sense of paprika, 75% of panelists

said it was no distinctive flavor chips while 25% said there

was no longer distinctive flavor empingnya. It is shown that

the peppers were given not impart a distinctive flavor chips

dominant than themselves.


M13-3

4.3.2. Organoleptic Assessment Test Against passions sense

Liking for the fourth test chips using 7 different flavors

hedonic scale,It does not like, do not like, kinda do not like,

neutral, somewhat love, love, very love.

Friedman test was used in this study to determine

whether there is any difference in the level of the four kinds

of taste preferences is tested chips panelists. The hypothesis

used is:

H0: There is no difference in taste preference level for the

four different flavors crackers


different level of preference

The results obtained with SPSS is:

Table 4.1. Output of SPSS of Friedman test

N 80

Chi-Square 14.139

Df 3

Asymp. Sig. .003

From Table 4.2 Statistical values obtained Friedman (Chi-

Square observation) of 14.139. By setting the real level of

1% ( = 0.01) obtained by chi-square table 11.3 that the null

hypothesis is rejected (r2 observasi X

2,t-1 tabel ) and

concluded there is at least one kind of chips that have a sense

of different level of preference.

Of the 80 panelists average of 21.3% expressed a great love

of the original flavor chips, the next 17.5% expressed love to

taste chocolate chips butter, 16.3% said very like the spicy

sweet flavor chips and 31.3% expressed love to taste paprica

chips. In general it can be said that the chips taste paprica

highly preferred by 80respondents.

IV.CONCLUSION

From the research that has been done can be concluded that

the facts on the ground suggest that there is no desire of the

producers to innovate product chips. This is because the

resulting raw crackers always sold out, in addition to the

limitations in the processing of fast chips. From the

organoleptic tests against a variety of flavors provided

crackers (original flavor, sweet taste spicy, buttery chocolate

taste and flavor paprica) can be stated that the passions of the

sense, we can conclude there is at least one kind of flavor

chips that have a different level of preference ie crackers

taste paprica greatly liked by the respondents

REFERENCES

[1] Balance Economic Daily, 12 October 2002. “Raising

Tanamanmalinjo.”

[2] Horizon Daily, 17 June 2004. Diversification

Buahmalinjo Processing Technology.

[3] Isnafia Arief, Irma, 2007. Hedonic test. Ministry of

Industry.

[4] Industrial Services of West Sumatra, 2002. List of Small

Business Distribution and Employment in West Sumatra

in 2002.

[5] Kompas, 19 April 2002. So determination Regional

Basis malinjo

[6] Ministry of Industry, 2002. Industry Data / Business

Processing of Horticulture in Indonesia.

[7] Polli, B.N, 2007. Organoleptic assessment. Ministry of

Industry.

[8] Power Home Biz Guide, 2006. 10 Tips To Attract

Consumer Packaging Buying Products. Virginia USA

[9] Sinar Harapan, 2003. Copyright Design Products

[10] Suryati, Tuti, 2007. Organoleptic Data Analysis

Parametric and Nonparametric.

Ministry of Industry.


Tony Karnain, Md Nor bin Bakar and Hossein Mohammadikia Mathematics Education/Universiti Teknologi Malaysia

[email protected]

Abstract: The purpose of our study was to explore students’

use of metacognitive skills during problem posing activities.

This qualitative research explored the metacognitive skill of 21

secondary school students in a rural area while posing

individually mathematical problems. Thinking-Aloud

protocol was conducted during the problem posing activities.

The audio recordings of Thinking-Aloud protocol for the

students provided the data to address this question. Analysis

of their written work and thinking-aloud protocols provided

evidence of how students used metacognitive skills while

problem posing and revealed different levels of these skills.

Analyses of the Thinking-Aloud protocol also provided

evidence for the metacognitive skills associated with planning,

monitoring, and evaluation. The students used planning and

monitoring skills equally. Furthermore, different levels of

sophistication of planning were apparent. Students who

combined these metacognitive skills demonstrated a higher

level of monitoring. However, from our analyses that there

was considerable overlap in the metacognitive activities

associated with monitoring and evaluation.

Keywords: Metacognitive skill, problem posing, secondary

school students.

I. INTRODUCTION

Today, one of the main goals of education is to make

the students gain the thinking skills and strategies which

they will use throughout their lives, rather than storing

information [1]. Likewise, mathematics education must

provide opportunities for students to develop their ability to

think and reason critically, and this should be done through

sharing and reflecting on how students think through and

reason about a problem [2]. One alternative to develop

mathematical power in students is through the generation of

mathematical problems (problem posing) by the students

themselves [3]. Children‟s expression of mathematical ideas

through the creation of their own mathematics problems

demonstrates not only their understanding and level of

concept development, but also their perception of the nature

of mathematics [4]. Subsequently, from a teaching

perspectives, many researchers also have noted that

students' posed problems can be useful to teachers in

assessing students' understanding of mathematics ( [5], [6],

[7]).

Problem posing has long been recognized as an

important pedagogical tool in the teaching of mathematics

([8], [9], [10]). It includes an approach of teaching students

how to think analytically and how to analytically examine

the world they live [11]. It has also been argued that

problem posing promotes a deep understanding of

mathematics ([5], [12], [13]). Elementary teachers have

used posing tasks to gain insights into their students'

mathematical understanding for the purpose of guiding

instruction (e.g., [5], [14]). In his research [15] argued that

the first function of problem posing aproach is to help

students think like mathematicians by posing their own

mathematical questions and trying to solve them. This could

lead to “new” knowledge constructed by the students.

Many reasons have been voiced for utilizing

problem posing in mathematics instruction. For example, in

real-world situations, problems often are not coherently

stated and students need to learn to identify them and

formulate them more clearly ([9], [16]). It can lead to more

student-centered [5] and student inquiry oriented [17]

instructional practices. Development of skills in recognizing

problem structure and analogical reasoning ([18], [19]).

Mathematical problem posing has been attracting

keen attention of the mathematics education community for

more than three decades [20]. For instance, In his doctorate

dissertation,[21] argued that by adopting the “Problem

Posing Approach” students tended to be innovative, skilful

and knowledgeable and problem solvers. Then, Problem

posing activities have also improved student‟s activities,

motivation and achievement in learning mathematics [22].

Furthermore, [12] believed that problem posing can change

the orientation of mathematics lessons from a goal of

finding the correct answer and recording an appropriate

method, to finding the correct question from a infinite array

of imaginative possibilities. Most studies have shown that

problem posing can provide a positive impact on students

([23], [24], [25], [26], [27]). In short, by empowering

students with knowledge regarding their intention to pose

problems, it is more likely that they will acquire the skills

and resources necessary to effectively solve problems and,

in turn, use these higher-level skills to their life [28].

Subsequently, successful completion of

mathematical problem also requires more than the

application of knowledge, it requires the combination and

coordination of both cognitive strategies and processes and

metacognitive behavior [29]. More recently, the

Partnership for 21st

Century Skills has identified self-

directed learning as one of the life and career skills

necessary to prepare students for post-secondary education

and the workforce [30]. Students‟ metacognitive skills can

be improved through explicit instruction ([31], [32]). Such

instruction is most effective when teachers incorporate it

into subject specific learning activities ([33], [34]).

Educators can incorporate a variety of instructional

strategies to promote the development of students‟

metacognitive skills. Reference [35] found that deep

conceptual learning was characteristic of students who

Exploring the Metacognitive Skills of Secondary School

Students‟ Use During Problem Posing



demonstrated the metacognitive skills of knowing what the

task requires, planning a strategy, monitoring their progress,

and self-checking their work. Furthermore, [36] reported

students‟ use of metacognitive skills enabled them to

transfer past knowledge to unfamiliar problems.

The concept of metacognition has been considered in

recent years in the field of education and as a concept that

is worked on [1]. In mathematics education, the major goal

of implementing metacognitive is to help students develop

knowledge and awareness of their own thought processes

[37]. This link between metacognition and problem posing

has also been found in the mathematics classroom. In a

sense, metacognition has an important place in the

education of children and adults alike ([38], [39]). Students

without metacognitive approaches are basically learners

without direction to review their progress, complishments,

and future directions [40]. In addition, developing students‟

metacognitive abilities can also assist to inspire innovative

and creative minds. [26]. in other words, metacognition

enables students to work on self-learning, helping them take

responsibility for their own learning especially in

mathematics [37]. In conclusion, using metacognitive skills

can have high impact on mathematics performance of

learners, even when controlled for the influence of

intelligence ([41], [42]).

Our research has been designed to gain insight into

students‟ use of metacognitive skills in relation to their

problem posing activities. By using data sources that

include a think aloud protocols and students written works,

We endeavored to capture a rich picture of students‟

thinking while problem posing. This research has potential

to enrich our understanding of how students apply

metacognitive skills during problem posing activities.

II. METHODOLOGY

This qualitative study examined the metacognitive

skills of secondary school students‟ use while problem

posing activities. This study involved 21 students in a rural

area in Kepulauan Riau (Indonesia). Since the aim of the

study was to examine the metacognitive skills rather than

simply assess mathematics expertise, it was necessary to

supply a nonroutine problem that would challenge the

students. Verbatim transcriptions of the audio recorded

Thinking-Aloud protocol were completed for 2 of students.

Our analyses of the transcripts were guided by the coding,

seeking patterns, and theme analysis methods described by

Patton [43].

The purpose of the Thinking-Aloud protocol was

twofold. First, the sessions were part of the intervention by

giving the students an opportunity to become more aware of

their thinking while problem posing by articulating their

thinking. Second, these sessions provided a source of data

to address the research question to examine the

metacognitive skills students use while problem posing.

After students written works were analyzed, The two

problem posers were individually interviewed to probe the

metacognitive skills that occurred during problem

posing.and to examine particularly the responses to

statements implicitly assessing the metacognitive processes

expressed by the students while posing the problem. An

open ended question is given to the student adopted from

Stickles [44].

Parking Lot Flyers Instrument

The SpreadtheWord Advertising Company needs to

distribute flyers for ten different businesses. They are going

to place the flyers on cars in the parking lot at a nearby

shopping mall. There are 1000 cars in the lot. The

businesses each have their own flyer. The LotaMoney

Company is paying for flyers for all the cars. Consequently,

a worker places a flyer on each of the 1000 cars for them.

The rest of the businesses cannot afford one flyer for each

car. A second business can afford one flyer for every other

car. Consequently, a second worker places a flyer from the

second business on every other car starting with the second

car in the lot. A third business can afford one flyer for every

third car, and a worker places a flyer from the third business

on every third car starting with the third car in the lot, and

so on. How many cars would be necessary so that one car

would get all 10 flyers?

Using the above problem, pose some related problems.

Fig.1 Example of Problem-Posing Question from the Parking Lot Flyers

Instrument (Cited from Stickles, 2006)

III. RESULTS AND DISCUSSION

During the activity, We observed that all students in the

class were actively engaged in posing the problem. A small

number (2 out of 21 or about 9.52%) of the students posed a

problem, and the rest of those did not contain sufficient

information to solve the problem. Examples of the

problem-posing statements posed through problem

generation for the Nested Squares instrument are in Figure

2.

Problem:

A teacher set up 15 baskets. He asked the students to

throw a ball in each basket, the second student to throw a

ball in every other can, the third student to throw a ball in

every third basket, and so on. How many baskets would

have at least 5 balls in them when all 15 students have

went?

Fig. 2 Examples of Problem-Posing Statements from the Parking Lot

Flyers Instrument

The students retained their focus throughout the

duration of the activity, and they were persistent in their

attempt to work through the problems. The transcripts of

the audio recorded of two case students provide additional

support for tha data analyses. We used the planning,

monitoring, and evaluation metacognitive categories to

guide our analyses of the students‟ data. We begin with an

overview of each type of metacognitive category. We

interpreted statements that referred to the given

information, goal of the problem, or selection of relevant

strategies as planning. For example, “Okay let me write

down what I know first”(S1). Monitoring was

characterized by the “in the moment” checking of their

work at intermediate stages. For example, “I need to make

sure it‟s suitable”(S1). Evaluation was characterized by


statements about the verification of the final answer. For

example, “if the answer I get makes sense”(S2). Our

analysis revealed that the students demonstrated planning

and monitoring equally for thinking aloud problem posing

protocols.

A. Planning

Examination of the transcript excerpts We coded as

planning revealed the following metacognitive skills:

making sense of the task, extracting the given information,

being aware of the goal, seeking any examples used in the

past, and mapping a solution. Within some of these skills,

We noted varying levels of sophistication in the way the

students employed planning strategies. We begin with

evidence of the students trying to make sense of the

problem before launching into their solution to the new

problem. Statements that demonstrated this were: “Let me

think of what‟s this”(S2) and “I‟ve to write down

everything first so that I can get an idea of it”(S1). I‟m

thinking there‟s numbers in there that were not doing

anything right, but I don‟t know if they‟re relevant (S2).

The students were able to identify the goal of problem.

Commonly, the students restated what was asked in the

problem. The language used to express this included, “I‟ve

got to determine” (S2), “I need to find out” (S1) , and “I

need to find” (S2). Two comments stood out as being more

interpretive. S1 expressed the goal of the problem in his

own words showing that he had a clearer understanding of

the problem. He said, “So I need to find out how many...”.

A component of planning demonstrated by the students was

their identification of previous strategies that were relevant

to the current problem. At an elementary level, the student

referred to his notes in search of examples of related

problems. As an example, (S1) commented “Give me one

second, I‟m just going to grab my book. Okay. See most of

the examples were converted to combination ”. S2 took this

a step further, identifying the way in which a past problem

was different from the current problem: Okay, so what I

used to do was find the total of cars. S1 and S2 varied in the

way they made use of previously learned strategies. At the

simplest level, the students had a tendency to execute

familiar questions without thinking through how that

question would link to other steps that would eventually

satisfy the goal of the question. Using previous knowledge

in this way hindered the learners from moving forward in

the new question.

B. Monitoring

Three types of metacognitive monitoring emerged

from our analysis of the thinking aloud protokol transcripts:

screening, and justification and a little revision. All

monitoring began as screening where the students checked

an intermediate action. Students exemplified screening with

statements like, “Wait, I‟ll check if it can be solved” (S1),

“Oops, that doesn‟t make sense” (S2). Other types of

monitoring were coupled to screening. We noted a number

of instances where after screening, the students justified

why a question did or did not make sense. In the following

excerpt, S2 recognized that the question obtained was

reasonable because it was in the expected domain. S2: Is

that the reasonable question? S1: Well that would make

sense because the numbers are almost similar with the first

question and I need to start it from here. (S1 and S2). The

following exchange between S1 and S2, demonstrated

screening followed by revision. S1and S2 suspected an

error, and S2 corrected the mistake.

S1: But that‟s wrong I think.

S2: Let me try another sentences

S2: Oh! That‟s what went wrong.

In a number of cases, the students alluded to the need

to revise their approach but did not immediately know how

to redirect their efforts. One example of this occurred when

S2 commented, “Okay well that‟s really frustrating because

I can‟t find the solution of the first question because I don‟t

know what‟ the exact formula”. Other instances of this were

signaled by language like: “just one second I‟ve got to think

about this” (S1), and “I have to think it in my head” (S2).

C. Evaluation The students‟ comments about their new question to

the problems revealed two levels of evaluation: intuition

and reason. First, We present one example of what We

interpreted as intuition. Common to these examples was the

students‟ “feelings” that the answers were right or wrong.

She concluded the session with, “I think I‟m going to go

with permutation. I‟ve got a good feeling” (S2). In the

following discussion, S2 presents two hunches. Initially, S2

mistakenly thought that the new question was a permutation

could be the answer. After further consideration S2

suspected that a more rigorous approach to try to solve the

new problem is required. S1 suspected that his solution was

not question because it was based on an assumption. S1

noted, “And then, I assume but I didn‟t really, I don‟t

know, I think I missed something”. The students also using

reasoning to evaluate their answer. S1 understood that the

final answer for the problem could be checked by

comparing its topic. In addition, S2 realized that his

attempt to find the result of the new question did not match

the goal of the first problem. He commented, “Yeah but it‟s

asking for the number of cars. That‟s not the correct one”.

IV. IMPLICATIONS AND CONCLUSION

The thinking aloud protocols provided evidence of

how students used metacognitive skills while problem

posing and revealed different levels of these skills.

Analyses of the Thinking aloud protocols provided

evidence for the metacognitive skills associated with

planning, monitoring, and evaluation. The students used

planning and monitoring skills equally. Planning skills

included making sense of the problem, extracting the given

information, identifying the goal, seeking any examples

used in the past, and mapping a solution. Furthermore,

different levels of sophistication of planning were apparent.

Lower level planning was demonstrated when students

restated the goal. In contrast, higher level planning was

demonstrated when students interpreted the goal, compared

the context for their use of strategies in the past to the

context of the new problem. Students‟ different levels of

planning reflect the characteristics of novice and expert


problem solvers described by Heyworth [45]. The students

demonstrated monitoring when they screened for errors,

justified their judgments, and made revisions to correct

wrong turns. Students who combined these metacognitive

skills demonstrated a higher level of monitoring described

by Delvecchio [46]. A part of this process included periods

of reflection when the students took time out from

executing actions to think about what revision actions they

would pursue next. Students‟ attention to thinking before

acting was evidence that they valued metacognitive

activities as part of their problem posing process. The

students demonstrated evaluation through their comments

on the correctness of their final question. The students

showed two levels of evaluation: intuition and reason.

Intuition was the students‟ sense of the correctness of a

solution. Reason was demonstrated when students

elaborated on why a solution was correct or not. Students

who were able to explain why an answer was incorrect

demonstrated a deeper analysis of their solution to the

problem. Reference [47] supports the importance of

students‟ analysis of errors as a means to reduce conceptual

errors. It is apparent from my analyses that there is

considerable overlap in the metacognitive activities

associated with monitoring and evaluation. Both involve

students checking their work. In the case of monitoring,

students check intermediate actions, and during evaluation

they check a final answer. Metacognitive evaluation

includes students proposing alternate solutions and

reflecting on what new things they learned by attempting

the problem.

ACKNOWLEDGMENT

The authors acknowledge with thanks for the

research facilities availed at SMAN SIANTAN

(KABUPATEN ANAMBAS INDONESIA) during the

experiment and preparation of this paper.

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Abstract— Education is manifestation of civilization. One

of the education processes which are important is character

education. A factor which must be paid attention to in

character education is teacher. In learning process, teacher

has the important role to build the attitude and cognitive

ability of the students. Teacher as the educator is not just

transferring knowledge but also transferring value. It is

important to develop the learning that can give positive

contribution in character establishment, for example by

mathematics.

It is often to find that a mathematics teacher is just giving

the materials without giving the value or the sense of

mathematical concept. In developing the character which

can be built in mathematics, a teacher should understand

every character in mathematical concept. If teachers

understand the mathematics character, so they can establish

the values of every mathematical concept. This mathematical

concept can establish the discipline, visionary, responsible,

consistent and honest characters.

In this journal, the writers use ‘everyone is teacher’

method which can give the opportunity for students to have a

role as a teacher for their friends. By using this method,

everyone in class can get material and value not only from

the teacher but also from students and others. So it will be

formed the generation that has high quality of intellectual

and golden characters. This method is very useful for

students because this method is watching, speaking,

listening, writing, drawing, and emotional activities..

Index Terms— character, education, mathematical concept,

students, teacher

INTRODUCTION

Education in Indonesia influence to the nation achievement

very much. Education has close meaning with the teacher.

Teacher influence the students directly. The education quality

that‟s got is based on teacher quality. Teacher having honest

and straightforward in delivering knowledge to the students

will be a good teacher.

Having good intention is the result of the teacher‟s

character. Strong and good character will make the teachers

can be followed by the students. The teacher‟s character will

influence the effective learning system. The teacher‟s

characters that are patient, distinct, confident will deliver

knowledge well and will be the model for the students.

According to Fatmawati, in her paper - nowadays, the

obstacle of character establishment is the conventional

teaching technique underlay the learning process. Just using

books, the teacher dominate in class very much and teacher

haven‟t be able to make good interaction between the teachers

and students.

The teacher‟s duty is not only transferring knowledge but

also transferring value. Teachers help the students to find their

character. It needs teacher‟s character which is good to

establish student‟s character which is good because teacher is

the model for their student.

In order to make student‟s characters which are the same

with the mathematical character, the teachers teach by

transferring mathematical concept to the students.

REVIEW OF

LITERATURE AND RATIONALE Teacher‟s character

To get high quality and golden generation is needed moral

character of the teacher. The moral character means giving

good example to the students. The characters can be paid

attention in their daily attitude. Teacher is a leader in the class.

In relation with the leader, Calabrese and Roberts in The

International Journal of Education Management (2002:229)

explain that a leader with good character can give advantages

for his self and the people around him. On the contrary, when

a leader is weak in character so it will give lost for his self and

the people around him. The teacher position as the leader in

the class is prosecuted to have good character.

Good character make the teacher can be the model for the

students. According to Ryan Dand Lickona which is quoted

Research in Character Education (2008:45), character is an

individual which is good moral and done consistently. The

statement is supported by Sherman which is quoted by

Calabrase and Roberts in The International Journal of

Education Management (2002:229) that someone‟s character

appears from the individual behaviour which is in an action

form that will be repeated in the future.

The teacher‟s character can be made a model for the

students easily when the students do their duties in the class

which involve heart, mind, and action (Bassiouny, 2008:45-

Role of Teacher and Mathematical Concept to Build

Student‟s Character by Using „Everyone is Teacher‟

Method

Muhammad Rifki Taufik1, Eprina Eksa Gutami

2

1) Mathematics Education, Mathematics and Science, UNY, Yogyakarta, [email protected]

2) Mathematics Education, Mathematics and Science, UNY, Yogyakarta, [email protected]




46). Because of the sincereity in delivering knowledge, good

character, and the appropriation with the value and norm, can

motivate the students to have good character.

Mathematical concept Concept and Contextual that have the same meaning from

mathematics is an abstract mathematical object. Mathematics

uses zero symbols for meaning and mathematics thinking way

is based by axiom and deductive reasoning (Juhartutik, 2011)

Wardhani (in Nur, 200:2) said that mathematics learning

which is full of concept press on context abstractly. In

mathematics, the development process and ideas reasoning

begin from real life. From real life, there are concrete

examples physicaly about mathematics problems.

Mathematics in real life is not only in plain view but also can

be imagined.

By imagining mathematics problems, it can apply

mathematical logics concept. The concept in mathematics

should be learned to be able to know other concept in

mathematics. Mathematics is said real by Wardhani (2004:6)

can be applied in daily life. By the statement, mathematics is

also exact knowledge. To answer the problems need problems

solving by looking for the solution of the problems.

The evidence that mathematical concept can be applied in

real life is that there are problems which are connected to daily

life, Mathematics question have many kinds of choice. There

are mathematical questions in phenomenological questions in

order the students can be interested in the concept.

The student‟s approximation method Making the students to be more comfortable and

increasing the students passion to get knowledge is the main

duty of teacher. By approximation of students can be got an

effective class because the education in the class is harmonic.

Approximation of the students can be done personally by

implant the motivation and implant benefaction that must be

done. Devine and friends (in Baaiouny: 2008) told that the

teachers should explain what benefaction must be done in life

because benefaction is life values that must be understood.

The transition time has big influence in establishing the

character in 12th – 13th years old. The teenagers feel want to

know everything such us the information or the new things.

The teachers can benefate inquirin of the students in

establishing the character. Good character can make the

students to be high quality generation.

The relevant observation Raymond L. Calabrese (2002), in his research declared

that a leader must have good character in order the persons

who are leaded can followed him. The leader in the class is the

teachers who should have good character which can be

followed by the students. Ethical character can influence the

students very much.

Sri Wardhani (2004), in her research arranges the

contextual learning has the aim to benefete mathematical

concept in order can benefeted in daily life. Beside the

mathematical concept, the students who know mathematics

are hoped to get reasoning ability in students which can be

known by critical, logical, and systematic thinking and have

objective character and honest in solving the problems either

in mathematics or social field.

Progress

Basically, learning process in a communication process

which consist of information delivering as material learning

from the teachers by using a certain method so that the

students can accept, understand and apply mathematical

concept in daily life by the positive point of view.

The known mathematical concept which is the mother of

all knowledge makes easier to apply mathematical concept in

the real life by positive point of view. Pleasing learning and

developing the student passion to accept the mathematical

concepts is the unique way to apply in the real life.

The developing of mathematical concept in character

establishing process in daily life can be determiner to make

the students have good character as the studied mathematical

concepts.

Following the time development which is be better,

education become main determiner for someone will be

success or not, useful or not. Useful people will give

advantages for other people. Useful people is based on how

much the knowledge he has.

There are many education institution formed to increase

the education quality in Indonesia. But it is rare for the

teachers can be made a model. The real model is related to the

teaching process, relation and interaction as long as the

education process which will be the model of other people

nowadays or future. In a learning process, behaviour of the

teacher will become the effective communication and

influence very much (90%) to students (anonim:2010). For a

teacher, becoming a model is not a demand but the effect for

the students to become a model for the students.

Mathematics is an exact knowledge. Fathani (2009) said

that in mathematics there are many kind of system which is

formed by some axiom and theorems and in each system has

consistent character. Mathematics has a system which must be

obeyed and consistent. For example, 2+2=4, this statement

obtains in the daily life for good. This character is also applied

in the daily life, for example when someone choose a decision,

so he must be consistent with his decision. Beside that,

mathematical logics also the imagion of the real life. The

implication is applying promise concept, conditional, and

effects. If someone has been promised to anyone so he should

obey his promise. So that, the mathematical concept can be

used as the mediator of forming the character of the students

to become the model in the future.

According the education expert Prof. Dr. Budiono in the

national conference LSM XX (Budiono: 2012), to create a

success learning system, basicaly a learning system must make

the pleasing learning. There are many variation learning model

can be made as the effort to increase the achievement of the

students. The delivering way is pleasing and relax but not


decreasing the sense of the material is the delivering way

which is favorite for the students and very effective to apply in

the class.

The teaching system by combining the teacher‟s character

and mathematical concept which is applied for the students

can establish the student‟s character to be discipline,

visionary, responsible, consistent and honest. So the learning

is not only centered in the students but also applying everyone

is teacher system also the role of the teacher is very important

in giving example.

Conclusion Learning process which is offered in this paper is a

learning system which is not only support the achievement the

students but also can establish students character to be

discipline, visionary, responsible, consistent and honest.

Besides that, the students is hoped to be the good model for

their friends and become the wise leader in the future.

REFERENCES

[1] T. Amelia. (2012, January 14th). “ Optimasi peran parenting dalam

pengawasan penggunaan media internet demi membangun karakter

positif remaja.” In International Conference of Guidance and Conselling

Padang State University. [Online]. Available:

http://edukasi.kompasiana.com/2012/01/30/optimasi-

peran-parenting-dalam-pengawasan-penggunaan-media-

internet-demi-membangun-karakter-positif-remaja/. [2] Anonim. (2012, April 14th). “Menjadi guru Teladan yang Profesional

Sebagai Motivator kelas.” [Online]. Available:

http://semangatbelajar.com/menjadi-guru-teladan-yang-

profesional-sebagai-motivator-kelas/ #.

[3] Budiono, “Pembelajaran Matematika Yang Menyenangkan,” in Nation

Conference LSM XX Yogyakarta State University, 2012.

[4] Calabrese, Raymond L, and R.Roberts, Character, “School Leadership,

and The Brain: Learning How To Integrate Knowledge With Behavioral

Change,” The International Journal Of Education Management, 16, 4/5;

ProQuest Education Journals pg. 229, 2002.

[5] Crow and alice Crow, “Educational Psychology Lester 198,” PT Bina

Ilmu, Surabaya, 1984.

[6] Fathani and Andul Halim, “Matematika : Hakikat dan Logika,”

Yogyakarta, Ar-Ruzz Medi, 2009.

[7] N. Fatmawati. (2012, April 14th). “Pemanfaatan Internet Sekolah

Sebagai Sumber Belajar Alternatif Dalam Meningkatkan Hasil Belajar

Siswa Pada Mata Pelajaran TIK (Teknologi Informasi Dan

Komunikasi).” [Online]. 34th JHS of Surabaya. Available:

http://blog.elearning.unesa.ac.id/tag/kendala-membina-karakter.

[8] Indiati, Intan dan Listyaning Sumardiyani. (2012, April 14th).

Pengembangan Model Reflective Microteaching Untuk Pembentukan

Calon Guru Profesional. [Online]. Available:

http://jurnalaksioma.net/?p=166.

[9] Margunani, and Siti Fatimah. (2012, April 14th). “Keterampilan Guru

dalam Pengelolaan Kelas pada Mata Pelajaran Akuntansi di SMA

Negeri se Kabupaten Kebumen.” [Online]. Available:

journal.unnes.ac.id/index.php/DP/article/download/442/395.

[10] Ahmed Taher, Noha El-Bassiouny, and Ehab M. Abou-Aish, “The

Importance Of Character Education For Tweens As Consumers,” A

Conceptual Model With Prospects for Future Research, Journal of

Research in Character Education, Vol. 6, No. 2, 2008.

[11] S.Wardhani, “Pembelajaran Matematika Kontekstual di SMP”, Nation

Instructor Trainning/Mathematics Development on JHS Elementary

Degree, 2004.

http://edukasi.kompasiana.com/2012/01/30/optimasi-peran-parenting-dalam-pengawasan-penggunaan-media-internet-demi-membangun-karakter-positif-remaja/



http://semangatbelajar.com/menjadi-guru-teladan-yang-profesional-sebagai-motivator-kelas/

http://semangatbelajar.com/menjadi-guru-teladan-yang-profesional-sebagai-motivator-kelas/

http://adf.ly/7An5A

http://adf.ly/7An5A

http://adf.ly/7An5A

http://adf.ly/7An5A

http://blog.elearning.unesa.ac.id/tag/kendala-membina-karakter

http://jurnalaksioma.net/?p=166


Abstract— Pictures or other learning aids are frequently used

by teachers in elementary schools as media for teaching

mathematics, especially geometry. In line with the development of

technology, Augmented Reality (AR) technology can be used as

an alternative learning media for Geometry. The application of

AR technology for education has been discussed in many

literatures. This paper discusses the application of AR technology

for elementary education in order to increase the attractiveness

and motivation of the student in learning geometry. A book that

has been integrated to AR technology can present the geometric

objects in a virtual machine utilizing camera and computer. In

that geometry book there is a marker that can be identified as the

geometry object to be presented. The application will display the

geometry object in 3D on the screen. This presentation of

geometry object utilizing AR technology can be used as an

alternative learning media as well as to introduce the

implementation of AR technology for elementary education.

Keywords: Augmented Reality (AR), geometry, learning aids,

marker

I. INTRODUCTION

esearch on geometry learning tool in elementary schools

based on attractive, iconic, and a valid symbolic, practical

and effective way have shown to foster creative thinking

abilities learners in the subject matter of simple flat geometry

object[1]. Survey of the use of visual aids in teaching plane

geometry at the elementary school level have also been

conducted to determine how the use of the learning aids for

plane geometry at the elementary level[3]. The study shows

there are several difficulties of which are difficult to make the

necessary learning aids in flat geometry lesson, difficulty to

construct the learning concepts through aids, difficulty pushing

students to be more active or more involved physically,

difficulty pushing students more active / more emotionally

involved, difficulty involving the use of the five senses as

channels of information simultaneously (sight, hearing, smell,

and feelings), difficulty to encourage students involved in high-

level cognitive activities (problem solving, creative thinking,

creativity creating, innovating, etc.) developmentally

appropriate child psychology [3].

in line with the development of technology, Augmented Reality

(AR) has been used for various things including education.

Geometry education tool with AR technology for high school

and university education also been made in austria by using a

head mounted display equipment (fig. 1) . this system tool

provide a natural setting collaboration of teachers and students

(fig. 1) [2].

Fig 1. Collaboration class (right), Head Mount Display equipment (left)

This study tries to apply the AR technology in a simple way

as learning aids or media in teaching geometry for elementary

education especially about 3 dimensional objects. In this study,

the implementing of AR technology adapted to the device

available in most primary schools in Indonesia. This geometry

learning aids is not have to use the equipment such as head

mounted displays (HMD) to facilitate the use of these tools,

because there is no school that has the equipment, and the

equipment is still quite expensive to be provided in elementary

school level in Indonesia generally. For the easiest and simplest

solution in developing geometry learning aids customized with

AR technology, the implementation is made by a regular

computer and camera. The media of this tool is a geometry

handbook integrated with a symbol as the marker inside the

page.

II. MAGICBOOK CONCEPT

This learning aids use the physical book contained a marker

as a media for AR technology implementation named

magicbook. Magicbook interface on a several paper similar to

each other. In some papers the magicBook interface has two

components; a handheld one or more displays (HHD) or can be

a HMD and the physical book. The HHD is a handle with a

Sony Glasstron display mounted at the top, an InterTrax

InterSense inertial tracker at the bottom, a small camera on the

front of the Glasstron display and a switch and pressure pad

(fig. 3). The Sony Glasstron is a bioccular color display with

two LCD panels of 265x235 pixel resolution. The camera

output is connected to a desktop computer and the video-out

of the computer is connected back into the HHD. So by

looking through the HHD users experience a video-mediated

Object Representation on Geometry Learning

using Augmented Reality Approach

Nelly O. Adiwijaya

R


reality[5]. The books used in the MagicBook interface are

normal books with text and pictures on each page. Certain

pictures have thick black borders surrounding them as marker.

When the reader looks at these pictures through the HHD,

computer vision techniques are used to precisely calculate the

camera position and orientation relative to the picture. The

computer then generates virtual images that Appear precisely

registered with the real pages.

Fig 3. Magicbook with HHD

In this paper the concept of magicbook is not using the

HDD. Representation of virtual object using a personal

computer and a small camera connected or a built-in camera.

The physical book which user used within marker is the same

concept of another magicbook. The output images that appear

on the screen can be seen by all students. A user in this case a

teacher can show the 3D virtual objects by directing

magicbook before the camera. The computer vision techniques

are used to translate the marker into a 3D virtual object. The

virtual object on the screen can be seen by students directly or

through the projector in front of the class if any.

III. DETECTION MARKER AND CAMERA CALLIBRATION

The books used in the MagicBook interface are normal

books with text and pictures on each page. Certain pictures

have thick, black borders that are used as tracking marks for a

computer vision-based camera tracking system. When the

marker exposes the user in front of camera, computer vision

techniques precisely calculate the camera position and

orientation relative to the tracking mark. The camera tracking

uses the augmented reality tool kit (ARToolKit) tracking

library, an opensource software library for developing vision-

based augmented reality applications (see the ARToolKit Web

site) [6]. Once the computer calculates the camera position, it

generates virtual images that appear precisely registered with

the real pages.

IV. THE APPLICATION OF GEOMETRY LEARNING AIDS

Development of learning aids especially for geometry

education in line with development of technology at the

elementary level in Indonesia is one of the business

development field exploration of AR technology.

Implementation of AR technology here is tried in a simplest

way hopefully can be accepted by a school that only have a

regular desktop computer devices without any special tools to

visualize. This geometry magicbook learning aids use the

concept that has been developed previously. Magicbook

concept integrated into the regular geometry textbooks

(figure.4) used by students or teachers teaching geometry

lesson. Geometry handbook has been adapted to the

magicbook concept that contain the certain image as marker in

it. These markers are then to be translated by a computer with

a camera calibration method.

Fig. 4 Geometry textbook

The use of these applications can be performed in class or a

computer lab with a teacher guide. If the elementary school has

a computer in every classroom and equipped with a viewer, the

teacher can demonstrate to the students directly in the

classroom. Teachers as users simply point the camera to the

page with marker that has been linked to a computer with the

AR program to display the geometry virtual object. The

students then can see the results of the transformation marker

in the handbook becomes a virtual object on a computer screen

or projector screen. Figure 5 is an example of a geometry book

to be magicbook can display virtual objects.

Fig. 5 Magicbook display the 3D geometry virtual object

The result of this research can be an alternative simply

modern learning aids in geometry education for elementary

schools in the development country like indonesia. An AR

technology recognizing need the simpler way and familiar

device to be accepted. Many elementary schools in Indonesia

do not have a computer lab moreover the special device like

HDD or HMD to implement the AR technology. Using the

standard AR technology, ARToolkit is compatible for this


case. Through at least one computer machine, the schools can

use the AR learning aids and it maybe possible to do. This

implementation of the research hopefully can encourage the

students to learn the lesson in line with technology

development. And in addition this learning aids should

encourage students involved in high-level cognitive activities

(problem solving, creative thinking, creativity creating,

innovating, etc).

V. CONCLUSION

In line with the development technology especially in

Indonesia, the concept of AR technology can be simply

implemented in elementary school for geometry education. The

basic and standard implementation of AR technology can give

an alternative way representing a learning aids. This way can be

a non expensive tool but up to date and easy to be accepted by

the user. In addition this learning aids can encourage the

attractiveness and motivation of the student in learning

geometry.

For the next implementation, this concept can be

implemented in another lesson such as learning aids for

chemical education or biology, still in the simply way so the

user or schools in Indonesia easy to use this technology.

ACKNOWLEDGMENT

The author would like to thank prof. Slamin for the

discussion of educational mathematics.

REFERENCES

[1] Sugiarto, i. Junaedi, st. B. Waluya, “Pembelajaran Geometri Berbasis

Enaktif, Ikonik, Simbolik Untuk Menumbuhkan Kemampuan Berpikir

Kreatifpeserta Didik Sekolah Dasar”, journal of primary educational,

vol.1, no. 1, 2012

[2] H. kaufmann, M. Papp,” Learning Objects For Education With

Augmented Reality”, http://citeseerx.ist.psu.edu/viewdoc/download?doi=

10.1.1.100.2194&rep=rep1&type=pdf

[3] Siregar,R. Romayanti, “Survei Penggunaan Alat Peraga Dalam

Pembelajaran Geometri Bidang Datar Di Sd Kecamatan

Padangsidimpuan Utara T.A 2012/2013”, Fmipa Unimed, 2012

[4] H. Kaufmann, D. Schmalstieg,” Mathematics And Geometry Education

With Collaborative Augmented Reality”, Computers & Graphics, volume

27, issue 3, june 2003, pages 339–345

[5] M. Billinghurst, H. Kato, I.Poupyrev, “MagicBook: Transitioning

between Reality and Virtuality”, Computer Graphics and Applications,

IEEE, volume 21, issue 3, May/Jun 2001

[6] ARToolKit Documentation, http://www.hitl.washington.edu/artoolkit

/documentation/


M18-1

A. B. Astuti, N. Iriawan, Irhamah and H. Kuswanto

1Abstract-Microarray is an analysis technique to monitor

gene expression activity simultaneously. In this case, gene

expression data is defined as the data of microarray

experiments. The problems that commonly arises from gene

expression data is limited availability of the number limited

budget, resources and time. Though the availability of the

number of samples is limited, the measurable characteristic

variables can be hundreds or even thousands of gene

expression. By these special characteristics, it is possible that

the nature of the distribution of gene expression data will be

very complex in which the distribution of the data obtained is

probably not a normal distribution. Various studies conducted

using frequentist approach apply t-student statistic, however

this approach requires strict compliance with the assumption

that the distribution of the data comes from a normal

distribution with a large enough sample size. Bayesian analysis

is an analysis that may answer this challenge where the data

analysis is driven by the nature of the data using posterior

probability distribution. The purpose of this study is to identify

the appropriate distribution of gene expression data as a result

of microarray experiments and to test hypotheses through

Bayesian confidence intervals using Highest Posterior Density

(HPD). The data used in this study is the gene expression data

of human colon tissue in healthy and diseased (infected tumor),

a data set that previously used in [1]. The results showed that

the distribution of gene expression data is asymmetry

(skewed/neo normal) and gene expression data in diseased

(infected tumor) and healthy conditions have different

distributions. Based on the overlapping distribution and

boundaries of HPD it is known that most of the data indicate

no difference gene expression in human intestinal tissue on

diseased (infected tumor) and healthy conditions. But the

exploration of the data indicated that the genes in a healthy

condition is more expressive than the diseased condition.

Manuscript received April 4, 2013. Highest Posterior Density for

Identifying Differences in Gene Expression Microarray Experiments.

A. B. Astuti is with the Mathematics Department of Mathematics and

Natural Sciences, Brawijaya University Jl. Veteran Malang 65145

Indonesia ; e-mail: [email protected]

N. Iriawan is with the Statistics Department of Mathematics and

Natural Sciences, Institut of Teknologi Sepuluh Nopember Surabaya,

Kampus ITS Sukolilo, Surabaya 60111 Indonesia; e-mail:

[email protected]

Irhamah is with the Statistics Department of Mathematics and Natural

Sciences, Institut of Teknologi Sepuluh Nopember Surabaya, Kampus ITS

Sukolilo, Surabaya 60111 Indonesia; e-mail: [email protected]

H. Kuswanto is with the Statistics Department of Mathematics and

Natural Sciences, Institut of Teknologi Sepuluh Nopember Surabaya,

Kampus ITS Sukolilo, Surabaya 60111 Indonesia; e-mail:

[email protected]

Keywords: Bayesian Interval Confidence, Differences in

Gen Expression, Highest Posterior Density, Microarray

Experiments

I. INTRODUCTION

Microarray is an analysis technique to monitor the

activity of thousands genes simultaneously, thus the gene

expression data is the data obtained from

microarray experiment [2]. The problems that commonly

arises from gene expression data is limited availability of the

number limited budget, resources and time. Though the

availability of the number of samples is limited, the

measurable characteristic variables can be hundreds or even

thousands of gene expression. By these special

characteristics, it is possible that the nature of the

distribution of gene expression data will be very complex in

which the distribution of the data is probably not a normal

distribution [3].

Bayesian analysis is a statistical analysis method that

does not consider the number of samples which make it

possible to be applied for which make it possible to be

applied for large or small amounts of data. Performance of

Bayesian analysis based on the distribution data. The

posterior probability distribution is obtained from the

multiplication of the prior distribution (based on past data

information) and the likelihood function (based on

observational data obtained). The parameters in the Bayesian

analysis model is treated as random variable in the model

parameter space [4]. The advantage of Bayesian analysis is

to provide inference from an unknown variable based on the

posterior distribution of the data. Moreover, the analysis also

allows for the combination of different prior distribution as

well as facilitates the iterative updating of new information

which thus overcome the problem of uncertainty and

complexity of the models in the data [5].

Various studies have been conducted to identify

differences in gene expression

as a result of a microarray experiment using the student's t-

test, among others [6]; [7]; [8]; [9]; [10]; [11]; [12]. While

[1] have proposed a Bayesian Mixture Model. The use of

student's t-test requires strict compliance with the

assumption that is the distribution of the data comes from a

normal distribution with large enough sample size. This

research uses Highest Posterior Density (HPD) methods and

the concept of overlapping distribution to identify

differences in gene expression in diseased and healthy

conditions.

Higest Posterior Density for Identifying Differences in

Gene Expression Microarray Experiments


M18-2

II. REVIEW OF THEORY

A. Microarray Experiments and Microarray Data

Microarray Experiment is a technique of data

collection by using the platform (reference/guidelines/base)

that is the result of duplication of the original object

identifier [13]. The measurement results of the microarray

technique called microarray data [13]. There are several

different technologies for microarray techniques,

one example is the technology of Synthetic oligonucleotide

microarray [14]. Gene expression data is the data from

microarray experiments thus the

gene expression data have characteristics of microarray data.

Data obtained from experiments with microarray

technique has the following characteristics [15]: the basic

distribution of data has a complex shape, the number of

samples that can be observed very limited because of limited

funds, manpower, time and the availability of samples and

the characteristics of the variables that can be observed very

large. It can reach tens thousands of characteristics in each

experiment.

Based on the characteristics possessed by the

microarray data therefore it requires special treatment as the

usual parametric statistical method for comparison requires a

large enough sample size. If compliance with the number of

samples is violated then the conclusion of his analysis can

not be accounted for [16].

B. Bayesian Analysis

Bayesian analysis is a statistical analysis method based

on posterior probability distribution model which is a

combination of the two information is information of past

data as prior information and the observed (sample) is used

as a constituent likelihood function to update the prior

information [13], [17], [4]. The Rational of Bayesian

analysis derived from Bayes Theorem thinking concept

invented by Thomas Bayes in the year 1702-1761. In

Bayesian analysis, the parameters of the model is seen as

a random variable in the parameter space .

Suppose there are x observational data with likelihood

function

)|( xf then the known information about the

parameters before the observations were made is referred

to as prior namely )(p . Furthermore, to determine the

posterior probability distribution of , namely )|( xp

based on the rules of probability in Bayes Theorem [18] as

follows:

)(

)()|()|(

xf

pxfxp

where

(2.1)

)]|([)( xfExf = Rx

dfxf )()|( if

continuous and

)]|([)( xfExf =Bx

pxf )()|( if discrete.

)(xf is a constant called the normalized constant [4]. The

equation (2.1) can be written as:

)()|()|( pxfxp

(2.2)

Posterior Likelihood Function x Prior

According to equation (2.2) it is known that the posterior

probability proportional the product of the likelihood

function and the prior probability of the model parameters.

This means that the update's information prior to use the

information in the likelihood of data sampling to obtain

posterior information that will be used for decision making.

C. The Concept of Confidence Interval of Highest

Posterior Density (HPD)

C.1. The Concept of Equilibrium in the Density

Distribution of Symmetry

The basic concept of the formation of the confidence

interval on the data distributed symmetry (normal

distribution) are as

follows:

1)//( 2/2/ nsZxnsZxP (2.3)

According to equation (2.3) can be seen that

)()( BxPBxP with )/( 2/ nsZB . This

means that the jump with the length of B the right side x

will have a value of density of )( BxP the same height

as the density when it jump to left side of with the length of

B x , as high as

)( BxP [15].

On the symmetrical distribution (normal distribution),

the location of the mean, median and mode lies in the same

location so that the equation (2.3) at the boundary control

points will automatically have the equilibrium value of the

density. This means the moverment to the left and to the

right of the data center by a given standard deviation has the

same density values or equilibrium. This concept is referred

to as the concept of equilibrium density or the Highest

Posterior Density (HPD) [15]. C.2. The Concept of Equilibrium in the Density

Distribution of Asymmetry (Skewed/Neo Normal)

The basic concept of the formation of the confidence

interval on the data is asymmetrical distributed (skewed/ neo

normal) can-not use the concept of the equation (2.3) due to

the location of the mean, median and mode which lies in a

different location. In this case, the concept of HPD uses

location as a reference mode of data center. At HPD concept

for data distributed skewed, the limits to the distance jumps

to the left and right are different lengths but will have the

same high density values [15].

The algorithm of formation equilibrium density

(HPD) for asymmetrical distributed data (skewed/neo

normal) is as follows [15]:

(1). Determine the mode of the density is not symmetry

(skewed)

(2). Put your data center in this mode


M18-3

(3). Create jump steps to the left and to the right of the mode

to determine the lower limit of the interval,

ax (LCL=Lower Control Level)) and the upper limit

bx (UCL=Upper Control Level)) to keep control of

the equilibrium density, )()( bxfaxf to

obtain the probability interval for 1 or

1)()(

b

a

dxxfUCLxLCLP

III. METHODOLOGY

A. Data

The data used in this study is the one used in [1] i.e.

the gene expression data of human colon tissue in diseased

(infected tumor) and healthy (uninfected tumor) conditions

in which the method of detection of gene expression that

there are 2 methods of Poly Detector and mRNA. The

Number of samples used in the study is 11 patients with

diseased conditions in which gene expression was observed

with Poly Detector method, 10 patients healthy conditions in

which gene expression was observed with Poly Detector

method, 29 patients diseased conditions in which gene

expression was observed by the method of mRNA and 12

healthy patients in which gene expression was observed by

the method of mRNA.

B. Methods

1. Identify the most appropriate distribution as well as

estimates the parameters for gene expression data of 11

patients at the diseased condition in which gene

expression was observed with Poly Detector method.

2. Identify the most appropriate distribution as well as

estimates of parameters for gene expression data of 10

patients at the healthy condition in which gene

expression was observed with Poly Detector method

3. Identification of overlapping distribution based on the

results of identification steps (1) and (2). 4. Determine the limits of HPD based on the results of step

(3)

5. Repeat steps (1) through (4) for gene expression data 29

diseased patients where gene expression was observed by

the method of mRNA and 12 healthy patients in which

gene expression was observed by the method of mRNA. Data analysis using statistical software Minitab 16, EasyFit

5.2 and Maple 5 R-4.

IV. RESULTS

A. Identify the Distribution and Parameter Estimators

for Gene Expression Data Diseased and Healthy

Conditions

The results of the identification of the data distribution

and parameter estimators for gene expression in diseased and

healthy conditions using 2 methods applied show that there

is a difference in term of the distributions between diseased

and healthy conditions. It is also known that most of the data

has asymmetric distribution (skewed/neo-normal). Based on

the results of data exploration it is known that most of the

data indicate that gene expression in healthy condition is

more expressive than the diseased condition. For instance

the distribution of data on diseased condition (black line)

and healthy (dashed red line) with Poly Detector method on

gene ID H55933 follows:

2500020000150001000050000

0.00018

0.00016

0.00014

0.00012

0.00010

0.00008

0.00006

0.00004

0.00002

0.00000

X

De

nsit

y

Lognormal 8.4 0.66 1145.2

Distribution Loc Scale Thresh

Weibull 1.44 5699.81 3469.12

Distribution Shape Scale Thresh

Distribution Plot

Fig. 4.1. Distribution Data on Diseased Condition

(Lognormal (3P)) and Healthy Condition (Weibull (3P))

with Poly Detector Method on Gene ID H55933.

B. Identification of Overlapping Distribution and Limits

of HPD on Gene Expression Data Diseased and

Healthy Conditions on ID 10 Genes with Average

Value Largest Gene Expression.

The results of the overlapping distribution and

boundaries HPD data on diseased and healthy conditions are

listed as follows:

Table 4.1.

Overlapping Distribution and HPD Boundaries of 10 Genes

with Average Largest Gene Expression.

No Genes

ID

Overlaping Distribution and

HPD Boundaries

Diseased-PL vs

Healthy-PL

Diseased-mRNA vs

Healthy-mRNA

1 H55933 Overlapping Overlapping

2 T52342 Overlapping Overlapping

3 J02763 Overlapping Overlapping

4 R02593 Overlapping Overlapping


6 H20709 Overlapping Overlapping



9 R22197 Overlapping Overlapping


M18-4

10 X63432 Overlapping Overlapping

Based on Table 4.1. it is known that all ID genes have a

distribution and HPD boundaries overlapping between

diseased and healthy conditions. This means that the

statistical test revealed no differences in gene expression

between human colon tissue in diseased (infected tumor) and

healthy (uninfected tumor) conditions.

V. CONCLUSION

Based on the results of research it can be concluded

that the gene expression data as a result of a microarray

experiment has the form asymmetrical (skewed/neo-normal)

distribution in both diseased and healthy conditions.

Moreover, this type of distribution is also different in the

two conditions. There are overlapping distributions and HPD

boundaries of gene expression data on the diseased condition

(infected tumor) and healthy condition (uninfected tumor)

suggests that there is no difference of gene expression in

human colon tissue between the diseased condition (infected

tumor) and healthy condition (uninfected tumor). But the

results of data exploration is known that most of the data

indicate that gene expression in healthy condition is more

expressive than the diseased condition

REFERENCES

[1] K. A. Do, P. Muller and F. Tang, “A Bayesian Mixture

Model For Differential Gene Expression”,

Research in Department of Biostatistics, The

University of Texas, 2004. [2] S. Knudsen, “A Guide to Analysis of DNA Microarray

Data”, Second Edition,. John Wiley & Sons,

Inc., New Jersey, Canada, 2004

[3] P. Muller, G. Parmigiani, C. Robert and J. Rouseau,

“Optimal Sample Size for Multiple Testing: the

Case of Gene Expression Microarrays”, Tech.

rep., University of Texas, M.D. Anderson

Cancer Center, 2002.

[4] A. Gelman, J. B. Carlin, H. S. Stern and D. B. Rubin,

“Bayesian Data Analysis”, Chapman & Hall,

London, 1995.

[5] K. Mengersen, “Modul 1 Bayesian Analysis. Short

Course on Bayesian Modeling”, Statistics

Department, ITS, Surabaya, 2009.

[6] N. Harijati, “A Study of the Resistance of Chickpea

(Cicer Arietinum) to Ascochyta Rabiei and the

Effect of Age of Plant Tissue on Disease

Development”, Ph.D, Thesis, La Trobe

University, Australia, 2007. [7] M. Schena, D. Shalon, R. W. Davis and P. O. Brown,

“Quantitative Monitoring of Gene Expression

Patterns with a Complementary DNA

Microarray”, Science. 270, 1995, pp. 467–470.

[8] M. Schena, D. Shalon, R. Heller, A. Chai, P. O. Brown,

and R. W. Davis, “Parallel human genome

analysis: Microarray-based expression

monitoring of 1000 genes”, Proceedings of the

National Academy of Sciences, 93, 1996, pp.

10614–10619.

[9] J. L. DeRisi, L. Penland, P. O. Brown, M. L. Bittner, P.

S. Meltzer, M. Ray, Y. Chen, Y. A. Su and J.

M. Trent, “Use of a cDNA Microarray to

Analyze Gene Expression Patterns in Human

Cancer”, Nature Genetics. 14, 1996, pp. 457–

460. [10] P. Baldi and A. D. Long, “A Bayesian Framework for

the Analysis of Microarray Expression Data:

Regularized T-Test dan Statistical Inferences

of Gene Changes”, Bioinformatics, 17, 2001,

pp. 509-519.

[11] I. Lonnstedt and T. P. Speed, “Replicated Microarray

Data”, Statistica Sinica, 12, 2002, pp. 31–46.

[12] V. G. R. T. Tusher and G. C, “Significance Analysis of

Microarrays Applied to the Ionizing Radiation

Response”, In Proceedings of the National

Academy of Sciences, Vol. 98, 2002, pp. 5116–

5121.

[13] G. E. P. Box and Tiao, “Bayesian Inference in

Statistical Analysis”, MA: Addison-Wesley,

Massachusetts, 1973. [14] J. D. Duggan, M. Bittner, Y. Chen, P. Meltzer and J. M.

Trent, “Expression Profiling Using CDNA

Microarrays”, Nature Genetics, 21, 1999, pp.

10-14.

[15] N. Iriawan, “Modeling and Analysis of Data-Driven (in

Indonesia)”, Volume I. ITS Press, Surabaya,

2012.

[16] P. Sebastiani, H. Xie and M. F. Ramoni, “Bayesian

Analysis Of Comparative Microarray

Experiments By Model Averiging”,

International Society For Bayesian Analysis, 1,

number 4, 2006, pp. 707-732.

[17] A. Zellner,”An Introduction to Bayesian Inference in

Econometrics”, John Wiley, New York, 1971.

[18] J. K. Gosh, M. Delampady dan T. Samanta, “An

Introduction to Bayesian Analysis Theory and

Methods”, Springer, New York, 2006.


M21-1

Abstract— The measurement error is an error that appears when

the value of the note is not exactly the same as the true value in

relation to a measurement process, so that the true values of the

explanatory variables is represented by a value obtained through

a process of measurement that are not necessarily in accordance

with the true value. The presence of measurement error causes

biased and inconsistent parameter estimates and leads to

erroneous conclusions. The measurement error models can be

used to resolve these problems. This paper will discuss the

estimation of parameters under the assumption that the variance

of the measurement error , is known. We use data on cases

of malnutrition in the province of East Java to illustrate the

estimation of the parameters of this model.

Index Terms— measurement error models, method of least

squares, malnutrition

I. INTRODUCTION

here are two forms of linear regression models. The first

form is the classical linear regression model that assumes

variables X is considered fixed and the errors are

independent random variables distributed ). The

second form is a regression model where X is assumed to be

freely obtained from the diffuse X population distributed

and vectors ) are independent with

the vectors ) . In both models, the estimates of

β is the maximum likelihood estimator unbiased for β [1].

However, sometimes the actual data do not meet the

assumptions used in the two forms of regression. If the

explanatory variable X can’t be observed directly or can’t be

measured precisely (measured without error) then there will be

problems of measurement error. The presence of measurement

error because parameter estimators biased and inconsistent and

lead to incorrect inferences [2]. To overcome these problems

we used a measurement error models.

The difference between linear regression models with

measurement error models lies in the independent variables. In

measurement error models, independent variables are

unknown or random variables that have a particular

distribution, while the linear regression independent variables

are considered fixed or do not have a particular distribution.

I.M. Hutabarat is Lecturer at Department of Mathematics, Cenderawasih

University (Uncen), Indonesia (phone: 08114800899; e-mail:

[email protected])

A. Saefuddin is now with the Department of Statistics, Bogor Agricultural

University (IPB), Indonesia (e-mail: [email protected]).

Hardinsyah is with Department of Community Nutrition, Bogor

Agricultural University (IPB), Indonesia, (e-mail:

[email protected]).

Djuraidah is with the Department of Statistics, Bogor Agricultural

University (IPB), Indonesia (e-mail: [email protected]).

The difference between the two models are also shown in the

parameter estimation and the use of assumptions.

II. LINEAR REGRESSION MODEL WITH

MEASUREMENT ERROR

A. Model

Measurement error can be caused by various factors. In

general, measurement error divided into two types: random

error and systematic error. Random error is caused by any

factors that randomly affect measurement of the variable

across the sample. Systematic error is caused by any factors

that systematically affect measurement of the variable across

the sample [3].

In matrix notation, regression equation with measurement

error can be written:

(1)

In model (1) shows that measurement error models have a

similar form with the conventional regression model.

The assumption model of measurement error is:

(2)

where, ~ NI means "normal distribution and independent" and

is a diagonal matrix with diagonal elements given in the

matrix, as well as the assumed known.

By the least squares method assuming that the variance of the

measurement error ( ) is known, then estimation regression

coefficient is as follows:

where

B. Estimation of true X values

Based on the knowledge of the parameter about the

structural relationship and an observation (Yi,Zi), it is possible

to construct an estimator of Xi superior to Zi. In constructing

an estimator of Xi, the unknown Xi, can be treated as fixed or

random, and the two assumptions lead to different procedures.

Estimation for each of the assumptions of the Xi.

a. if Xi fixed

(3)

Estimation in Measurement Error Models on Cases of

Malnutrition in the Province of East Java

Ida Mariati Hutabarat1,2

, Asep Saefuddin2, Hardinsyah

3, Anik Djuraidah

2

T






M21-2

where is covariance matrix

and .

b. if Xi random

Treating Xi, as random and replacing parameters with

estimators, the predictor of Xi, , is

where

, and

Having obtained the true X values, then to test the effect of

the true X values to variable Y, then the hypothesis is the

same as the conventional regression model.

III. APPLICATION OF THE CASE MALNUTRITION

DATA

In this paper, the model regression applied in cases of

toddler malnutrition in the East Java Province in 2010.

Variables such that is the percentage of toddler malnutrition as

variables response (Y) and the percentage of households have

access to clean water (X1), the percentage of poor people (X2),

the percentage infants contracting from infectious diseases

(X3), the percentage of income spent monthly for food (X4),

the percentage of the posyandu (integrated service point)

(X5), the percentage of infants receiving exclusive breast-

feeding (X6). The data used in this research are secondary data

that have been collected by Statistics Indonesia (BPS) namely

the National Socio-Economic Survey (Susenas) data and

basic health research (2010) at 38 district in East Java

Province.

From the six explanatory variables, there is only one that

significantly influence to the response variables at α = 5%.

The variables that significantly influence infant malnutrition in

the province of East Java in 2010, is the percentage of the poor

(X2). So the only variable percentage of poor (X2) which I

use in the analysis to create a regression model with

measurement errors for the percentage of severely

malnourished children under five in the province of East Java

in 2010. Estimated percentage of poor population contains

measurement error arise from two sources. First, instrumental

error such as questionnaire instrument which has not

accommodate the poor people category. Second, personal

errors associated with the analysis used to determine the

household (family) poor.

If the assumed variance of the measurement error arising

from these two sources is estimated , then the

regression model with measurement error that are formed are

as follows:

The model explains that the toddler malnutrition Will

increase 0.198 percent if the variables of poor households

(X2) increased by one percent on the condition that the other

variables are constant.

The assumption of residual that normal distribution is met,

we can estimate the value the assumed fixed, namely:

TABLE I

PARAMETER ESTIMATION OF REGRESSION MODEL WITH

MEASUREMENT ERROR

Parameter estimate SE coef T p-value

0.8289

0.0404

1.06

4.91

0.297

0.000**

Based on the analysis of partial parameter and analysis of

variance shown in Table 1 using a significance level of 1%, it

can be concluded that the percentage of poor households affect

the percentage of the toddler malnutrition. The coefficient of

determination (R2) generated by 40.1%, which means that the

regression model with measurement error can explain the

variability of the percentage of the toddler malnutrition at

40.1%, while the rest (ie 59.9%) is explained by other

variables outside of the model.

TABLE II

ANALYSIS OF VARIANCE REGRESSION MODELS WITH

MEASUREMENT ERROR

Source DF SS MS F p-value

Regression 1 133.71 133.71 24.09 0.000**

Residual error 36 199.85 5.55

Total 37 333.563

Test results obtained residual normality KS value of 0.129 and

p-value 0.111. By using α by 1 percent, then reject H0

otherwise fail, which means that the residual meet the

assumptions of normal distributed.

IV. CONCLUSION

Estimation in regression models with measurement error is

.

In cases of the toddler malnutrition as the response variable Y

with covariates Percentage of Poor People (X2) obtained

REFERENCES

[1] W.A. Fuller, Measurement Error Models. New York:

John Wiley & Sons, 1987.

[2] X. Chen, H. Hong, and D. Nekipelov. Nonlinear Models

of Measurement Errors. Journal of Economic Literature

2011, 49:4, 901–937, 2011

[3] Anonim. Measurement Error. http://socialresearch

methods.net/kb/measerr.php, diunduh pada Mei 2012.


Abstract— Consider the data are pairs ( , )j jt y , where the

relationship between predictor variables jt and response

variable j

y is assumed to follow heteroscedastic nonparametric

regression models ( ) , j j j jy f t where 1,2, ,j n . The

regression curve shape f is unknown and assumed to be smooth,

and contained in the space of [0, ]C as continuous functions.

j are independent random errors with zero mean and one

variance. Regression curve f is approximated by non-trend

Fourier series 0

1

1( ) cos

2

K

k

k

f t a a kt

. Estimation of

heteroscedastic nonparametric regression curves obtained from

solving optimization Weighted Penalized Least Square (WPLS):

1 2

(0, )0

2( ( )) ( ( )) [ ( )]

f CMin n y f t W y f t f t dt

.

Solution of the above optimization WPLS is Weighted Non-

Trend Fourier Series estimator, which can be presented in the

form of ˆ ( ) ( )f t H y , for a matrix ( )H that depends on the

bandwidth parameters . The properties of the Weighted Non-

Trend Fourier Series estimator in heteroscedastic nonparametric

regression is a biased estimator for the regression curve, and it is

in the class of linear estimators under observation. Beside that if

random errors have normally distribution in the regression

model then Weighted Non-Trend Fourier Series estimator in

nonparametric regression heteroscedastic also normally

distribution.

Keywords : Heteroscedastic Nonparametric Regression, Non-Trend

Fourier Series, Parameter Bandwidth, WPLS

I. INTRODUCTION

Regression analysis can be used to estimate the pattern of

relationships between predictor variables jt and the response

variable j

y . Consider the data are pairs ( , )j jt y with the

I Nyoman Budiantara is a lecturer at Departement of Statistics, Faculty of

Mathematics & Natural Sciences Institut Teknologi Sepuluh Nopember,

Surabaya, Indonesia phone: 081553527408, e-mail:

[email protected]. .

Rahmawati Pane is a student at Departement of Statistics, Faculty of

Mathematics & Natural Sciences Institut Teknologi Sepuluh Nopember,

Surabaya, Indonesia. e-mail: [email protected].

regression model ( ) , j j j jy f t where 1,2, ,j n .

The function f is the regression curve and j

random errors

are assumed independent normally distributed with zero mean

and 2 variance. When regression curve shape in regression

analysis is known then the regression is called a parametric

regression [4], [5], whereas when the pattern of data follow

the linear/quadratic/cubic model then the regression approach

that suitable for the data are linear/quadratic/cubic parametric

regression [6].

In real life, the real shape pattern of the relationship

between predictor variables jt and the response variable

jy

is unknown. In such cases, if parametric regression model is

forced to model the pattern of data then it will give a

misleading conclusion. Nonparametric regression is a

regression approach which is appropriate for the data pattern

of the unknown form of the regression curve or for no

complete information about the past shape of the data pattern

[7], [10]. Nonparametric regression models that get much

interest are Fourier series [8], [1] and [3], Kernel [8], [11] and

[6], Spline [2], [10] and Wavelets [1]. Nonparametric

regression approach has a high flexibility, since the data is

expected to find its own shape curve estimation regression

without influenced by the subjectivity of the researcher.

Among the nonparametric regression models mentioned

above, the Fourier series is a model that has very special and

good statistical and visual interpretations [8]. Fourier series

estimator is obtained from an optimization of Penalized Least

Square (PLS) [3]. Besides that Fourier series estimator is able

to handle character data/ functions that are smooth and follow

the periodic/recurrent/seasonal pattern at specific intervals [3].

Bilodeau [3] has developed a nonparametric regression

Fourier series to handle data pattern which is seasonal and

have the up-trend or down-trend and homoscedastic. The

pattern of up-trend or down-trend is shown by adding a linear

equation term in the Forier series models. Trend Fourier series

estimator developed by [3] and [8] is generally very suitable

for data pattern which is not only seasonal but also have the

up-trend or down-trend and homoscedastic. Problems will

arise in the use of Fourier series estimator if data pattern

seasonal but does not also have the up-trend or down-trend

and heteroscedastic. Therefore, it is necessary to develop a

Fourier series estimator which does not contain elements

either up-trend or down-trend and heteroskedastic.

In this study, a non-trend Fourier series estimator is derived

to estimate the heteroscedastic nonparametric regression

curves including its problem related to the estimator derived.

Non-Trend Fourier Series Estimator in Heteroscedastic

Nonparametric Regression

I Nyoman Budiantara and Rahmawati Pane


According to [3], this non-trend Fourier series estimator is

able to solve the weaknesses of the trend Fourier series

estimator in nonparametric regression. Non-trend Fourier

series estimator proposed in this study is expected to have

several advantages including (a) able to handle data with non-

trend periodic/seasonal patterns in nonparametric regression,

(b) able to solve nonparametric regression Fourier series

problems for the heteroscedastic cases.

II. NON-TREND FOURIER SERIES ESTIMATOR IN

HETEROSCEDASTIC NONPARAMETRIC REGRESSION

Consider the data are pairs ( , )j jt y , the relationship

between predictor variables jt and the response variable

jy is

assumed to follow heteroscedastic nonparametric regression

model:

( ) , 1, 2, ... ,j j j jy f t j n (1)

Regression curve shape is unknown and assumed to be

smooth, and contained in the space of [0, ]C as continuous

functions with:

[0, ] ; of continuous functions on the interval 0,C g g

j are independent random errors with zero mean and one

variance. Heteroscedastic regression curve f is approached

by non-trend Fourier series:

0

1

1( ) cos

2

K

k

k

f t a a kt

. (2)

Estimation of heteroscedastic nonparametric regression curves

f is obtained by solving optimization of the Penalized

Weighted Least Square (WPLS):

1 2

(0, )0

2( ) ( ) [ ( )]

f CMin n y f W y f f t dt

(3)

with the weight matrix 1

2 2 2

1 2diag ( , ,..., )nW

. Vector

1 2, ,...,T

ny y y y and f have the size (nx1). is

bandwidth parameter. To solve the optimization of (3) is done

by solving Goodness of fit:

1( ) ( ) 'G G f n y f W y f

and penalty:

2

0

2( ) ( ) [ ]P P f f t dt

By substituting ( 1)10 1 22

( , , ,..., ) KK . First

solved Goodness of fit. Heteroscedastic nonparametric

regression model in equation (1) can be written in the form of: 1/2( )y B t W ,

with:

1 1

2 2

1 cos cos

1 cos cos( )

1 cos cosn n

t Kt

t KtB t

t Kt

and 1

1/2 2 2 2

1 2diag ( , ,..., )nW

.

Goodness of fit in equation (3) can be stated as:

1( ) ( ) ( )G n y B t W y B t (4)

Since 0

1

1( ) cos

2

K

k

k

f t a a kt

, then the integral:

222

0210 0

2 2 1( ) cos .

2

K

k

k

df t dt kt dt

dt

By doing a bit of elaboration, the equation can be written

as:

2

4 2

10

2( ) .

k

k

k

f t dt k

.

.

The result is obtained:

42

04

0 0 0

0 1 02( )

0 0

f t dt

K

(5)

,D

the matrix 4 4 4(0,1 ,2 ,..., )D diag K .

When Goodness of fit in (4) and Penalty in (5) are combined

then the optimization of WPLS in (3) can be expressed as:

( 1)

( ) ( )K

Min G P

1 ( ) ' ( )( !)Min n y B t W y B t DK

(6)

If a little elaboration in the optimization (6) is carried out

then use partial derivatives to solve the optimization, finally

the normal equation is obtained:

1 12 ( ) 2 ( ) ( ) 0.n B t Wy n B t WB t D

Estimator for is given by:

1

1 1ˆ ( ) ( ) ( )n B t WB t D n B t W y

.

Non-trend Fourier series estimator to estimate the

heteroscedastic nonparametric regression curve is given by the

following equation:

ˆ ˆ( ) ( )f t B t (7)

11 1( ) ( ) ( ) ( )B t n B t WB t D n B t W y


( )H y

with 1

1 1( ) ( ) ( ) ( ) ( ) .H B t n B t WB t D n B t W

III. PROPERTIES OF NON-TREND FOURIER SERIES ESTIMATOR

IN HETEROSCEDASTIC NONPARAMETRIC REGRESSION

The following presents some important basic properties of

non-trend Fourier series estimator (7). First, the nature of the

Fourier series estimator in heteroscedastic nonparametric

regression is in linear estimator class in the observations

because it can be expressed as a linear combination of

observation (response). Non-trend Fourier series estimator of

(7) in the heteroscedastic nonparametric regression estimator

is a bias estimator for the regression curve f because:

ˆ ( ) ( ) ( ) [ ]E f t E H y H E y

= ( )H f f

Another property of non-trends Fourier series estimator in

heteroscedastic nonparametric regression is if the random

error in nonparametric regression models is normally

distributed then the estimator also normally distributed.

Assume that the random error:

1

20,

n

N W

Non-trend Estimator Fourier series (7) is also normally

distributed with mean given by:

ˆ ( ) ( ) ,E f t H f

and variance-covariance matrix is given by:

ˆ ( ) ( ) ( ) ( ) ( )Var f t H Var H H WH .

The next properties of non-trends Fourier series estimator in

heteroscedastic nonparametric regression is the estimator

highly depend on the bandwidth parameters and the value

of K. The best non-trends Fourier series estimator relates to

the optimal values of and K. Generalized Cross Validation

(GCV) method can be used to obtain the optimal values of

and K.

IV. CONCLUSION

Suppose the heteroscedastic nonparametric regression

models is ( )j j j jy f t for 1, 2, ...,j n

The shape of regression curve f is unknown and assumed to

be smooth, which means contained in the space of continuous

functions [0, ]C . The random errors j are independent

with zero mean and one Variance. The regression curves ( )f t

are approached by a non-trend Fourier series. The estimation

of heteroscedastic nonparametric regression curves is obtained

by solving the WPLS optimization:

1 2

(0, )0

2( ) ( ) [ ( )]

f CMin n y f W y f f t dt

a. The result of solution of WPLS optimization is the non-

trend Fourier series estimator, which can be presented in

the form of

ˆ ( ) ( )f t H y

for a matrix ( )H that depends on the bandwidth

parameter .

b. Non-trend Fourier series estimator in heteroscedastic

nonparametric regression is biased estimator for a

regression curve but it is in the in linear estimator class in

the observations.

c. Non-trend Fourier series estimator in heteroscedastic

nonparametric regression will normally distributed if the

random error in nonparametric regression models is

normally distributed.

d. The best non-trend Fourier series estimator in

heteroscedastic nonparametric regression is highly depend

on the optimal values of and K which can be obtained

using the GCV method.

REFERENCES

[1] A. Antoniadis, J. Bigot, and T. Spatinas, ”Wavelet estimators in

Nonparametric Regression: A Comparative Simulation Study”,

Journal of Statistical Software, vol. 6,

pp.1-83, 2001

[2] H. Becher, G. Kauermann, P. Khomski, and B. Kouyate, “Using

Penalized Splines to Model Age and Season of Birth Dependent

Effects of Childhood Mortality Risk Fabtors in Rural Burkina Faso”,

Biometrical Journal,vol.51, pp. 110-122, 2009

[3] M. Bilodeau, “Fourier Smoother and Additive Models”, The Canadian

Journal of Statistics,vol. 3, pp. 257-269, 1992.

[4] I. N. Budiantara, “Spline Model with Optimal Knots”, Journal of Basic

Science, State University of Jember, vol. 7, pp. 77-85, 2006.

[5] I. N. Budiantara, Statistical Inference for Spline Model”, Journal of

Mat-Stat, vol. 7, pp. 1-14, 2007.

[6] M. Y. Cheng, R. L. Paige, S. Sun, and K, Yan, “Variance Reduction for

Kernel Estimatiors in Clustered / Longitudinal Data Analysis”, Journal

of Statistical Planning and Inference, vol.140, pp. 1389-1397, 2010.

[7] M. Kayri, and G. Zirhhoglu, “Kernel Smoothing Function and Choosing

Bandwitdh for Nonparametric Regression Methods”, Ozean Journal

of Applied Sciences, vol. 2, 49-60, 2009.

[8] A. Tripena, and I. N. Budiantara, “Fourier estimator in

Nonparametric Regression”, International Conference On Natural

Sciences and Applied Natural Scienes, Ahmad Dahlan University,

Yogyakarta, 2007.

[9] N. Wang, “Marginal Nonparametric Kernel Regession Accounting for

whitin-Subject Correlation”, Biometrika, vol. 90, pp. 43-52, 2003.

[10] S. N. Wood, “On Confidence Intervals for Generalized Additive

Models Based on Penalized Spline Regression”, Aus. N. Z. J. Stat.,

vol. 48, pp. 445-464. 2006.

[11] C. O. Wu, and C. T. Chiang, ” Kernel smoothing on varying

coeficient with Longitudinal Dependent Variable Models”, Statistica

Sinica, vol.10, pp. 433-456, 2000.


Abstract—Unlike it counterpart in parametric regression

modeling, the development of nonparametric regression for count

response are moving slowly. In this research we developed a new

nonparametric regression approach for modeling count response

using local polynomial smoothing. By assuming generalized

Poisson distribution for count response, this model should robust

for over dispersion problem that often occurred in count data

modeling. Using maximum likelihood method for finding the

estimator, we called it as local (maximum) likelihood estimator. In

this paper we construct a confidence band of the unknown

regression function, which is difficult to build in nonparametric

regression context. The construction of the confidence band needs

estimated bias and variance of local likelihood estimator that we

have been derived earlier. We conducted some simulation to show

the behavior of the estimator as well as the confidence band.

Index Terms—generalized Poisson distribution, local

polynomial smoothing, local likelihood, nonparametric regression,

confidence band

I. INTRODUCTION

n the context of parametric regression analysis, Poisson

regression is a standard and baseline model for describing the

relationship between count response with some covariates.

Following its name, count response is assumed to follow the

Poisson distribution which have restricted properties called

equi-dispersion (i.e. mean should be equal to variance). This

situation is hard to fulfill by observational data, and often the

opposite situation where the observed variance exceeds the

observed mean, called over-dispersion, is occurred. Fitting

such data using Poisson regression model will seriously under

estimated the variance and can lead to misleading conclusion in

the inference [1]. As an alternative, there are others model

such as: Negative Binomial regression model [2], Poisson Log

Normal (PLN) model and Poisson Inverse Gaussian (PIG)

model [3] and also Generalized Poisson regression model [4].

The last model is preferred because not only more general than

Poisson regression (i.e. in special case it reduces to Poisson

Regression), but it is simpler comparing to others

In many cases, the relationship between response and

covariates cannot describe by simply fitting some parametric

1 PhD student at Department of Statistics, Institut Teknologi Sepuluh,

Surabaya, Indonesia and lecturer at Sekolah Tinggi Ilmu Statistik, Jakarta

Indonesia, e-mail: [email protected] 2,3 Lecturer at Department of Statistics, Institut Teknologi Sepuluh, Surabaya,

Indonesia , e-mail: [email protected] ,

sonny_s@ statistika.its.ac.id 4Lecturer at Department of Applied Statistics, Sekolah Tinggi Ilmu Statistik,

Jakarta, Indonesia , e-mail:[email protected]

function such as linear, exponential or polynomial function. In

such case, nonparametric regression seems to be a reliable and

reasonable choice. The aim of nonparametric regression is to

minimize the assumption about regression function and let the

data seeking for the function itself [hardle]. In nonparametric

regression, scatter plot smoothing is the simplest method to

estimate regression function. There are several approaches for

determined the regression function, such as kernel, spine and

local polynomial technique. These techniques known as local

fitting methods because the estimation of regression function is

done locally around some interval of points.

Unlike it counterpart in parametric regression model, the

development of nonparametric regression for count response

with local fitting is moving slowly. There is not much research

in this area, except [5], [6]. Local likelihood is a concept

introduced by [7] and developed more intensively by [8]. This

method extends the nonparametric regression analysis to

maximum likelihood based regression model which also known

as likelihood-based smoother. In this model, the mean of

response variables are assumed depends on covariates with

some nonlinear link function. Although, there are no presumed

function for the regression curve itself.

In this research we develop a nonparametric regression model

for count response using local polynomial approach for the

estimation of regression function. The count response is

assumed to have generalized Poisson distribution.. We called

the estimator as local likelihood estimator because it is

determined by local maximum likelihood method. Based on

Taylor development of degree p and considering the

generalized Poisson regression locally, in a neighborhood of

some points of interest of the covariate, we also present the

bias, the variance and the confidence band of the regression

function. We also present some simulation result to show the

behavior of the local likelihood estimator as well as the

confidence band of the regression function.

II. LOCAL LIKELIHOOD ESTIMATOR

Let Y be the response variable, which is a count, and x is a

predictor variables. The distribution of Yi (i=1,2,…,n) at given

xi is following the generalized Poisson distribution, with the

probability density function given by:

1(1 ) (1 )

( , , ) exp , 0,1,2,1 ! 1

ii

yy

i i i ii i

i i i

y yf y y

y

(1)

With

On the Confidence Band of Local Likelihood Estimates in

Generalized Poisson Regression Model

Erni Tri Astuti1, I Nyoman Budiantara

2, Sony Sunaryo

3, Mohamad Dokhi

4

I



( | )i i i

E Y x

and 2( | ) (1 )i i i iV Y x

The parameter plays as dispersion parameter. When ,

it will reduce to Poisson probability density. When this

model is under dispersed, and when it will over disperse

relative to Poisson distribution respectively [9]. In the local

generalized Poisson regression model, instead of considering

some specified regression function, the dependence of mean

response with a covariate is describe by a smooth

nonparametric regression function s:

exp( ( ))i i

s x (2)

Assume that the function s has a continuous

derivative at the point . For data points in a

neighborhood of or , with h is a

bandwidth, we approximate via a Taylor expansion by a

polynomial of degree p:

0

0 0 0 0

( )( ) ( ) '( )( ) ( )

!

pp T

i i i i

s xs x s x s x x x x x

p x β (3)

where ,

with

0( ), 0,1, ,

!

j

j

s xj p

j (4)

For data points in a neighborhood of , the

contribution to the log likelihood function is weighted by some

kernel function . By assuming generalized

Poisson distribution for response variable , these

considerations yield the conditional local kernel weighted log-

likelihood:

, 0

1

0

ln ( 1) ln(1 ) ln( !)1 1( , , )

i in

i i i

i ip h

i

h i

y y y yL x

K x x

β (5)

where and is a Kernel

weight. The choice of the kernel function is not a crucial

issues, because the result is almost similar for any kind of

kernel function including Epachnecnikov, Gaussian or Boxcar

Kernels [10]. The estimator for regression function, is the

solution of (p+2) equation :

0 021

( )0 , 0,1, ,

(1 ( ))

nvi i

h i i

ij i

y xLK x x x x j p

x

(6)

021

( ) ( )( ) ( 1)

1 ( ) 1 (1 ( ))

ni i ii i i i

h i

i i i i

x y xy x y yLK x x

x y x

(7)

The solution of the system which is called local (maximum)

likelihood estimator can be solved by iterative procedure such

as Newton Raphson Methods. The log-likelihood function

above depends on two quantities, the smoothing parameter (h)

and the order of polynomial (p). The model complexity is

effectively controlled by the bandwidth h. As h increases from

0 to +∞, the model runs from the most complex model

(interpolation) to the simplest model and [10] stated that a too

large bandwidth under parameterizes the regression function

causing a large modeling bias, while too small bandwidth over

parameterizes the unknown function and result in noisy

estimates. Ideal or optimal model is lying between the two

models, which can be obtained by different criteria’s, one such

criteria is cross validation (CV) [11].

Bias and Variance of the Estimator

The estimator β is biased because there is an approximation

error in Taylor expansion (3). By considering a further

expansion with (p+a) degree for approximate s(x), the

estimated bias for local likelihood estimator is given as in [12]

'' * 1 ' *

, 0 , 0ˆ ˆ ˆˆ ( ) ( , ) ( , )p p h p hx x b β L β L β (8)

where ' *

, 0( , )p h xL β and '' *

, 0( , )p h xL β are the gradient vector and

Hessian matrix of the local likelihood given by

* *

* **

, 0

1

0

ln ( 1) ln(1 ) ln( !)1 1( , , )

i in

i i i

i ip h

i

h i

y y y yL x

K x x

β (9)

with * exp( )T

i i ir x β

and

1 2

1 0 2 0 0( ) ( ) ( )p p p a

i p i p i p a ir x x x x x x

(10)

For example, if we set p=1 and a=2, then (8) can be expressed

1*

*

1 0* 31

*

0* 21

ˆˆˆ ˆ ˆ ˆ( ) (1 2 )ˆ ˆ(1 )

ˆ

ˆ ˆ(1 )

nTi

i i h i i i

i i

ni i

h i i

i i

y K x x

yK x x

b β x x

x

(11)

where 0 1ˆ ˆ ˆ, , , p and is the solution of (6),(7) and

ir is

the solution of (9).

On the other hands the estimated variance of the estimator can

be computed by

1 1

' '' ''

0 , 0 , 0ˆ ˆ ˆˆ ( ( ), ) ( , ) ( , )p i p h p hV s x y x x

nV β L β S L β (12)

where ''

, 0( , )p h xL β is the Hessian matrix of (5) and

2

0

1

nT

h i i i

i

K x x

nS x x

And for p=1 and a=2, the estimated variance is

1 1

'' ''0

1 1, 0 1, 0

0

ˆexp( )ˆ ˆ ˆˆ ( , ) ( , )ˆˆ1 exp( )

h hx x

nV β L β S L β (13)

with ''

1, 0ˆ( , )h xL β is Hessian matrix evaluated at β .

Confidence Band of Regression Function

The confidence interval is an important tool for evaluating he

estimator precision. But in nonparametric regression context,

constructing such confidence interval is difficult because of

non-negligible bias. However with our estimated bias and

variance defined previously, we can construct a confidence

interval or confidence band for regression function. Because

the estimated bias and variance involves of higher order

derivative curve, whose estimation can be unstable, they need

to be averaged to prevent from abrupt change [8]. So define

0

1

ˆ ˆˆ ˆ( ) ( ) ( )p

nA

j p j i i

i

b b K x x

(14)


0

1

ˆ ˆˆ ˆ( ) ( ) ( )p

nA

j p j i i

i

V V K x x

(15)

with

0

0

0

1

( )( )

( )

h i

i i n

h i

i

K x xK x x

K x x

Under some regularity condition [13], the asymptotic

distribution of the local likelihood estimator ˆj at a point x=x0

ˆˆ ˆ( )

(0,1)ˆˆ ( )

A

j j p j D

A

p j

bN

V

(16)

So by invoking asymptotic normality the point wise confidence

interval with (1 ) coverage probability j falls in random

interval

1 /2

ˆˆ ˆ ˆˆ( ) ( )A A

j p j p jb z V (17)

From (4) we have 0( ) !, 0,1, ,j

js x j j p , so equivalently

the confidence band for the regression function

0 1 /2

ˆ ˆˆ ˆ ˆ( ) ( ) ( )j A j A j

p ps x b s z V s (18)

However according to [8], the coverage probability of (17)

or (18) can converge slowly to the nominal level (1 ) . There

are two reason for this. One is that the number of data point

used to estimate the regression function at a particular point

can be much smaller than n and the other is that the bias can

possibly be non-negligible. It will show in our simulation next.

III. SIMULATION RESULT

We conducted some simulation with some purposes. First is

to show the behaviour of the local likelihood estimator as the

bandwidth parameter h and polynomial degree p are increased.

Second the behaviour of confidence band of regression

function before and after averaging process. And finnaly to

show the coverage probability of the confidence band at

nominal level 0.95. For that, we use sample of size n=100, 200

and 500. We generate x from Uniform distribution on [-1,1].

And from each xi we generate the count response from

generalized Poisson distribution with 3 different regression

function

We also use Epanechnikov kernel for weight and the dispersion

parameter is set to 0.2. Fig.(1) shows the behavior of the

estimator when we increased the bandwidth parameter from

h=0.005 to h=0.5 for regression function s1(x).

Fig 1. Estimated regression function (black) with h=0.005, h=0.1, h=0.2 and

h=0.5 and the true regression function (red)

As we can see the estimated curve runs from the complex

model (interpolation) to more simplest model. The ideal

bandwidth or ideal model can be select by considering the

value of CV which is minimum. The influence of the

polynomial degree p can be seen in Fig. 2 as we use s3(x) for

true regression function.

Fig 2. Estimated regression function with p=0 (red), p=1 (green), p=2 (blue)

and the true regression function (black)

As we can see that the higher the degree of polynomial (p=2)

then the estimator can reaches peak or valleys of the data

better than p=0 or p=1, and can approximate the true

regression function nicely.

-1.0 -0.5 0.0 0.5 1.0

0

5

10

15

0.005

X

Y

-1.0 -0.5 0.0 0.5 1.0

0

5

10

15

0.1

X

Y

-1.0 -0.5 0.0 0.5 1.0

0

5

10

15

0.2

X

Y

-1.0 -0.5 0.0 0.5 1.0

0

5

10

15

0.5

X

Y

-2 -1 0 1 2

0

5

10

15

20

x

y


Fig. 3 The local likelihood estimator (black), 95% confidence band of true

regression function (red) and the true regression function (blue)

Figure 3 is an example of 95% confidence band for true

regression function with coverage probability 0.91. This

coverage probability means that 91% of points in true

regression function are included in the confidence band. The

behavior of this coverage probability is that the estimator can

reach

IV. CONCLUSION

A new approach of nonparametric regression for count

response has been developed using local polynomial technique.

We also derived estimated bias and variance of the estimator

and constructing a confidence band for the unknown regression

function. Simulation result shows that the performance of the

estimator depends on the choice of bandwidth parameter h and

polynomial degrees p. The confidence band of the regression

function shows coverage probability near the nominal level

0.95 as expected

REFERENCES

[1] E.T. Astuti and T. Yanagawa , “Testing Trend for Count Data with

Extra-Poisson Variability”, Biometrics,58, 2002, pp. 398-402.

[2] A. Ferrari, G. Letac and J.Y. Tourneret, J.Y, (2007), “Exponential

families of mixed Poisson distributions”, Journal of Multivariate

Analysis, 98, 2007, pp. 1283 – 1292

[3] J.P. Boucher, M.Denuit and M. Guillen, M., “Risk Classification For

Claim Counts: A Comparative Analysis of Various Zero-Inflated Mixed

Poisson and Hurdle Models”, North American Actuarial Journal, 11:4,

2007, 110-131

[4] F.Famoye, “Restricted Generalized Poisson Regression”, Communication

in Statistics-Theory and Methods, 33, 2002, pp.1135-1154.

[5] J.A. Santos and M.M. Neves,” A Local Maximum Likelihood Estimator

for Poisson Regression”, Metrika, 68,2008, pp. 257-270.

[6] Y.Terzi and M.A. Cengiz,M.A.,” Using of Generalized Additive Model

for Model Selection in Multiple Poisson Regression for Air Pollution

Data”, Scientific Research and Essay, 4:9, 2009, pp. 867-871.

[7] R. Tibshirani and T. Hastie,” Local Likelihood Estimation”, Journal of

the American Statistical Association, 82:398,1987, pp. 559-567.

[8] J. Fan, M. Farmen and I. Gijbels, I, “Local Maximum Likelihood

estimation and Inference”, Journal of the Royal Statistical Society

Series B (Statistical Methodology), 60:3, 1998, pp. 591-608 .

[9] P. C. Consul and G. C. Jain, “ A Generalization of the Poisson

Distribution”, Technometrics, 15:4, 1973, pp. 791-799.

[10] J. Fan and I. Gijbels, Local Polynomial Modeling and Its Application,.

Chapman and Hall. London, 1997.

[11] L. Gyorfi, M. Kohler, A. Krzyzak and H.Walk, A Distribution-Free

Theory of Nonparametric Regression , Springer, New York, 2002.

[12] E.T. Astuti, I.N. Budiantara, S. Sunaryo and M. Dokhi, “Bias dan

Varians dari Estimator Linier Lokal pada Model Regresi Poisson

Tergeneralisir”, presented at Seminar Nasional Pascasarjana XII- ITS,

Surabaya, July 12, 2012.

[13] J. Fan, N.E. Heckman and M.P. Wand, M.P.,” Local Polynomial Kernel

Regression for Generalized Linear Models and Quasi-Likelihood

Functions”, Journal of the American Statistical Association, 90:429,

1995, pp. 141-150.

-2 -1 0 1 2

0

5

10

15

20

0.5

x

y

The Third Basic Science International Conference – 2013 M24-1

1Abstract—Hourly rainfall data has a high variation in time

and has many zero values. The data has a skewed distribution,

which made the modeling and prediction of rainfall becomes more

complicated. In general, these data has non-linear relation in time,

therefore Bayesian neural network (BNN) with adjusting

procedures would be proposed to in this paper. This model will be

compared with natural BNN and standard neural network (NN),

i.e., feed forward neural network (FFNN). The criteria used for

comparison is mean square error (MSE). These methods were

applied for analyzing rainfall data in Jatisrono station, central

Java, Indonesia. The result shows that BNN with adjusting

procedure outperforms the natural BNN and FFNN.

Index Terms— Adjusting procedure, Bayesian neural network,

feed forward neural network, hourly rainfall.

I. INTRODUCTION

ourly rainfall data has a high variation in time and skewed

distribution, which makes the modeling and prediction of

rainfall becomes complicated. In general, the data has non-

linear relation in time. To model this relationship, one of the

time series methods frequently used is neural network (NN).

NN is a method of modeling the nonlinear relationship that is

based on the processing of human neurological system. Several

studies have applied NN in hydrology, including rainfall [1]-

[6].

In the case of forecasting hourly rainfall, it is commonly we

observe over-fitting. To overcome this, the Bayesian approach

is proposed for estimating the NN model parameters [7].

Bayesian Neural Network (BNN) method was first introduced

by [8], [9] and [10] they use a Bayesian approach with network

Back propagation (BP). In the case of time series, BNN

method has been applied, such as is used in the data of Wolfer

sunspot numbers and Canadian lynx [11], import export

economy data [12], the annual rainfall data [13] and modeling

Manuscript received April 7, 2013. This work was supported by the LPPM

and Statistics Department of Institut Teknologi Sepuluh Nopember, Surabaya,

Indonesia.

K. Fithriasari is PhD Student of the Statistics Department, Institut

Teknologi Sepuluh Nopember (ITS), Surabaya, Indonesia (e-mail:

[email protected])

N. Iriawan is with the Statistics Department, Institut Teknologi Sepuluh

Nopember (ITS), Surabaya, Indonesia(e-mail: [email protected])

B. S. S. Ulama is with the Statistics Department, Institut Teknologi

Sepuluh Nopember (ITS), Surabaya, Indonesia(e-mail: [email protected])

Sutikno was with the Statistics Department, Institut Teknologi Sepuluh


H. Kuswanto is with the Statistics Department, Institut Teknologi Sepuluh


of rainfall and stream flow input (stream) [14].

Many efforts were made by researchers to improve the

model for obtaining the smaller error. One of them is using

adjusting procedures in modeling time series [15], [16]. Based

on the study, BNN with adjusting procedure is proposed to

model and predict the hourly rainfall at Jatisrono station,

Central Java, Indonesia. The results will be compared with the

classical NN e.g. Feed Forward Neural Network (FFNN) and

BNN models without adjustment (natural BNN). Statistical

criteria used for comparison is the Mean Square Error (MSE).

II. FEED FORWARD NEURAL NETWORK (FFNN)

Rainfall at the specified location is affected by the past data

and rainfall in surrounding locations. Suppose that tx is the

rainfall data at tth

time and k t lx

is the past l lags value on

thk locations, then the corresponding FFNN architecture for

modeling hourly rainfall can be shown in Fig 1.

1

2

1

j

J

X1(t-1)

X1(t-2)

X1(t-d)

W11

V1

X1(t)

Input Layer

Hidden Layer

Output Layer

b1J

1

X2(t-1)

X2(t-d)

I

Xk(t-l)

XK(t-d)

1

b2

b11

b1j

Vj

VJ

WIJ

Fig. 1. FFNN architecture for rainfall model

FFNN model according to Fig 1. can be presented as follows

2 1 * 11 1 1

J K d

j jt k t l d k l jj k l

x g b v f b x w

, (1)

where tx is predicted variable (output variable), ijw is matrix

from input to hidden layer, 1 jb is bias for hidden layer, jv is

weight from hidden to output layer, 2b is bias for output

Prediction of Hourly Rainfall using Bayesian Neural

Network with Adjusting Procedure

Kartika Fithriasari, Nur Iriawan, Brodjol S. S. Ulama, Sutikno, and Heri Kuswanto.

H



mailto:%[email protected]

mailto:%[email protected]




layer, .f is nonlinear activation function for hidden layer,

.g is linear activation function for output layer, d is number

of time-lag , J is number of hidden nodes and K is number of

location.

III. BAYESIAN NEURAL NETWORK

Bayesian learning is one of the methods for estimating the

model parameters based on prior and posterior distribution.

NN model estimated by this learning is called Bayesian Neural

Network model. Before doing Bayesian learning for the model

in Eq.1., the prior of the parameters ( ijw and jv ) were

determined. These prior are proposed to follow the normal

distribution [17] which can be written as follows

2

2

,

,

ij w w

ij v v

w Normal

v Normal

where w , 2w , v and 2

v are hyperparameters with the

following distribution 6(0,10 )w Normal , 2 (0.001,0.001)w Invers Gamma ,

6(0,10 )v Normal and 2 (0.001,0.001)v Invers Gamma .

If tx is rainfall in certain time and location, then

tx Eksponensial and its likelihood is represented as

1

1

1

,..., | , | ,

exp

n

ij j ij jn t

t

nn

tt

L x x w v f x w v

x

(2)

In the Bayesian approach, predictions are made by integrating

over the posterior distribution. This posterior can be obtained

by multiplying the likelihood function with the prior

distribution of parameters. BNN has very complex posterior

distribution so the integrations are approximated by Markov

Chain Monte Carlo (MCMC) methods [18]. In MCMC, the

complex ting in of marginalization integrals is approximated via

drawing samples from the joint probability distribution of all

the models parameters and hyperparameters [19]. MCMC

method used in this paper is the Gibbs sampler is implemented

as in WinBUGS.

IV. ADJUSTING PROCEDURE

Adjusting procedure is a modification method of time series

data at the lower level (hourly) generated by the stochastic

model. This procedure was done so that the data are consistent

with a given higher level data (daily). Assume z is known

daily rainfall and sx is generated hourly rainfall data at time s ,

the adjusting procedure is procedure of modifying sx to obtain

adjusted values sx . Define this procedure can be found in [15]

1

/ 1,..., ,H

s s h

h

X X Z X s H

(3)

where H is the number of lower level variable within one

period higher level.

V. RESULT AND DISCUSSION

BNN model will be applied to model the rainfall data

at Jatisrono station, Central Java, Indonesia, captured during

January 2010 to January 2011. The rainfall data has different

monthly characteristics, therefore the modeling for each month

is performed separately. The modeling is done for January

period. Jatisrono rainfall affected by rainfall intensity in

preceding period and rainfall in surrounding locations e.g.

Pabelan. Assume that ty is rainfall values in jatisrono at

time t , hence

tty Eksponential

and 1t t

y .

where ty can be calculated using Eq. 1. Time-lag tried for

modeling is one and 24 time lags [16]. The number of nodes in

the hidden layer is set at two nodes, so 1; 24l , 2K

and 2J . Therefore, the input variable vector is defined as

follows

'

1 1 2 1 1 24 2 24, , ,

t t t tx x x x

x , (4)

where 1 1tx

, 1 24t

x

, 2 1tx

and 2 24t

x

are respectively the

rainfall in one and 24 time lags on Jatisrono and Pabelan.

In this paper to estimate the model parameters used

MCMC performed using WinBUGS. WinBUGS doodle

structure appropriate for modeling of hourly rainfall in

Jatisrono, can be seen in Fig. 2.

Fig. 2. Doodle structure for hourly rainfall model

Posterior mean and median values of the BNN parameters can

be seen in Table 1.


Table 1. Mean posterior distribution of parameters

Node Mean 2.50% median 97.50%

v[1] -2.149 -2.357 -2.147 -1.941

[2] -1.427 -1.628 -1.424 -1.237

w[1,1] -1568 -2671 -1503 -1004

w[1,2] -1185 -2065 -1150 -519.6

w[2,1] -1822 -3077 -1751 -1193

w[2,2] 325.6 130.8 314.6 598.9

w[3,1] -994.1 -1657 -954 -648.6

w[3,2] 56.56 16.77 52.39 119.8

w[4,1] -2.599 -32.84 -5.457 34.11

w[4,2] 1765 812.3 1739 2933

b2[1] -3.197 -3.388 -3.199 -2.992

b1[1] 24.46 16.09 23.43 41.25

b1[2] 0.4686 -0.02227 0.4544 1.06

The prediction of hourly rainfall by BNN was adjusted using

Eq. 3. Comparison of MSE for the three models namely

FFNN, natural BNN and BNN with adjusting procedures can

be seen in Table 2.

Table 2. MSE value

MODEL MSE

FFNN 2.52

NATURAL BNN 2.50

BNN WITH PROSEDUR ADJUSTING 2.16

From table 2. It appears that the BNN with adjusting

procedure has the smallest MSE. Therefore, we propose to

model hourly rainfall in Jatisrono using BNN method with

adjusting procedures.

VI. CONCLUSION

In This paper, BNN with adjusting procedure has been

applied to model and forecast hourly rainfall at Jatisrono

stations in Central Java, Indonesia. The model is compared by

FFNN and natural BNN. The results show that BNN with

adjusting procedure has the smallest MSE. It shows that the

BNN with adjusting procedure is better than FFNN and natural

BNN.

ACKNOWLEDGMENT

This article is a part of Laboratory’s research grant and

doctoral research at Statistics Department of Institut

Teknologi Sepuluh Nopember (ITS), Surabaya, Indonesian,

granted by LPPM Institut Teknologi Sepuluh Nopember

(ITS). We thank Head of Balai Besar Sungai Bengawan Solo

for providing the hourly and daily rainfall data.

REFERENCES

[1] M. French, W. Krajewski, and R. Cuykendall, “Rainfall

forecasting in space and time using a neural network,”

Journal of Hydrology, 137, 1-31, 1992.

[2] K. Luk, J. Ball, and A. Sharma, “An application of

artificial neural networks for rainfall forecasting,”

Mathematical and Computer Modelling, 33, 683-693,

2001.

[3] G. Lin, and L. Chen, “Application of an artificial neural

network to typhoon rainfall forecasting,” Hydrol.

Process., 19, 1825–1837, 2005.

[4] M. C. Ramírez, H. F. Velho, and N. J. Ferreira,

“Artificial neural network technique for rainfall

forecasting applied to the São Paulo region,” Journal of

Hydrology, 301, 146–162, 2005.

[5] N. Q. Hung, M. S. Babel, S. Weesakul, and N. K.

Tripathi, “An artificial neural network model for rainfall

forecasting in Bangkok, Thailand,” Hydrol. Earth Syst.

Sci., 13, 1413–1425, 2009.

[6] T. Santhanam, and A. Subhajini, “An efficient weather

forecasting system using radial basis function neural

network,” Journal of Computer Science, 7 (7), 962-

966, 2011.

[7] C. Doan, and S. Liong, “Generalization for multilayer

neural network Bayesian regularization or early

stopping,” APHW 2004: The 2nd APHW Conference,

2004.

[8] D. J. MacKay, “A Practical Bayesian Framework for

Backpropagation Networks,” Neural Computation, 4

(3), 448-472, 1992.

[9] D. J. MacKay, “Bayesian Methods for Adaptive

Models,” Ph.D dissertation, Calif. Inst. of Technology,

Pasadena CA. 1991.

[10] W. L. Buntine, and A. S. Weigend, “Bayesian Back-

propagation,” Complex System, 5(6):603-643, 1991.

[11] F. Liang, “Bayesian neural networks for nonlinear time

series forecasting,” Statistics and Computing, 15, 13–

29, 2005.

[12] W. Jiang, L. Zhang, and P. Wang, “Nonlinear time

series forecasting of time dalay neural network

embedded with Bayesian regularization,” Applied

Mathematics and Computation, 205, 123-132, 2008.

[13] X. Pan, and J. Wu, “Bayesian neural network ensemble

model based on partial least squares regression and its

application in rainfall forecasting,” International Joint

Conference on Computational Sciences and

Optimization, 49-52, 2009.

[14] C. Jiang, “The application of Bayesian neural network

in rainfall forecasting,” Key Engineering Materials, 439

- 440, 1300-1305, 2010.

[15] D. Koutsoyiannis, and C. Onof, “Rainfall disaggregation

using adjusting procedures on a Poisson cluster model,”

Journal of Hydrology, 246, 109-122, 2001.

[16] E. Hidayah, “Implementing of temporal rainfall

disaggregation model using bayesian PAR1 model

combined with adjusting and filtering procedure in

sampean catchments area,” Journal of Applied Sciences

Research , 8 (1), 314-320, 2012.


[17] M. P. Wiper, A. P. Palacios, and J. M. Marin, “Bayesian

software reliability prediction using software metrics

information,” Quality Technology and Quantitative

Management (inpress) , 9 (1), 35-44, 2012.

[18] R. M. Neal, Lecture Notes in Statistics: Bayesian

Learning for Neural Network. New York: Springer-

Verlag, 1996.

[19] J. Lampinen, and A. Vehtari, “Bayesian Approach for

Neural Network - Review and Case Studies,” Neural

Network , 14 (3), 7-24. 2001.


Abstract— Traditional multivariate statistical process

control (SPC) techniques are based on the assumption on

the successive vector which are independent. In

multivariate process system with presence of serial

correlation, Vector Auto-regressive models (VAR) that

should be used to approximate the system, estimate and

monitor the VAR residuals as a serially independent

multivariate series. VAR models are important class for

analyzing multivariate time series data. In this study, we

considers the problem of monitoring the mean vector of a

process in which observation can be modeled as a first-

order vector autoregressive VAR(1) process and study how

to generalized to VAR(p) process base on residuals. Due to

the effect of shift in mean process on VAR residual chart

by Pan and Jarrett (2007), we investigate the performance

using data from an industrial process to determine the

control limit of monitoring system for multivariate time

series data.

Key words: Vector Auto-regressive models (VAR), VAR(p)

residuals, control limit.

I. INTRODUCTION

N univariate autoregressive model, disturbances are a set of

effects of various factors. This factors have serial

correlations that come from variables process in which

contribute variation in system. Some of them are

unmeasurable, while others variables probably either

measurable or conversely even if modelled in univariate

simple model. In this situation, some of disturbance

components should be potential for autocorrelating processes

in the vector of autoregressive component. On the other hand,

in VAR model, ones a component would be predict, it is

usually refer to order determination for ensure a consistency

criteria of model. Generally, in the theory of time series, order 1p should be determined by simulation empirically, while the

1Post Graduate Student at Department of Statistics Institut Teknologi Sepuluh Nopember, Surabaya, Indonesia

e-mail: [email protected] 2Department of Statistics

Institut Teknologi Sepuluh Nopember, Surabaya, Indonesia e-mail: [email protected] and

[email protected] 3Department of Informatics Engineering

Institut Teknologi Sepuluh Nopember, Surabaya, Indonesia e-mail: [email protected]

2approximation of the MSE matrix will always increased by

the increasing value of p. This means that selection of the

order-p will always correspondences with forecasts precision,

including the precision of the impulse response that depends

on the precision parameter estimation only. In this case, it

require an optimum procedures or criteria to optimize the

VAR model.

Due to general aspect on order determination in time series

theory, it should be determine by a simulation empirically,

while the approximation of mean square matrix always

increase with increasing of p value. This means that order p

selections have an effect to forecast precision, include a

impulse response precision that depend on forecast precision

of parameter estimate only. Some of potential autocorrelated

component can be remove out of the disturbance to AR

component [2]. Moreover, it still require a procedure or

optimum criteria for VAR model, include dealing with moving

average (MA) component structure.

The advantage of VAR(p) models approach is referring to

dynamic process that make it meaningfull because more

reasonable to the real processes. A real example can be seen in

VAR(p) models that, all of systematic variables will be

accommodated in this model, and just white noise and error

measurement as a part of disturbance. Other advantage of

residual VAR model is it can be estimated with OLS

procedure instead of the more complex MLE procedure [3,4].

In many application, investigation to the response impulse can

be extend to high-dimensional system to find out response

within variables. This analysis be required when there is

reaction of one variable to impulse of other variable can be

identified causally.

Moreover, the circumstance of assumption about

autocorrelation structure in a process still remain other easy

circumstance for resolve either through on data generating

process as well as on multivariate normal generating based on

uncorrelated residuals. Properties of stasionerity or time

invariant on data generating using VAR(p) models are

important requirement that can be used in determining

estimator behavior and forecast calculation, as well as in

interval forecasting. The properties mention above, also using

to ensure mean, variance, and auto-covariance invariant over

time. Some cases in economic field shows that models

construction based on data generating, sometime have not

guaranteed and satisfied the stationarity assumption. Main

axamination of test can be dealt to model stability checking, ,

according to fact that stability hence stationarity [2].

Following to non random effect on multivariate time series,

shift of structure parameter as impact of accumulation effect

Vector Auto-Regressive Control Chart and Its

Application in Industry

1J. K. Wororomi,

2M. Mashuri,

2Irhamah and

3A. Z. Arifin

I

https://webmail.statistika.its.ac.id/src/compose.php?send_to=jkw2009%40mhs.statistika.its.ac.id

https://webmail.statistika.its.ac.id/src/compose.php?send_to=m_mashuri%40statistika.its.ac.id



on shock occurrence in variables. Commonly, those effect

accumulation can be determined via coefficient matrices of

MA representation by using numeric approximation due to

structural change as an impact of shift processes. In [3,4], this

approximation by using control chart constructing due to

controlling of structure changes on mean shift, disperse shift,

and coefficient matrices shift.

However, this paper proposed to assert interaction between

variables in VAR models related to covariance matrix

estimation and order p on particular period by the function of

impulse response empirically. In case study of Woodmod data,

we investigate the innovations matrices of various models in

simulation to conduct control limits on phase I controlling

using multiple Woodmod data.

II. VECTOR AUTOREGRESSIVE MODEL

A. Review Stable Model

The order p of VAR Model or VAR(p) can be expressed by

(1)

with random vector of , denoted

to coefficient matrices , as vector

intercept of . While denoted as

white noise or innovation process of K-dimensional with

and for . In

stable condition, covariance matrix can be assumed non-

singular.

Investigation to consistencies of the VAR(p) models on (1),

can be initiated from VAR(1) model

(2)

Distribution of should be determined uniquely by

distribution of process. If eigenvalue of matrix have

modulus value less than 1, then VAR(1) process is called as

stable process. This condition equivalent to

. Moreover, VAR(p)

model can be extended to p>1 or more precisely, is a

VAR(p) process as well in (2), that is correspond to Kp-

dimensional of VAR(1)

(3)

can be defined, with

, ,

with mean vector and

as the auto-covariance.

, and matrix with size

.

The process is obtained as or mean and covariance

can be expressed as which constant for all t and

the auto-covariance are also time invariant.

Formally is stable process

(4)

In the other words, process in (1) is stable if satisfied (4)

and

(5)

with denoted as lag of i-th matrix on MA

representation as

(6)

On the other hand, linkages of the VAR models which

constructed via MA representation on [2] as and

, for because and are

absolute summable which involves the white noise process

and so process determined by white noise or innovation

process. We also convey that, for given assumption has been

addressed to the process give direct impact to process.

The model build-up here is consider to (9) and multivariate

innovation algorithm can be refer to [1].

B. Impulse Response Function

The Analysis of impulse response function in multivariate

time series is often of interest to know the response or

interaction within variables on the system.

In applied work, it is often of interest to pay attention on the

accumulated effect on the period of shock occurance in one

variable. This effect can be determined by summation of MA

coefficient matrix. Suppose the k-th column of

which contain response accumulation on n-period to the shock

unit within k-th variable in the system. This quantity are

recognizing as n-th interim multipliers (i.e impulse response).

The total of accumulation effect for all future period will be

obtained by taking summation of all MA coefficient matrix.

The MA Operator is an inverse form of the VAR

operator that can be expressed by

as a term of long-run effect that

can be obtained from

(7)

Determination of the response impulse function via MA

representation as in (4) can be rewritten in form

(8)

with as matrix with size of and

as white noise process with covarian matrix equal

to identity matrix, . The response impulse function is

(9)

with , the elements of here can be interpreted as

response in the system to innovation . For given index of j,k

on the elements of can be interpreted as the effect

occurrence in j-th variables of innovation unit on k-th

variables which have been occurred on the previous i-th

period.


C. Variance Error Variance Decomposition

The next investigation are how to accomplish the innovation

to the system recognizing, in particular to VAR model

interpretation. Suppose that identification scheme in MA term

which has build recursively with orthogonal innovation white

noise. In optimal forecast error context, h-th step will be

written as

(10)

Let mn-th elements of denoted as so that, h-th step

forecast error of j-th component on process is

(14)

since are uncorrelated and have an unit variance, the

mean square error of or

.

with the result that

(11)

with k-th columns of .

Equation (11) usually will be interpreted as innovative

contribution on k-variable of variance forecast error. This

analogy to MSE of h-step forecast j-variable that has been

presented on [2] as

(12)

with

III. RESULT AND DISCUSSION

As a case study, we consider a multi-dimensional system

consisting first and second differences to adjust the woodmod

dataset. Let shows five variables

which described as first and second differences on the figure.1

are respect to number of fibers per square milliliter in

Springwood (FSp), number of fibers per square milliliter in

Summerwood (FSm), fraction of Springwood (fSp), fraction

of light absorption by Springwood (fSp1), and fraction of light

absorption by Summerwood (fSm1).

The example as mention above is a part of real-life

production process and we wish to show the effectiveness of

using VAR residual chart to detect special causes in multiple

and or/ multivariate time series. The raw data are found having

serial correlation in five variables.

In the stage of data pre-processing, the transformation by

first and second differences has shown stationarity on data

Woodmood raw data as depict on figure 1.

Due to generation of VAR residuals chart procedure for

obtain an approriate innovation matrix from Woodmod data,

we estimated the VAR parameters using OLS method, and

choose a VAR(1) for second differences as to appropriate

VAR model process with innovation matrix has been positive

semi definite.

VAR Modelling

Generating data process based on second differences

VAR(1) for p=5,T=1000, and K=5 depict on figure 2, it shows

that VAR (5) process is also stationary with positive definite

of the covariance matrix. We have extend the simulation to

some input parameters (i.e for p=1,2,3,4; T=30,50,100,500) in

this simulation to justify asymptotically behavior of VAR

residual before applied VAR control chart in phase I.

0 500 1000-5

0

5

10Y,1

0 500 1000-5

0

5

10Y,2

0 500 1000-5

0

5

10

15Y,3

0 500 1000-5

0

5

10

15Y,4

0 500 1000-5

0

5

10Y,5

Figure 2. VAR(p) generating process

VAR(1) residual control chart

The true process is unknown, but we can investigate the

consistency of the VAR(1) models based on second

differences in MA term. Particular investigation of the VAR

residual model can be interpreted on MA term or impulse

response as shows in figure 5. in Appendix.

0 2 4 6 8 10 12 14 16 18 20-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

Monthly Production

Nu

mb

er

of fib

ers

pe

r sq

ua

re m

illilite

r &

its

fra

ctio

n

FSp

FSm

fSp

fSp1

fSm1

(a). Woodmod raw data after first difference

0 2 4 6 8 10 12 14 16 18-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Monthly Production

Nu

mb

er

of fib

er

pe

r sq

ua

re m

illite

r &

its

fra

ctio

n

FSp

FSm

fSp

fSp1

fSm1

(b). Woodmod raw data after

second difference

Figure 1. Raw data transformation


When we set VAR(1) residual models as appropriate in this

model, then we presetting UCL at type I error of 0.0027 and

0.005 on VAR residual chart. We found signals at the almost

on all point, except in 3th ,4

th,6

th,7

th,and 15

th. Conversely, when

we change type I error to 0.005, limit of UCL increase and

reduce the signals of limit control.

IV. CONCLUSION AND SUGGESTION

In this study, we considers the problem of monitoring the

process in which observation can be modeled as a first-order

vector autoregressive VAR(1) process and study how to

generalized to VAR(p) process base on residuals. Due to the

effect of shift in mean process on VAR residual chart by Pan

and Jarrett (2007), we investigate the performance using data

from an industrial process depend on structure of the time

series.

T2 chart using Chi-Square distribution with α=0.0027 give

more unrealistic when designed on Woodmod data or time

series data that come from small sample. In our design of

VAR residual control chart, it shown some fault detection on

all variables. To overcome these problem (result), we can use

other residual model by interpreted on MA term or impulse

function simultaneously (causality analysis) to investigate best

innovation matrix that provide parsimonious model.

APPENDIX

Model estimating using OLS has been obtained innovation

matrix and its coefficient matrix from VAR residual, and by

the Cholesky decomposition, we investigate the impulse

response and FEVD of VAR model with various input

parameters (i.e for p=1,2,3,4; T=30,50,100,500, and 1000).

As an example we give causality analysis to depict the

impulse response In fig.5 for p=5,T=100, and K=5.

REFERENCES

[1] Brockwell P.J., and Davis R.A., (1991), Time Series: Theory and

Methods, second edition, Springer-Verlag, New York,Inc.;

[2] Lütkepohl H., (2005), New Introduction to Multiple Time Series

Analysis, Springer_verlag Berlin Heidelberg;

[3] Pan,X. (2005), Notes on shift effects for T2-type charts on multivariate

ARMA residuals, Computers and Industrial Engineering 49 (2005) 381-

392

[4] Pan X. and Jarrett J., (2007), Using vector autoregresive residual to

monitor multivariat processes in presence of serial correlation, Int. J.

Production Economics 106 (2007) 204-216;

[5] J. Jones. (1991, May 10). Networks (2nd ed.) [Online]. Available:

http://www.atm.com

[6] (Journal Online Sources style) K. Author. (year, month). Title. Journal

[Type of medium]. Volume(issue), paging if given.

Available: http://www.(URL)

[7] R. J. Vidmar. (1992, August). On the use of atmospheric plasmas as

electromagnetic reflectors. IEEE Trans. Plasma Sci. [Online]. 21(3). pp.

876–880. Available: http://www.halcyon.com/pub/journals/21ps03-

vidmar

2 4-1

0

1

2

Y1 to U

1

2 4-0.1

0

0.1

Y1 to U

2

2 4-0.2

0

0.2

Y1 to U

3

2 4-0.05

0

0.05

Y1 to U

4

2 40

0.01

0.02

0.03

Y1 to U

5

2 4-2

-1

0

1

Y2 to U

1

2 4-1

0

1

2

Y2 to U

2

2 40

0.1

0.2

Y2 to U

3

2 4-0.2

0

0.2

Y2 to U

4

2 4-0.1

0

0.1

Y2 to U

5

2 40

1

2

3

Y3 to U

1

2 4-0.5

0

0.5

Y3 to U

2

2 40

0.5

1

Y3 to U

3

2 40

0.1

0.2

Y3 to U

4

2 40

0.02

0.04

0.06

Y3 to U

5

2 40

1

2

3

Y4 to U

1

2 4-1

-0.5

0

0.5

Y4 to U

2

2 40

0.1

0.2

Y4 to U

3

2 40

0.2

0.4

Y4 to U

4

2 40

0.05

0.1

Y4 to U

5

2 4-1

-0.5

0

0.5

Y5 to U

1

2 4-0.5

0

0.5

Y5 to U

2

2 40

0.2

0.4

Y5 to U

3

2 40

0.5

1

Y5 to U

4

2 40

0.2

0.4

Y5 to U

5

Figure 5. Impulse responses

0 2 4 6 8 10 12 14 16 180

5

10

Observation number

T S

qu

are

S

ta

tistic

T-Square for VAR residuals

0 2 4 6 8 10 12 14 16 180

5

10

Observation number

T S

qu

are

S

ta

tistic

T-Square for VAR residuals

Figure 4.

(a) T2 chart using Chi-Square distribution with α=0.0027;

(b) T2 chart using Chi- distribution with α=0.005

(a)

(b)

http://www.atm.com/

http://www.(url/


M26-1

1Abstract—Extreme rainfalls events usually have negative

effect for environment and human. It can cause flood or

landslide. Therefore, prediction of extreme rainfall events

for different return period is essential for safe and optimal

design structure. In this paper we apply Peak Over

Threshold (POT) method to predict extreme rainfalls for

several return periods in Malang Regency. We investigate

characteristic of extreme rainfalls by fitting shape and

scale parameters of Generalized Pareto Distribution. Mean

residual life plot and assessment of shape parameter

stability across a range of different thresholds are used to

determine threshold value. Maximum likelihood method is

used for parameter estimation and probability plots,

quantile plots, return level plots and density plots for

model validation. Using daily rainfalls data for total period

of 14 years from Januari 1996 to December 2009 in

Malang Regency, we show that generalized pareto

distribution fitted the data well then extreme rainfalls in

different return periods are predicted using the model.

Index Terms— Extreme rainfalls, generalized pareto

distribution, maximum likelihood, mean residual life plot, peak

over threshold, return period, threshold value.

I. INTRODUCTION

Extreme rainfalls events usually have negative effect for

environment and human. It can cause flood or landslide which

is occured immediately. Rainfalls in Malang Regency are

important to support of agriculture sector. However, extreme

rainfall can be serious threat. Therefore investigation of the

extreme rainfalls are required for mitigation efforts.

Unfortunately, we do not know exactly when the next

extreme rainfalls with certain level will occure. Thus, we can

Manuscript received April 6, 2001. This work was supported by PGB ITS

under Grant No. : 0750.256/I2.7/PM/2011.

Amran, Post Graduate Student at Department of Statistics, Institut

Teknologi Sepuluh Nopember, Surabaya, Indonesia (e-mail:amranihsani@

gmail.com).

Iriawan N., Department of Statistics, Institut Teknologi Sepuluh Nopember,

Surabaya, Indonesia.

Subiono, Department of Mathematics, Institut Teknologi Sepuluh

Nopember, Surabaya, Indonesia.

Irhamah, Department of Statistics, Institut Teknologi Sepuluh Nopember,

Surabaya, Indonesia.

only estimate the probabilities of level extreme in the future

and this can be done by extreme value analysis.

The study of extreme events are one of interesting field in

natural science, particularly, in extreme value analysis. The

goal of extreme value analysis is to quantify the stochastic

behaviour of a process at unusually high or low levels. The

stochastic behaviour of extreme events can be analysed by their

probability distribution function. Estimating probability of

extreme event has become an important statistical disicpline in

applied science and frequently used for environmental process

modeling.

Commonly, estimation of probability distribution of extreme

events are performed by Block Maxima (BM) method for

Generalized Extreme Value (GEV) distribution or Peak Over

Threshold (POT) method for Generalized Pareto (GP)

distribution. Both of BM and POT method have been used

widely to study extreme events. Adamowski [1], analyse GEV

distribution of daily precipitation data to study effect of

underlying trend in Ontario, Buishand [2], estimates extreme

rainfalls through GEV distribution of daily rainfall data from

several sites in Netherland. Davison and Smith [3] using POT

method to analyze extreme rainfalls, Leahy and Kiely [4],

investigate short duration rainfalls extreme using GP

distribution for rainfalls data in Ireland.

BM method employ series of maximum observation in

certain range or block to characterize parameters of GEV

distribution, thus, there are some extreme observation which

are exclude in the analysis. Conversely, POT method consider

all of extreme observation in the analysis, thus this method use

data more effecient [9].

In this paper, we apply POT method to predict the next

extreme rainfalls in Malang regency which is has not been done

yet. The prediction is denoted by return level, it runs for

several return periods and temporal dependence is evaluated

for increasing the accuracy of GP model.

II. METHODOLOGY

A. Data sets

Daily rainfalls data were measured at Ngajum station in the

Malang Residences. The location has 349 m heights from sea

level. Extreme rainfalls were determined by selecting certain

threshold value. The number of 5145 data were measured

Application of the Peak Over Threshold Method for

Extreme Rainfalls Modeling in Malang Regency

Amran, Iriawan N., Subiono, and Irhamah


M26-2

during 1996 to 2009 would be characterized their distribution.

The skewness values is 3.95, it indicates asymmetric

distribution .

B. Generalized Pareto Distribution

Let X be a sequence of independent and identical distributed

random variables. For a certain threshold value u, define Y = X

– u, known as excess [10]. The distribution of Y, conditional X

> u can be approximated by GP distribution [7], [8]:

F(y; , ) = (1)

where y > 0, and are shape and scale parameters

respectively. Shape paremeter value shows behaviour of tail of

distribution. If < 0 then the GP distribution has a point until

the end that is known as short-tailed distribution, when = - 1,

GP known as uniform distribution. If = 0, GP behave as

exponential distribution. On the other hand if > 0 known as

heavy-tailed distribution. Maximum likelihood method will be

employed to estimate and values.

C. Return Level

Return level (RLN) is the level expected to be exceeded once

every N years [6]. The N- Return period is usually specified in

years. Suppose that GP distribution is appropriate model for y,

the N period return level is denoted as follows:

(2)

where u is threshold value, ny is number of observations per

year and u is probability of an individual observation

exceeding u [6], [9].

Return level RLN is described by a simple graph known as

return level plots for easy interpretation. Return level plots

tend to concave line with no finite bound for > 0, linear line

for = 0, and convex line for < 0.

D. Model Validation

We use four steps validation for assessing the quality of a

fitted GP model, these are probability plot, quantile plot, return

level plot, and density plot. GP model fit data well, if

probability plot and quantile plot of model and data points

could be approximated by a linear line, return level plot will

shows suitability between shape parameter values and their

graphs, and density estimation should be consistent with the

histogram of data [6]. GP model will fit with data if results for

these steps are convenient.

III. RESULTS

We use R-package extRemes for daily rainfalls data

modeling, in Ngajum station.

A. Threshold Selection

Figure 1 shows mean residual life plot over interval of

threshold values. Mean residual life plot is presented with

approximate 95% confidence intervals. The graph shows

curvature from u = 0 to u ≈ 35, approximately linear from u ≈

35 to u ≈ 60, and decrease after u ≈ 60. Since, a reasonable

threshold values are obtained form linearity between mean

excess values and interval of thresholds, the plot suggests that

the possible interval i.e. [35, 60]. Threshold value u is

convenient if modified scale parameter and shape parameter are

stable above u [6]. The graphs are seen in fig. 2.

Fig. 1 Mean residual life plot for daily rainfalls data in Ngajum station.

Figure 2 shows modified scale parameter and shape

parameter against threshold values. In fig. 2 we can see that the

pattern is change for high threshold values that was suitable

with the change in pattern in the mean residual life plot.

However, a reasonable interval of possible threshold value that

is [30, 45]. Fig. 2 shows shorter interval compare than interval

from fig. 1. Since, interval in fig. 2 also include in interval in

fig. 1, hence, interval of possible threshold value [30, 45]

appears reasonable.

B. Parameter estimation and Validation

According to results which are obtain from threshold

selection process, then maximum likelihood method was

performed for estimating parameters of GP distribution and

validation process for measuring quality of model [5], [6]. The

results are showed in Table 1.

Table 1 shows parameter estimation with their

corresponding standard errors for several threshold u. Scale

parameter and shape parameter reveal stability over threshold

values. Scale parameters are close to 21 and shape parameters

are close to zero with small standard error values.

TABLE I

PARAMETER ESTIMATION BY MLE


M26-3

Parameters

u

30 35 40 45

scale 21.55

(1.753)

22.343

(2.043)

20.956

(2.242)

21.072

(2.664)

shape -0.014

(0.059)

-0.035

(0.066)

0.001

(0.081)

0.003

(0.098)

loglikelihood 1294.104 1009.817 812.663 631.895

Exceedance rate

(per year) 23 18 14 11

Nu 319 248 201 156

Nu = number of exceedances

Temporal dependency is one of important aspect in POT

method. Dependence series usually appeared in extreme

rainfalls. However, the main assumption of GP model requires

independency of exceedances series. Thus, according to the

assumption, we also run declustering process [6]. But

parameters estimation which are obtained after declustering

process are not significantly different.

Plots in fig. 3a – 3d, consist of probability plot, quantile plot,

return level plot, density plot. We can see that all diagnostic

plots show valid result for all possible threshold values.

Probability plot and Quantile plot of model and rainfalls data

are close to linear line, return level plots close to linear, the

plots are suitable for all shape parameter estimation which are

close to zero. Density plots for model and data are fit.

Therefore, the model could be used to predict extreme through

return level for different return periods.

Fig. 3a. Diagnostic plots for threshold value, u = 30 mm.

Fig. 3b. Diagnostic plots for threshold value, u = 35 mm.

Fig. 3c. Diagnostic plots for threshold value, u = 40 mm.

Fig. 2. Modified Scale and Shape parameters


M26-4

Fig. 3d. Diagnostic plots for threshold value, u = 45 mm.

Return level take in to account in order to predict extreme

rainfalls. Based on parameters values which are estimated by

maximum likelihood method and assuming that extreme

rainfalls from stationary process, return level in (2) are

provided in Table 2 as follows:

TABLE II

RETURN LEVEL FOR THRESHOLD VALUES

N Return Level (mm)

u = 30 u = 35 u = 40 u = 45

5

128.704 127.683 129.579 130.043

(114.531,

152.310)

(114.353,

152.597)

(114.748,

157.749)

(114.963,

161.660)

10

142.642 140.789 144.156 144.819

(124.182,

169.581)

(123.519,

169.226)

(124.361,

176.910)

(124.447,

181.930)

25

160.866 157.639 163.438 164.394

(135.737,

192.164)

(134.215,

190.606)

(135.655,

202.255)

(135.354,

208.782)

50

174.501 170.035 178.032 179.233

(143.654,

209.059)

(141.353,

206.334)

(143.244,

221.439)

(142.516,

229.139)

Return levels tend to stable for interval threshold value and

it is increase for all combination of return periods. There is a

different phenomenom showed in return level for u = 35 mm.

For every return period, return level will increase for higher

threshold value, however, it did not happen for u = 35 mm.

Return levels of 35 mm are minimum for all return periods. It is

needed a further investigation to evaluate this phenomenom.

Generally, return level in Ngajum station are vary for every

return period and it can be seen in Table 2.

.

IV. CONCLUSIONS

Model GP distribution has been built for daily rainfalls data

in Ngajum station, Malang Regency. Threshold selection use

mean residual life plot and stability parameters plot to select

threshold value. Both of the graph have a similar pattern.

These analysis suggest that interval of possible threshold value

are [30, 45].

Based on the interval threshold values, maximum likelihood

method was performed on 30 mm, 35 mm, 40 mm, and 45 mm

and validation model was performed to assess quality of model.

All diagnonstic plots indicated that model fitted data well.

Therefore, the model could be used to predict extreme through

return level for different return periods.

Return levels tend to stable for interval threshold value and

increase for all combination of return periods. Generally, return

level in Ngajum station are (127.683, 130.043) for 5 years

return period, (140.789, 144.819) for 10 years return period,

(157.639, 164.394) for 25 years return period, and (170.035,

179.233) for 50 years return period.

There are some possible extension in this paper. How to

determine the best threshold values for more convenient way is

still needed. Stationary process assumption for extreme rainfall

is required for long time return period but, it is interesting to

evolve return level for nonstationary process.

REFERENCES

[1] J. Adamowski, K. Adamowski, and J. Bougadis, “Influence of trend on

short duration design storms,” Water Resour Manage, 24(3):401–413,

2010.

[2] T. A. Buishand, “Extreme rainfall estimation by combining data from

several sites,” Hydrologkal Sciences - Journal - des Sciences

Hydrologiques, 36,4, 8/ 1991.

[3] A.C. Davidson and R. L. Smith,” Models for exceedances over high

threshold (with discussion),” J. Roy. Stat. Soc. B, 52, 393-442.

[4] P. G. Leahy and G. Kiely, “Short duration rainfall extremes in Ireland:

Influence of climatic variability,” Water Resour Manage, 2010, DOI

10.1007/s11269-010-9737-2.

[5] D.Z.P. Bermudez and S. Kotz, ,” Parameter estimation of the generalized

Pareto distribution-Part I”. Journal of Statistical Planning and

Inference, 140, 1353-1373, 2010.

[6] S. G. Coles, An Introduction to Statistical Modeling of Extreme

Values. London: Springer-Verlag, 2001.

[7] M. Falk andA. Guillou,” Peaks-over-threshold stability of multivariate

generalized Pareto distributions,” Journal of Multivariate Analysis, 99,

715-734, 2008.

[8] J. Picklands, Statistical inference using extreme order statistics. Ann

Stat 3:119–131, 1975.

[9] L. Fawcet and D. Walshaw, “Modeling environmental extremes,” in 19th

conf. of The International Environmetrics Society, Kelowna, Canada,

June 8th , 2008.

[10] I. Li, W. Cai, E, and. P. Campbell, “Statistical Modeling of Extreme

Rainfall in Southwest Western Australia,” Journal of Climate, 18, pp.

852–863, 2005.


Abstract— Nonparametric multivariable regression model is a

development of nonparametric regression model with one

variable predictor. The smoothing spline function can be used to

approximate nonparametric multivariable regression models. In

order to obtain estimator and to construct confidence interval of

smoothing spline curve in the nonparametric multivariable

regression model, we can use bayesian approach. The smoothing

parameters selection simultaneously in nonparametric

multivariable regression model using the Generalized Maximum

Likelihood (GML) method. By computing posterior mean and

posterior variance of smoothing spline function, we obtain the

confidence interval for the smoothing spline function k

f , k =

1,...,q. We proposed this method with simulation data.

Keywords—Bayesian Confidence interval, GML,

Nonparametric multivariable, Smoothing spline.

I. INTRODUCTION

Smoothing splines have been used successfully in a wide

range of applications requiring flexible nonparametric

regression models. It is highly desirable to have interpretable

confidence intervals for these estimates for various reasons, for

example, to decide whether a spline estimate is more suitable

than a particular parametric regression. A parametric

regression model may be considered not suitable if a large

portion of its estimate is outside of the confidence intervals of a

smoothing spline estimate.

One way for constructing confidence intervals for

nonparametric estimates is bootstrap and bayesian approach.

The disadvantage of the bootstrap intervals is that they are

computer intensive. Reference [5] and [4] used bayesian

confidence interval for a smoothing spline in nonparametric

model. Reference [6] compared the performance of bayesian

confidence interval with bootstrap confidence interval for

Rita Diana is a student at Department of Statistics, Faculty of Mathematics

and Natural Sciences, Sepuluh Nopember Institute of Technology, Surabaya,

Indonesia; (corresponding author to phone: +6285232078886; fax:

+62315922940; e-mail: [email protected]).

I. Nyoman Budiantara is a lecturer at Department of Statistics, Faculty of

Mathematics and Natural Science, Sepuluh Nopember Institute of Technology,

Surabaya, Indonesia; (e-mail: [email protected]).

Purhadi, is a lecturer at Department of Statistics, Faculty of Mathematics

and Natural Science, Sepuluh Nopember Institute of Technology, Surabaya,

Indonesia; (e-mail: [email protected]).

Satwiko Darmesto is a senior lecturer at Center for the Study and Education

and Training Apparatus I, National Institute of Public Administration,

Bandung, Indonesia; (e-mail: [email protected]).

smoothing spline in nonparametric model via simulations.

Reference [1] used bootstrap confidence interval for regression

spline truncated in nonparametric model. Reference [3] also

used bayesian confidence interval for regression B-splines in

nonparametric model.

Furthermore, reference [2] constructed bayesian confidence

interval as a penalized spline with mixed model approach in

nonparametric model. Reference [10] used bootstrap

confidence interval for regression spline in nonparametric

additive model. Reference [8] extended method of [2] to

construct confidence interval for penalized spline in

nonparametric additive model. Reference [9] used bayesian

confidence interval for penalized spline in nonparametric

additive model with non-Gaussian data.

The description above shows that research on bayesian

confidence interval for regression spline dan penalized spline in

nonparametric multivariable model have been done. However,

the research on bayesian confidence interval for smoothing

spline in nonparametric multivariable model has not yet been

done. In this paper, we provide some evidence that the

bayesian confidence intervals for smoothing splines that we

construct have an average coverage probability across the

estimated function. The optimal smoothing parameters

selection method simultaneously in nonparametric multivariable

regression model using GML. We proposed this method with

simulation data.

II. BAYESIAN CONFIDENCE INTERVAL FOR

SMOOTHING SPLINE

A. Bayesian Smoothing Spline for one variable

Define a nonparametric regression model as

( ) , z [ , ]j j j jy f z a b , j = 1,2,…,n

where f is unknown function and εj are zero-mean independent

random errors with a common variance σ2. Assume a prior for

f as

1/2

1

( ) ( ) ( )m

v v

v

f z z g z

,

(1)

where 1 2( , ,..., ) ~ ( , ), m N α 0 I , and are

positive constants. ( ); [ , ]g z z a b is a zero-mean Gaussian

stochastic process with covariance function ,

1, 1( , )

n n

j l j lz z

V

Bayesian Confidence Interval for Smoothing Spline in

Nonparametric Multivariable Regression Model

Rita Diana, I. Nyoman Budiantara, Purhadi and Satwiko Darmesto


with 1 1 2( , ) ( ) ( ) [( 1)!] .

b

m m

j l j l

a

z z z u z u m du

Moreover,

, 1, 2,..., v v m and ( )g z are mutually independent.

Let 1( ,..., ) ,T

m α

,

1, 1={ ( )} ,n m

v j j vz Z

1( , , )m

where

-1( ) ( 1)!,v

v j jz z v v=1,2,...,m, then (1) can be written as

1/2( ) ( )Tf z g z α

and we also obtain

1/2 2( ) ~ ( , )Tg z N y Zα + ε 0 Z Z V I (2)

and 1/2( ) ( ) ~ ( , ( , ))T Tf z g z N z z α 0

(3)

Furthermore,

( )E f y Z + ψ

(4)

where 1( ( , ), , ( , )) .T

nz z z z ψ Let 2 /n and / .

Using properties of multivariate normal random variables and

(2), (3) and (4), we have

1 1( | ) ( ) ( )T T T TE f n n y Z ZZ V I y ψ ZZ V I y

(5)

and

1

| ( , ) ( )

( ) ( )

T T T T

T

Var f z z

n

y Z ψ

ZZ V I Z ψ

(6)

2 1

1 1

( , ) ( ( ) )

2 ( ( ) ) ( )

T T T

T T T T T

z z

I Z ZZ M Z

Z ZZ M ψ ψ ZZ M ψ

Reference [5] showed that if ,U V I n

1lim( )T

ZZ U y

1 1 1 1 1( ( ) )T T U U Z Z U Z Z U y

(7) 1 1 1 1lim ( ) ( )T T T

Z ZZ U y Z U Z Z U y

(8)

Combining results in (5), (7) and (8), [7] showed that

1 1 1 1 1 1 1 1

ˆ lim ( | )

( ) ( ( ) )T T T T T T

f E f

y

Z U Z Z U y ψ U U Z Z U Z Z U y

(9)

and

1 1 1 1 1

1 1 1 1 1

lim |

= ( , ) ( ) 2 ( )

( ( ) )

T T T T T

T T T

Var f

z z

y

Z U Z Z U Z Z U ψ

ψ U U Z Z U Z Z U ψ

(10)

If 1 1 1n VU U V I U then 2ˆlim | ( )Var f

y A where

2 ˆˆ n , 1 1 1 1 1( ) ( ( ) )T Tn A I U U Z Z U Z Z U and

ˆ ( ( )) .T n m y I A y

Therefore, by calculating each posterior mean and posterior

variance of f, we can construct 100(1 )% confidence

intervals for smoothing spline functions f(zj), j = 1,...,n in

nonparametric regression model is thus

2

2

ˆ ˆ( )j jjf z z a , j = 1,...,n (11)

where 2 is an estimate of 2 and jja are diagonal elements

of the matrix ( )A .

B. Bayesian Smoothing Spline for multivariable

A nonparametric multivariable regression model assumes

that

1

( ) , z [ , ]q

j k kj j kj k k

k

y f z a b

, j = 1,2,…,n

(12)

where fk are unknown functions and εj are zero-mean

independent random errors with a common variance σ2.

Assume a prior for fk as

1/2 1/2

1

( ) ( )km

kv kv k k k k

v

f z g z

(13)

where 1 2( , ,..., ) ~ ( , ), k k k km N α 0 I , and are

positive constants, kα and ( )k kg z are mutually independent,

and ( ); [ , ]k k k k kg z z a b is a zero-mean Gaussian stochastic

process with covariance function ,

1, 1( , )

n n

k k k k kj kl j lz z

V

with 1 1 2( , ) ( ) ( ) [( 1)!] .k

k

b

m m

k kj kl kj kl

a

z z z u z u m du

Let 1( ,..., ) ,T T T

qα α α 1( ,..., ) ,

k

T

k k km α

1( , , ),qT T T

,

1, 1={ ( )} ,n m

k kv kj j vz T

1 , , ,qΦ

1, ,kk k km

where

-1( ) ( 1)!,v

kv kj kjz z v v=1,2,...,mk; k=1,2,...,q, then (12) can be

written as 1/2 1/2

1 1 1

( ) ( )q q q

T

k k k k k k k

k k k

w f z g z

Φ α and

1/2 1 2

1

( ) .q

k k kk

y Tα + g z ε Hence, we also obtain

2

1

~ ( , )q

Tk k

k

N

y 0 TT V I

(14)

and 1 1

( ) ~ ( , ( , ))q q

T

k k k k k k

k k

w f z N z z

0 Φ Φ

(15)

Furthermore,

1

( )q

T

k k

k

E w

y TΦ+ ψ

(16)

where 1( , ), , ( , ) .

T

k k k k k knz z z z ψ

Let 2 /n and / .

Using properties of multivariate

normal random variables and (14), (15) and (16), we have


1

1

1

1

1 1

ˆ( | ) ( | )

= ( )

( )

k

q

k

k

qT T T

k k

k

q qT T

k k k k

k k

E w E f

n

n

y y

Φ T TT V I y

ψ TT V I y

(17)

and

1 1

1

1 1

| { ( )

( ) ( )

q qT T T T

k k k k

k k

q qT

k k k k

k k

Var w

n

y Φ Φ Φ T ψ

TT V I TΦ ψ

(18)

2 1

1 1

1

1

1 1

ˆ( | ) { ( ( ) )

2 ( ( ) )

( ) }

k

q qT T T

k k k

k k

T T T

q qT T

k k k k

k k

Var f

y Φ I T TT M T Φ

Φ T TT M ψ

ψ TT M ψ

with 1

+ + .q

k k

k

n n

θM V I V I

If the limit of posterior mean

value w is taken for , we find that

1lim( )T

TT M y

1 1 1 1 1( ( ) )T T M M T T M T T M y

(19)

1 1 1 1lim ( ) ( )T T T

T TT M y T M T T M y

(20)

Combining results in (17), (19) and (20), we have

1

1 1 1

1 1 1 1 1

1

ˆˆ lim ( | )

( )

( ( ) )

k

q

k

k

T T T

qT T T

k k

k

w f E w

y

Φ T M T T M y

ψ M M T T M T T M y

(21)

and

1

1 1

1

1 1 1

1

1 1 1 1 1

1

lim ( | ) lim ( | )

= { ( )

2 ( )

( ( ) )

q

k

k

qT T

k k

k

qT T T

k k

k

qT T T

k k k k

k k

Var w Var f

y y

Φ T M T Φ

Φ T M T T M ψ

ψ M M T T M T T M ψ1

}q

where 1 1 1 1 1( ) ( ( ) )T Tn H λ I λ M M T T M T T M and

ˆ ( ( ))T n m y I H y

with 1

.q

k

k

m m

Hence,

k

1 1 1 1 1

lim ( | )= 2

( ( ) )

T T

k k k k kk k k

T T T

k k k k

Var f

y B C

ψ M M T T M T T M ψ

where kkB is a matrix corresponds to rows

1

1

1k

ww

m

to 1

k

ww

m

and columns 1

1

1k

ww

m

to 1

k

ww

m

of matrix T 1 1( )

T M T and kC

is a subvector of 1 1 1( )T T

k k T M T T M ψ with elements from

1

1

1k

ww

m

to 1

k

ww

m

. Based on these posterior covariances and

posterior means, we construct bayesian confidence intervals for

the overall function f and its components in (12). The

100(1 )% bayesian confidence interval for kf , k=1,...,q is

2

ˆ ( )k

k kj jjf z z d (22)

where jjd are diagonal elements of matrix lim |kVar f

D y .

C. Optimal smoothing parameters selection method

The smoothing parameters selection are crucial for the

performance of smoothing spline function estimates. A

selection method of the smoothing parameters k k ,

k=1,...,q for smoothing spline estimators in nonparametric

multivariable regression model using bayesian approach, that is

Generalized Maximum Likelihood (GML) is given as

1 1/

1GML( , , ) ( ( )) (det ( ( )))T n m

q n y I H λ y I H λ

where det+ is the product of the nonzero eigenvalues. The

values of 1, , q are optimal by minimizing

1GML( , , ).q

III. SIMULATION STUDY

In the simulations, we generated our data from the

nonparametric multivariable regression model (12) with

kiz i n , k=1,2; i=1,...,n, and the functions were set to be

13

1 1( ) 6.36zf z e and

6 11 6 4 3 10

2 2 2 2 2 2( ) 10 [ (1 ) (12,7)] 10 [ (1 ) (4,11)]f z z z Be z z Be

where ( , )Be p q is the Beta function. The simulation settings

were set to have three different sample sizes n = 50, 100, 200.

The random errors i were generated from the standard normal

distribution. GML method is used to choose smoothing

parameters for all simulations. The intervals must be

interpreted “across-the function”, rather than pointwise. The

number of data points at which the confidence interval cover

the true values of f1(z1), f2(z2) and f1(z1)+f1(z2) are recorded.

These numbers are then divided by the sample size to form the

coverage percentage of the intervals on design points. We

summarize these coverage percentage in Table 1.

Table 1.

Coverage Percentages of 90% and 95% Confidence Interval

in Simulation

function Coverage Percentages

n=50 n=100 n=200

0.05 f1(z1)+f1(z2

) 0.940 0.850 0.885

f1(z1) 0.720 0.770 0.755

f2(z2) 0.700 0.780 0.760

0.10 f1(z1)+f1(z2

) 0.900 0.850 0.885

f1(z1) 0.700 0.760 0.740

f2(z2) 0.700 0.770 0.755


In simulations, we note that these confidence intervals are

not in general pointwise confidence intervals. The coverage

will tend to be less than nominal where the true curve has sharp

peaks or kinks and more than nominal where the true curve is

smooth. If the users interpret them appropriately across the

function, they will have a reasonable feel for the overall

accuracy of the estimate. The readers may judge them from the

plotted confidence intervals overlaying the true function of the

psychological information that is conveyed by the intervals. In

Figure 1, confidence interval smoothing spline function for

f1(z1), f2(z2) and f1(z1)+f1(z2).

0.0 0.2 0.4 0.6 0.8 1.0

-4e

+0

5-3

e+

05

-2e

+0

5-1

e+

05

0e

+0

0

z1

fz1

0.0 0.2 0.4 0.6 0.8 1.0

-4e

+0

5-3

e+

05

-2e

+0

5-1

e+

05

0e

+0

0

z2

fz2

-6e+05 -4e+05 -2e+05 0e+00

-6e

+0

5-4

e+

05

-2e

+0

50

e+

00

f1+f2

y

Fig. 1. 95% Confidence interval smoothing spline

function for f1(z1), f2(z2) and f1(z1)+f2(z2) with n = 50

IV. CONCLUSION

Bayesian confidence intervals have good frequentist

properties which provided that the smoothing parameter has

been estimated properly. As the shape of the smoothing

parameters used in GML method is fixed, further study may

consider to use the smoothing parameter in the form of random

variables and to develop methods for testing hypothesis in

nonparametric multivariable regression model.

ACKNOWLEDGMENT

The first author would like to thanks BPS-Statistics

Indonesia for the Ph.D. grant through Human Resources

Development Project in cooperation with Sepuluh Nopember

Institute of Technology, Surabaya, Indonesia with contract

number: 19/KS/01-VII/2010.

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[1] J. F. Carriere, “Non-parametric confidence intervals of instantaneous

forward rates”, Insurance: Mathematics and Economics, vol. 26, pp.

193–202, 2000.

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bands for penalized spline estimators”, Technical report, University

Gottingen, 2010.

[3] V. Mao and L. H. Zhao, “Free knot polynomial splines with confidence

intervals”, Journal of the Royal Statistical Society, series B, vol. 65, pp.

901-919, 2003.

[4] D. Nychka, “Bayesian confidence intervals for smoothing splines”,

Journal of the American Statistical Association, vol. 83, pp. 1134-1143,

1988.

[5] G. Wahba, “Bayesian Confidence Intervals for the cross-validated

smoothing spline”, Journal of the Royal Statistical Society, series B, vol.

45, pp. 133-150, 1983.

[6] Y. Wang and G. Wahba, “Bootstrap Confidence Intervals for Smoothing

Splines and Their Comparison to Bayesian Confidence Intervals”,

Journal of Statistical Computational and Simulation, vol. 51, pp. 263-

279, 1995.

[7] Y. Wang, Smoothing Splines Methods and applications, CRC Press

Taylor & Francis Group, California, USA. 2011.

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Confidence Bands for Additive Models with Locally Adaptive Smoothed

Components and Heteroscedastic Errors”, Technical Report, Georg

August Universitat Gottingen, 2010.

[9] S. N. Wood and G. Marra, “Coverage Properties of Confidence Intervals

for Generalized Additive Model Components”, Research Report, No.

313, Department of Statistical Science, University College London, 2011.

[10] L. Yang, “Confidence Band for additive Regression Model”, Journal of

Data Science, vol. 6, pp. 207-217, 2008.

z1

z2

f2(z2)

f1(z1)


1Abstract— Risk modeling of Dengue hemorrhagic fever (DHF)

cases is framed by some factors, such as spatial heterogeneity,

uncertainty components (or random effects), DHF nested within

two levels, and spatiotemporal varying. Nested factor could

happen such as DHF nested to location as level 1 and location

nested to population as level 2. This study develops and analyzes

spatial convolution (Poisson-Lognormal) model using Bayesian

approach, called Bayesian Poisson-Lognormal 2-level (BP2L)

spatiotemporal. In this model, spatial terms are treated as

random effects factors (namely uncorrelated and correlated).

BP2L spatiotemporal is a complex model, so the parameter

estimation needs the computational intensive approach. It

requires mathematical manipulation such as full conditional

distribution form gathered from its joint posterior in order to

estimate those parameters through Gibbs sampler or Metropolis-

Hasting. The investigation result showed that full conditional

distribution of model is closed form. Gibbs sampler, therefore, is a

right method for estimating the parameters.

Index Terms— Bayesian, closed form, correlated, DHF, full

conditional distribution, Poisson-Lognormal, uncorrelated

I. INTRODUCTION

engue hemorrhagic fever (DHF) analysis based location

used for monitoring and intervention tool. DHF case is

affected by the spatial heterogeneity as covariate and

random effects [1]-[5] introduced a spatial convolution

(Poisson-Lognormal) model accommodating random effects

(uncorrelated and correlated) and covariate. This spatial

convolution model was applied by [6],[7] in 31 districts of

Surabaya DHF data on 2010 and shown realistic result.

In other deep study, DHF case varies not only spatially but

also temporally [8], so that convolution model has been

developed into a spatiotemporal model by adding temporal

trend and log relative risk using Bayesian approach since 2007

by [9]. DHF case is also hierarchically structured data, as

shown in [11]. It has been demonstrated that DHF case is

Mukhsar is PhD Student of Statistics Department Institut Teknologi

Sepuluh Nopember (ITS) Surabaya; e-mail:

[email protected]

Iriawan, N., is lecturer of Statistics Department Institut Teknologi Sepuluh

Nopember (ITS) Surabaya. He is also vice rector 3 of Institut Teknologi

Sepuluh Nopemner (ITS) Surabaya; e-mail: [email protected]

Ulama, B. S. S., is lecturer of Statistics Department Institut Teknologi

Sepuluh Nopemner (ITS) Surabaya. He has also a head of statitiscal

computation of Statistics Departmenet Institut Teknologi Sepuluh Nopemner

(ITS) Surabaya; e-mail: [email protected]

Sutikno, is lecturer of Statistics Department Institut Teknologi Sepuluh

Nopember (ITS) Surabaya; e-mail: [email protected]

Heri, K., is lecturer of Statistics Department Institut Teknologi Sepuluh

Nopember (ITS) Surabaya; e-mail: [email protected]

nested to district as level 1 and each district is nested to

Surabaya city as level 2 (or 2-level hierarchy).

The purpose of this study develops spatial convolution and

temporal model applied on 2-level hierarchical data by using

Bayesian approach, called Bayesian Poisson-Lognormal 2-level

(BP2L) spatiotemporal. BP2L spatiotemporal would have a

complex joint posterior of parameters model, so that parameter

estimation needs the computational intensive approach. One

way to solve the estimation is by constructing full conditional

distribution and employing Gibbs sampler or Metropolis-

Hasting algorithm. These algorithms require the appropriate

method for generating the parameters of model [10],[11].

When the full conditional distribution has closed form, the

Gibbs sampler is simpler be used. Otherwise, Metropolis-

Hasting is more appropriate [12]-[14]. The simplest way to

identify the closed-form of full conditional distribution is by

characterizing the pattern of functional form of Poisson

distribution, normal distribution, gamma distribution,

logarithmic functions, exponential functions, integrals, or

Taylor series. When Gibbs sampler is appropriate, WinBUGS

can be used to estimate these parameters [15],[16].

II. BAYESIAN POISSON-LOGNORMAL 2-LEVEL

SPATIOTEMPORAL

The most commonly encountered district count based model is

Poisson model. It would be suitable when there is a relatively

rare event of DHF in relatively large population in each district.

Suppose the DHF count sty is identically distributed Poisson

with parameter st . Poisson variability is influenced by st

that depends on district or location s and time t. Then, the

exploring BP2L spatiotemporal as described in section 1,

therefore, could be expressed as[9],

~ ( )st st sty Poisson (1)

With

T0

1

exp , 1, , , 1, , , 1,..., ,P

st st pst p s s z s zp

e x u v t t s S t T p P

where S is the number of locations, T is length of time

observation, P is the number of covariates, ste is an expected

count in district sth at time t

th, pstx is p

th covariate in district s

th

at time tth,

su is uncorrelated random effect at district sth, sv is

correlated random effect (CAR model) at district sth, zt is

trend temporal, and s zt is log relative risk. Likelihood and

Full Conditional Distribution Investigation of

Bayesian Poisson Lognormal 2-Level Spatiotemporal for

Analyzing DHF Risk

Mukhsar, Iriawan, N, Ulama, B. S. S, Sutikno, Kuswanto H

D







joint prior distribution of (1), therefore, are defined

respectively as,

1( ,..., )t Stp y y A B λ ,

(2)

0{ , , , , , , , , , }p s s s u vu v λ

T0

1

1 1

exp

!

ityP

st p pst s s z i zT S p

stt i

e x u v t t

Ay

T0

1 1 1

exp expT S P

st p pst s s z s zt s p

B e x u v t t

and

( )stp C D (3)

0( ) ( ) ( ) ( ) ( )p s u s vC p p p p u p v

( ) ( ) ( ) ( ) ( ) ( ).s u vD p p p p p p

Based on equation (2) and (3), joint posterior would be

1( ,..., ) ,t Stp y y E F G λ (4)

where

T0

1

1 1

exp

!

styP

st p pst s s z s zT S p

stt s

e x u v t t

Ey

T0

1 1 1

exp expT S P

st p pst s s z s zt s p

F e x u v t t

0( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )p s u s v s u vG p p p p u p v p p p p p p

Definition 1. (Full conditional distribution) (Congdon,

2010). Suppose joint posterior of (4),

11

1

1 0

( ,..., ) ( )( ,..., ) ,

( ,..., ) ( )

( ,..., ) ( ) , { , , , , , , , , , }

t Stt St

t St

t St p s s s u v

p y y pp y y

p y y p d

p y y p u v

λ

λ λλ

λ λ λ

λ λ λ

then full conditional distribution for p is defined as

1 0

1

( ,..., , , , , , , , , , , )

[ .] ( ) ( ,..., ) ,

p t St p s s s u v

p p t St

p y y u v

p p y y

λ

and treats the other parameters exceptp , expressed as

p,

are constant.

Definition 2 (Closed form) (Hoff, 2009). Suppose that prior

of each parameter containing in λ following the standard

distribution as in Table 1, the full conditional distribution p

as an example, is written as 1[ .] ( ) ( ,..., ) ,p p t Stp p y y λ

would be closed form, if it can be rearranged to be a standard

distribution.

Based on Definition 1, prior distribution in Table 1, and joint

posterior (4), the full conditional distribution for each

parameter of model (1) can be created. Supposed that p is

treated as an example, the full conditional distribution would

be,

T T

1 1 1 11 1

. exp exp exp .

styT S S T S P

p st p pst st p psts t s pt s

e x e x H

(5)

21

exp22

pH

Equation (5) would be elaborated more deeply and it could be

represented as

T

1 1 1

1. exp ,

2

T S P

p st p pstt s p

y x J

(6)

2T

1 1 1

exp exp2

T S Pp

st p pstt s p

J e x

Taylor series around * 0p

could be employed to

approximate the T1

expP

p pstpx

[2], and found that

2

T T 2

1 1 1

1. exp 1 .

2

T S P

p st st pst p st pst pt s p

y e x e x L

(7)

1 1

exp

2

T S

stt s

e

L

Suppose,

T11

1 1 1

T S P

st st pstt s p

A y e x

and

2T

121 1 1

1 ,T S P

st pstt s p

A e x

then (7) can be written 2

11

212 11

12

2exp

21. exp .

22p p

A

A A

A

(9)

Based on the Definition 2, full conditional distribution for p

is closed form,

211 11

12 12

2 2, exp .p

A AN

A A

Full conditional distributions for the other parameters are also

closed form which can be created similar asp

, which are

listed in Table 2.


Corollary. Given BP2L spatiotemporal (1), if set of likelihood

(2) and prior (3) are following the assumptions in Table 1, then

its full conditional distributions are closed form.

III. CONCLUSIONS AND FUTURE RESEARCH

Full conditional distributions of BP2L spatiotemporal are

closed form. Gibbs sampler, therefore, would be used for

estimating the parameters. Further research for applying BP2L

spatiotemporal to Surabaya DHF data would be interesting.

ACKNOWLEGMENTS

This article is a part of Laboratory’s research grant and

doctoral research at Statistics Department of Institut Teknologi

Sepuluh Nopember (ITS), Surabaya, Indonesia, granted by

LPPM Institut Teknologi Sepuluh Nopember (ITS). We thank

Head of BPS and BMKG Surabaya city.

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Inference for Disease Mapping, Computational Statist.&

Data analysis, Elsevier, 50, 2552-2570,

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Computational Modeling Sciences Center, School of

Human Evolution and Social Change, Arizona State

University, Tempe, USA

[3] Clark, J. S., and Gelfand, A. E (2005). Hierarchical

Modelling for the Environmental Sciences, Statistical

Methods and Application, Oxford University Press.

[4] Congdon, P. D. (2010). Applied Bayesian Hierarchical

Methods, Chapmann&Hall, CRC Press, UK,

QA279.5.C662010.

[5] Eckert, N., Parent, E., Belanger, L., and Garcia, S.

(2007). Hierarchical Bayesian Modeling for Spatial

Analysis of the Number of Avalance Occurrences at the

Scale of the Township, Journal of Cold Regions Science

and Technology, Elsevier, 97-112,

DOI:10.1016/j.coldregions.2007.01.008.

[6] Gelfand, A. E, Diggle, P. J., Fuentes, M., and Guttorp, P.

(2010). Handbook of Spatial Statistics , , Chapman &

Hall, UK, QA278.2.H3742010

[7] Ghosh, M., Natarajan, K., Waller, L. A., and Kim, D.

(1999). Hierarchical Bayes GLMs for the Analysis of

Spatial Data: An Application to Disease Mapping,

Journal of Statistics Planning Inference, Elsevier, 75,

305-318, DII:SO378-3758(98)001150-5.

[8] Hamada, M. S., Wilson, A. G., Reese, C. H., and Martz,

H. F. (2008). Bayesian Reliability, Springer,

DOI:10.1007/978-0-378-77950-8.

[9] Hoff, P. D. (2009). A First Course in Bayesian Statistical

Methods, Springer,DOI 10.1007/978-0-387-92407-6.

[10] Iriawan, N., Ulama, B. S. S., Sutikno, Heri, K. (2012).

Report of Laboratory Research, LPPM ITS, Surabaya.

[11] Lawson, B. A. (2008). Bayesian Disease Mapping:

Hierarchical Modeling in Spatial Epidemiology, CRC

Press, Chapman&Hall, RA792.5.L3872008.

[12] Li, N., Qian, G., and Huggins, R. (2002). A Random

Effects Model for Disease with Heterogeneous Rates of

Infection, Journal of Statistics Planning and Inference,

Elsevier.

[13] Neyens, T., Faes, C., and Molenberghs, G. (2011). A

Generalized Poisson Gamma Model for Spatially

Overdispersed Data, Journal of Spatio temporal

Epidemiology, Elsevier, 1-10,

DOI:10.1016/j.sste.2011.10.004.

[14] Ntzoufras, I. (2009). Bayesian Modeling Using

WinBUGS, John Wiley&Sons, QA279.5.N892009, New

Jersey.

[15] Maiti, T. (1998). Hierarchical Bayes Estimation of

Mortality Rates for Disease Mapping, Journal of

Statistical Planning and Inference, Elsevier, 339-348,

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[16] Mukhsar, Iriawan N., Ulama, B. S. S., Sutikno,

Kuswanto, H. (2012). Spatial Bayesian Poisson-

Lognormal Analysis of Dengue Relative Risk Incidence in

Surabaya on 2010, Proccedings of International

Conference Mathematics Statistics and Its Application,

ITS, Surabaya.

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Modeling and Inference in Ecology, The Analysis of

Data from Populations, Metapopulations and

Communities, Elsevier, Academic Press.

Table 1. Prior distribution of BP2L spatiotemporal

0( ) ~ ()p flat

( ) ~ (0, )p N

1 2( ) ~ ( , )up G c c

1 2( ) ~ ( , )vp G d d

1 2( ) ~ ( , )p G a a

( ) ~ (0, )pp N

1 2( ) ~ ( , )p G e e

( ) 1( ) ~ ,

S

jj s

ss s

p ND D

1 2( ) ~ ( , )p G b b

( ) 1( ) ~ ,

S

jj s

ss v s

v

p v ND D


Table 2. Full conditional distributions of BP2L spatiotemporal

0 0 01 1

exp exp( ) log .T S

st stt s

y e K

211 11

12 12

2T T

11 121 1 1 1 1 1

2 2, exp ,

, 1 .

p

T S P T S P

st st pst st pstt s p t s p

A AN

A A

A y e x A e x

211 11

12 12

11 121 1 1 1

2 2~ , exp ,

, 1 .

Su us u

T S T S

st st u stt s t s

B Bu N

B B

B y e B e

211 11

2

12 12

211 12

1 1 ( ) 1 1

2 2~ , exp ,

, .

Sv v

s v s

T S S T S

st st v j v st v st s j s t s

C Cv N D

C C

C y e v C e D

211 11

12 12

11 121 1 1 1

2 2, exp ,

, 1 .T S T S

st st stt s t s

F FN

F F

F y e F e

2

22 ( )11 11

12 12

211 12

1 1 ( ) 1 1

2 21~ , exp ,

2

, .

S

S jj s

ss s

T S S T S

st st j st st s j s t s

G GN

G D GD

G y e G e D


1Abstract-Migration is the process of moving people from one

region to another. There are two aspects that follow the process,

those are individuals and regions. The individual data or the

micro data requires specific modeling to the individual

characteristic related to the decision to migrate. While the region

data or macro data requires different modeling to characterize

the region, as the origin and the destination of migration. The

population mobility become more complex at district/city levels

compared to inter-provincial or even international due to the

completeness data. The East Java Province is known as the

province that send migrants to other provinces in Indonesia and

even internationally. Several theories reveals that economic is one

of the dominant factors in migration, but it does not comply in

this cases. This province can be categories as strong economics as

Jakarta, but out migrations from East Java is still high. The high

economic growth in East Java province cannot resist the out

migration flows. The imbalance of economic growth evenly among

districts/cities should be one of major factors that have to be

overviewed closely.

Index Terms-East Java, Migration, Models

I. INTRODUCTION

Migration as a population problems, hold an important role

especially after globalization, technological advances, and the

ease of transportation access. Progress in some fields, like

health and technology, makes easy to control the quantity of

natural population by pressing a number of fertility and

mortality, but it does not apply to control the migration. From

the perspective of the individual, of course, it is more

advantageous because it provides more opportunities to make

choices for improving their living standards. Those facts, on

the other hand, are believed to be as a problem by the

government as policy makers. The migration consequences that

out of control, can affect many sectors such as economic,

social, educational, health, and others. An understanding of

migration patterns become very important in the framework of

development goals that cannot be detached from the

population problem.

Preatin is student at Department of Statistics, Institut Teknologi Sepuluh

Nopember - Surabaya, East Java, Indonesia (corresponding author to e-mail:

[email protected]).

Nur Iriawan is Vice Rector for Resources and Organization, and also as

senior lecturer at Institut Teknologi Sepuluh Nopember - Surabaya, East Java,

Indonesia (e-mail: [email protected]).

Ismaini Zain is lecturer at Institut Teknologi Sepuluh Nopember - Surabaya,

East Java, Indonesia (e-mail: [email protected]).

Wendy Hartanto is PCC and Deputy for Population Management National

Family Planning Coordination Board (BKKBN), Jakarta, Indonesia (email :

[email protected])

In developing countries, including Indonesia, understanding

of the migration phenomenon becomes more limited due to

availability of data. The registration of resident has not done

continuously well mainly related to the resident mobility.

Analyzing to the migration phenomenon, therefore, is fully

relying on the results of 10 yearly population censuses. The

population mobility become more complex at district/city levels

compared to inter-provincial or even international due to lack

of the completeness data.

Several theories of migration have been developed based on

some point of views of different disciplines such as sociology,

micro or macro economics, geography, and interdisciplinary

science. Figure 1 describes the scheme theory of migration

from some discipline of sciences [4].

Figure 1. The Scheme Theories of Migration

Many discipline of sciences interested in developing

migration model. It is because migrations are a complex

phenomenon that involves many dimensions. It requires a

comprehensive understanding which is not limited to particular

disciplines. Multidisciplinary modeling approach couple with

the right chosen variables would be more beneficial than just

using any particular theory approach [2]. Bijak [2] had been

improved in [4] describes the topological relationship of some

of the methods and models of migration as in Figure 2.

On the View of the Modeling Interregional Migration in

East Java: Selected Models

Preatin, Nur Iriawan, Ismaini Zain, Wendy Hartanto


Figure 2 Typology of Migration Methods and Models

There are two aspects that follow the process, those are

individuals and regions. The individual data or the micro data

requires specific modeling to the individual characteristic

related to the decision to migrate. While the region data or

macro data requires different modeling to characterize the

region, as the origin and the destination of migration. Figure 3

shows separation some models that are used to elaborate

migration viewed from the availability of data.

Figure 3. Separation of Selected Migration Models

II. MICRO MODELS

A. Logistic Model

Several studies using logistic models include [14], [18], and

[19]. McCullagh and Nelder [14] demonstrated logistic models

as a generally included in the model for binary scale responses

with log link function. The general form of logistic models as:

0 1 1log ...

1p px x

or

0 1 1

0 1 1

exp ...

1 exp ...

p p

p p

x x

x x

. (1)

Three-level logistic regression model with Bayesian

approaches had been used to modeling migration in Thailand

[11]. The model is used to see the influence of individual

factors, region, and time for individual decisions to migrate.

This approach had only succeeded to see the individual

decision to migrate is significant or not, while the regional

analysis had not been performed. Based on the data used in this

model, it would be very hard in preparation for analysis. It is

due to the difficulty to have the entire population data. Using

logistic models on individual data migration, on the other hand,

will involve migrants and non-migrants. Indonesia which still

relies on census data for the analysis of migrations, therefore,

need the use of computational intensive approaches due to the

involving large data.

B. Event History Analysis

Migration studies using event history analysis have been

began, among others [12], [7]-[10], and [38]. Migration is one

of the events that occurred on the individual demographics

such as change of marital status, changes in the level of

education, type of economic activity and other changes.

Migration in event history analysis is historically one dwelling,

which is focused to a time between switching [2]. Courgeau

[8], modeled the migration opportunities (transition) using

continuous time approaches:

, ,

1

0

( ), ( )

, , , ( ), ( )lim

a a a

i j k i j

a a a a a a

k k k k i j

dt

m t x t y t

P T t dt I j T t I i x t y t

dt

(2)

This Model elaborated some variables as a is an individual

having duration of stay Tka, k-1 is the number of migrate by

individual a, Ika is a random variable for region, individual

characteristics a is xia , and characteristics of area destination j

is yia. This model requires a special survey to see the migration

history of each individual during every individual lifetime.

C. Schedule Model

Figure 4 shows migration patterns according to age. Its

graduation was changed by a scheduled model, which is

defined as a sum of four components:

Migration

http://en.wikipedia.org/wiki/Peter_McCullagh


1. Pre-labor force, a single negative exponential curve with its

rate of decent 𝛼1.

2. Labor-force, a left skewed unimodal curve with mean age μ2,

rate of ascent λ2, and rate of decent 𝛼2.

3. Post-labor force, an almost bell shaped curve, with mean age

μ3, rate of ascent λ3, and rate of decent 𝛼3.

4. Post-retirement peak, exponential curve with rate of ascent

λ4.

5. Constant c.

α1 = rate of descent of pre-labor force component xj = low peak

λ2 = rate of ascent of labor force component xh = high peak

α2 = rate of descent of labor force component xr = retirement peak

λ3 = rate of ascent of post-labor force component X = labor force shift

α3 = rate of descent of post-labor force component A = parental shift

c = Constant B = Jump

Figure 4 Migration Model Schedule

Those four components would build the equation that

defines as:

1 1 2 2 2 2 2

3 3 3 3 3 4 4

( ) exp( ) exp{ ( ) exp[ ( )]}

exp{ ( ) exp[ ( )]} exp( )

M x a a x x

a x x a x c

(3)

Equation (3) is a full model with 13 parameters. Based on

comparative analysis of over 500 profile scheduled model done

in [25], the majority profile were match with a simpler model

containing 7 parameters that consist of two components and

constants.

III. MACRO MODELS

A. Gravity Model

Gravity models are widely used for the analysis of macro-

level data, mainly if the availability data are in the form of flow

from an origin to a destination migration. Bijak [4] was defined

the initial assumption of this model by employing Newton's

Gravity Law. That is migration between regions i and j is

proportional to the product of the mass (size of population)

areas of origin and destination (Pi and Pj) and inversely

proportional to the distance between the two regions (dij). The

mathematical expression of this model is:

.i j

ij

ij

PPm G

d (4)

This is a continuous model which evolves not only variables of

population size but also socio-economic variables and others.

Distance variable is also experienced growth. It would involve

travel time that related with the availability of transportation.

To include this variable in the model, the migration data needs

to be performed as the origin-destination matrices, so that the

interaction between the regions would be more perceptible.

B. Spatial Autoregressive (SAR)

SAR models had been used by [37] with mathematical

models:

1o o d d w w n o o d dy W y W y W y X X d

(5)

where the dependence is based on the origin and destination.

Weighting matrix is calculated by using Kronecker

multiplication result (origin-base), (destination-base), and

(origin-to-destination-base). SAR model is more profitable

than the use of gravity models when the migration data in the

form of origin-destination contains some missing values.

C. Multinomial Logit Model

Multinomial Logit Model was developed by adding the

spatial competition variable to see the competitiveness of the

migration destination area [16]. The model is mathematically

expressed as:

1

1

exp( ) 1; ,

1exp( )

n Kij jn k

ij jJn k kj

ij j

i

V c WP c k j

k dV c

(6)

Pijn is the opportunity to move from the area of origin i to

destination j, Vijn is the value obtained from the displacement of

the area i to area j, cj is competition variable for regional j, θ is

parameter for the competition variable, Wk is the size of region

k, dkj is a distance between region k and j, where j, k=1,2,…,K.

D. Poisson and Negative Binomial Regression

Poisson regression is used to model migration by employing

origin and destination region variables. Migration data is

assumed to be Poisson distribution, yi|β ~ Pois (μi); for i = 1,

2,..., n. Mean (μi) would be connected with the independent

variable using the log link function, log( ) T

i ix . It is

assumed that there is a linear relationship between independent

variable and log mean. Poisson regression is not appropriate

for the data having variance not equal to the mean. It is

because if these conditions are happened then there is over-

dispersion, and Poisson-Gamma Mixture Model would be an

alternative approaches to overcome. When the data follow

, ( );i i i jy Pois and , ( , )i k v Gamma k v ,

then the marginal distribution of y would be Negative Binomial

[17].

IV. CONCLUSION

Modeling migration must be adapted to the purpose of

research and the availability of data. For interregional

migration in East Java having limited data requires the


selection of an appropriate model. Development of existing

models to fulfill the analysis needs is necessary, especially when

the data is limited. The models as gravity models, SAR,

multinomial logit models, and negative binomial regression are

appropriate to be employed to model the migration people in

East Java. Bayesian approach, on the other hand, is suggested

to be employed, because it would be more flexible as data

driven approaches, but it requires computational intensive

capabilities.

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http://eprints.soton.ac.uk/40692/


http://dx.doi.org/10.1068/a38264






http://dx.doi.org/10.1111/1467-940X.00001

http://dx.doi.org/10.1111/0033-0124.01052

http://dx.doi.org/10.1111/0033-0124.01052

http://repository.ipb.ac.id/handle/123456789/45432



http://dx.doi.org/10.1111/j.1467-985X.2009.00630.x

http://dx.doi.org/10.1111/j.1467-985X.2009.00630.x


M31-1

Abstract— This article explores the use of generalized

linear model (GLM) in modelling AIDS cases in Indonesia.

The analysis was based on longitudinal cumulative data of

32 provinces during the period 2004-2011. Year, group of

provinces, and prevalence were proposed to explain

variability of AIDS cases. Some models are proposed,

i.e.GLM with normal link function for cases and log-

natural cases (ln Cases), and gamma link function. AIC

and deviance were used as goodness of fit criteria of the

model. The best model is linear model with ln cases as

dependent variable and Year and Group as independent

variables. This model can explain 83 % variablity of the

data According to the model, in 2020 there will be

247,037AIDS cases in Indonesia.

Index Terms— AIDS cases, GLM

I. INTRODUCTION

ince the first detection of Acquired ImmunoDeficiency

Syndrom (AIDS) in Indonesia in 1985, the amount of

peoples with AIDS (AIDS cases) has been increasing with

year. In 2011, AIDS cases in Indonesia became more than

29.000 [1]. There is the necessity to estimate AIDS cases for

several needs, i.e. drug stock, and medical attention for HIV

infected and AIDS patients. Estimation is usually done through

determining growth model for AIDS cases.

Several techniques had been applied for modelling the

growth of AIDS cases. The study by [2] estimated cumulative

AIDS cases in Indonesia with EM algorithm using the amount

of people infected by HIV with assumption of incubation

periods 5-10 years. Previously, the author [3] has developed a

model of AIDS cases in Belgium with GLM, where the annual

AIDS cases is assumed to be Poisson’s process. Ministry of

Health of Indonesia also published the estimated of AIDS cases

in Indonesia every year. These estimations use single times

series of national AIDS cases.

AIDS in Indonesia spreads differently in 32 provinces. Only

province of West Sulawesi doesn’t have AIDS cases until the

end of 2011. In 2011, some provinces have more than 1000

cases and rapidly have been growing since 1985. On the other

hand, in some provinces AIDS cases grow slowly and only

have less than 100. At least there are three groups of provinces

according to the growth of AIDS cases. The first is group of

H. Hanum is Senior Lecture in Statistics, Department of Mathematics,

FMIPA, Sriwijaya University (phone: +62711 580765; fax: +62711 580059; e-

mail: linhanum@ yahoo.com.au). She is now studying for her PhD in Statistics

at School of Graduate Studies, Bogor Agricultural University

provinces with high growth. These provinces have AIDS cases

more than 1000 in 2011. While the last group has provinces

with AIDS

cases less than 100. The longitudinal data for 32 provinces is

shown in Fig 1.

Fig. 1. Plot of AIDS cases in 32 Provinces of Indonesia Years

2004 - 2011

Availability of data for AIDS cases for each province

becomes the advantage for modelling. The growth model can

be built based on longitudinal data of provinces. It is also

possible to build some alternative models including advanced

model.

Problem statement

Some model can be proposed for estimating AIDS cases in

Indonesia. Firstly the model may be built without grouping the

provinces then compares with grouping model. Secondly,

considering the growth of AIDS cases, the model may be

nonlinear, according previous research its exponential. This is

the reason of choosing between normal or gamma link

function. What is the real growth type of AIDS in Indonesia.

Applying those models for Indonesian AIDS cases will

answer these questions

1) Does grouping infuence the goodnes of the model?

2) Which is the real growth model: linear or exponensial?

3) Does GLM using normal link function with dependent

variable ln cases give similar model with GLM using gamma

link function with cases as dependent variable?

II. MATERIAL AND METHOD

A. Material

1. Longitudinal data of AIDS cases in Indonesia is

observation of 32 provinces for years 2004-2011.

Generalized Linear Model for Estimating AIDS Cases in

Indonesia

Herlina Hanum

S


M31-2

As mentioned before, based on growth type (see

Fig. 1), the provinces can be divided at least into 3

groups. The first group for high growth of AIDS

cases with more than 1000 cases in 2011. This

group consists of Papua, Jakarta, East Java, West

Java, Bali, Central Java, and West Kalimantan

provinces. The second group consists of provinces

with moderate growth. The provinces included in

this group are South Sulawesi, Riau, Yogyakarta,

North Sumatera, West Sumatera, Banten, Riau

Archipelago, North Sulawesi, East Nusa Tenggara,

Jambi, South Sumatera, West Nusa Tenggara,

Jambi , and Bangka-Belitung. The rest provinces,

which have less than 100 cases in 2011, become the

member of the third group.

B. Method

In order to answer the questions above, we propose some

model to be analyzed. These model are

1. General linear model for Indonesia the provinces

with normal link function for

Y = Xβ + ε

with Y is the AIDS cases as defendent variable, X

the matrix consists of vector 1 and year of

observation for ungroup model.

2. Adding group as independent variable to ungroup

model .

3. Exponensial model ln Y = Xβ + ε, that is GLM with

normal link funtion of ln Y. With and without group

as independent variable.

4. GLM model using gamma link function with AIDS

cases as dependent variable, and year and group as

independent variables.

Goodness of fit of the model measures by Akaike

Information Criteria (AIC) for GLM. For each GLM model

AIC is

where is maximized model log likelihood and p is the

number of explanatory variables (including the constant) [4].

The second criteria is deviance. According to [4] deviance is

the most useful category of residual for GLM and also the

most general form. This criteria likelihood ratio statistic

comparing a proposed model specification relative to saturated

model. Deviance is

Where is likelihood for proposed model, and for

saturated model [6].

III. RESULT

The data were analyzed using SPSS 18. GLM for AIDS

cases with year as single covariate using linear link function,

has Akaike’s Information Criteria (AIC) 4325.084. Adding

Group to this model reduced AIC to 4196.56. It means Group

make the linear model has better fit to the data.

However, these AIC values are very large compared with

the AIC = 672.729 of linear model with ln Cases as dependent

variable. This situation is accepted since the data do not meet

the assumption of homoscedasticity. Although the covariates

are significant in chi-squares test, it may be a false conclusion

due to the violent of the assumption. Logarithmic

transformation of Cases overcomes this problem.

TABEL 1.

DEVIANCE AND AIC VALUES OF PROPOSED MODEL FOR AIDS

CASES

Model Deviance AIC

Y = f(year) 1969E8 4325,084

Y = f(year, group) 1201E8 4196,560

Ln Y = f (year) 1056,46 1121,29

Ln Y = f(year, group) 191,710 672,729

Ln Y = f(year, group,

prev)

187,83 666,32

Gamma, Y = f(year,

group)

160,005 2938,691

Another variable that may influence the growth of AIDS

cases in Indonesia is the population of each province. This

variable is represented by prevalence of AIDS. Adding this

variable into last models didn’t make it has better fit. So the

population of province does not contribute to AIDS cases in

that province.

Logically, linear model with ln Cases as dependent variable

similar with GLM using Cases as dependent variable with log

link function. Do they give similar goodness of fit ? In fact the

second model has AIC = 2938,691, much larger than the one

of first model. It means the first model is the better one. On

the other hand, another goodness of fit criteria i.e deviance

leads to conclusion that Gamma link function as better model

since it has less values.

IV. DISCUSSION

In this article, the grouping of provinces significantly

influences the goodness of model. Dividing the 32 provinces

into 3 groups is subjective. It is only based on the number of

AIDS Cases in 2011. There may be another grouping that can

give better models.

Choosing two competing GLM model based on deviance

and AIC is little bit confusing. Since both of these criteria lead

to better model is the one with smaller value. Considering AIC

is negative of 2log likelihood of proposed model, so smaller

value of log likelihood will gives greater AIC. While deviance

measure the distance of 2 likelihood. The closer likelihood of

proposed model to the one of saturated model, the smaller the

value of deviance.

Here deviance of first model (191) larger than that of the

second model (160). But the difference is not big enough to

certain that GLM with gamma link function is better model

compare with the difference of AIC of both model. Parameters

estimate for both model are little bit similar. They yields


M31-3

almost similar prediction. Furthermore, in model selection, the

better model is the simpler. These facts lead to select linear

model of ln Cases for estimating AIDS Cases in Indonesia. In

addition, linear model has another advantage. That is

percentage of variation of AIDS Cases that explain by the

model which represent by R2. The selected model

Ln Cases = -748.613 + 0.378 Year – 2.606 group

has R2 adjusted 0.829. Which can be simply interpreted as

82,9 % variances in Cases can be explained by the exponent of

the model. This model gives different growth for each group.

According to this model, in 2020 there will be 228890 AIDS

cases in first group, 16899 in second group, and 1248 in last

group. Totally, there will be 247037 cases in Indonesia.

It maybe interesting to model each group separately. The

result is both linear and exponential models of AIDS cases with

year as single independent variable didn’t good enough to

explain AIDS cases in each group. They only have R2

adj less

than 50%. So using whole provinces data is more useful.

As comparison, using single series of cumulative Indonesian

AIDS cases, the growth model is linear.

Cases = -7738969 + 3862,3 Year

With R-Sq(adj) = 98,3%. This model is very good fit the

cumulative data. But it cannot explain the variability growth of

AIDS cases in provinces. Its only useful for estimating

nationally AIDS cases.

Some authors i.e [5] and [7] suggest Generalized

Estimating Equations(GEE) for longitudinal data. It will yield

better model if there is correlation between observations in a

subject, in this case is province. Unless the result is the same

with the one of GLM. However it is better to try in the next

time.

V. CONCLUSION

Some conclusions can be derived. Firstly, grouping the

provinces is necessary. Since it explain some variation in

AIDS Cases for some group of provinces. Secondly, AIDS

cases has Exponential growth model. The best model for

AIDS Cases in Indonesia based on longitudinal data is

Ln Cases = -748 + 378 year – 2.6 Group.

REFERENCES

[1] Directorate General CDC & Environmental Health, Ministry of Health,

Republic of Indonesia, Cases of HIV/AIDS in Indonesia. Report. Jakarta:

Ministry of Health, 2012.

[2] H. Hanum, “Studi simulasi algoritma EM dalam pendugaan kasus

infeksi HIV,” M.S. Thesis, Dept. Applied Statistics., Bogor Agricultural

Univ., Bogor, Indonesia, 1996.

[3] S. Wood, Generalized Linear Models. UK: University of Bath,1993.

[4] J. Gill, Generalized Linear Models: A Unified Approach, Series

Number: 07-134. California: Sage Publication, 2001.

[5] J.W Hardin and J.M. Hilbe, Generalized Estimating Equations. Boca

Raton, Florida: Chapman & Halls CRC Press, 2003.

[6] A.J. Dobson, An introduction to Generalized Linear Models. 2nd ed.

Boca Rton, FL: Chapman & Hall/CRC, 2002.

[7] Liang, K.-Y. and S.L. Zeger, Longitudinal data analysis using

generalized linear models. Biometrika, 73, 13-22, 1986.


I INTRODUCTION

EVERAL recent papers explain methods to model teaching

quality. For example paper by Ahmed et al. (2010) and

Barone et al. (2010). We have published several papers to

explain how to determine teaching quality of lecturer based on

questiner (e.g. Setiawan & Parhusip (2011a), Setiawan &

Parhusip (2011b) and Parhusip & Setiawan (2011). Related

paper is also presented in Setiawan (2011a) that can be

considered related to this paper. It is used binomial models

for answer of every item in the questioner. In this paper, it is

explained how to determine teaching quality of lecturer based

on questioner using objective Bayesian and multinomial

models.

II THEORY

Bayesian inference is often critized for its reliance on prior

distributions whore choice influences the conclusions. In

particular, in testing theory the necessity of assigning prior

probabilities to the two hypotheses appears awkward. The

objective Bayesian approach overcomes this criticism by an

objective choice assumed model and the available data. In this

paper we propose an objective Bayesian to analyze data of

questioner using multinomial distribution and objective

Bayesian methods.

We consider x = ( x1, x2, ...., xm ) as answer of items in a

questioner that has m questions (items) where xi is the number

of respondent that gives skor 1, 2 or 3 for the i-th questions.

Variable xi = ( xi1, xi2, xi3) can be considered as a multinomial

distribution with parameter n and p = ( p1, p2, p3). In this case

n is the number of respondent and pi is the proportion of

respondent that give scor i where i = 1, 2, 3. The probability

density function of xi = ( xi1, xi2, xi3) is

321

321

321

321321,,

)),,(|),,(( iii xxx

iii

iii pppxxx

npppxxxf

where xi1, xi2, xi3 = 0, 1, 2, ...., n, xi1 + xi2 + xi3 = n,

0 < p1, p2, p3 < 1 dan p1 + p2 + p3 = 1. The Fisher information

can be computed to be

)1(

)1(

1

1)1(

)1(

),(

212

1

21

21211

1

21

ppp

pn

pp

n

pp

n

ppp

pn

ppI

and the reference prior is given by

Adi Setiawan is a lecturer at Department of Mathematics, Faculty of

Science and Mathematics, Satya Wacana Christian University Jl. Diponegoro

52-60 Salatiga 50711 (corresponding author to provide e-mail:

[email protected]).

12

1

3

12

1

2

12

1

1

2/1

321

32111

1),,()(

ppp

ppppppp

.

Then, the reference prior is the Dirichlet( ½, ½, ½ )-

distribution. The posterior density function of p = ( p1, p2, p3 )

given x = ( x1, x2, x3 ) is

)),,(|),,(( 3213212 iii xxxppp

)),,(|),,((),,( 3213213211 pppxxxfppp iii

321

321

12

1

3

12

1

2

12

1

1iii xxx

pppppp

12

1

3

12

1

2

12

1

1321

iii xxxppp

.

Thus, the posterior 3( p | xi ) is Dirichlet( xi1 + ½, xi2 + ½,

xi3 + ½ )-distribution. The quotient of the density of xi =

( xi1, xi2, xi3) for two parameter values p = ( p1, p2, p3 ) and

q = ( q1, q2, q3 ) is given by

321

321

321

321

321

321

,,

,,

)|(

)|(

iii

iii

xxx

iii

xxx

iii

i

i

qqqxxx

n

pppxxx

n

qxf

pxf

and

3

33

2

22

2

11 lnlnln

)|(

)|(ln

q

px

q

px

q

px

qxf

pxfiii

i

i .

Kulback-Leibler divergence between the probability density

function f(xi | p) and f(xi | q) is given by

3

33

2

22

1

11 lnlnln)|(

q

px

q

px

q

pxEqpK iiip

3

33

2

22

2

11 lnlnln

q

pnp

q

pnp

q

ppn .

The intrinsic discrepancy between f(xi | p) and f(xi | q) is

)|(,)|(min),( pqKqpKqp .

Then the intrinsic statistic is given by

dpxppqqpExqd i

ppi )|(),(]),([),( 2 .

The intrinsic statistic cannot be found in closed form, but may

easily computed by numerical integration. Point estimation

q* will minimize intrinsic statitic, i.e.,

),(minarg)(** iq

i xqdxqq

where

= { ( q1, q2, q3) | 0 < q1, q2, q3 < 1 and q1 + q2 + q3 = 1 }.

To describe the method, suppose we have x = ( x1, x2, x3 ) =

(1,12,2) i. e. it is only 1 respondent gives score 1, 12

respondents give score 2 and 2 respondents give score 3.

Based on multinomial distribution model and by using

Determining Teaching Quality of Lecturer Based on

Questioner Using Multinomial Distribution & Objective

Bayesian

Adi Setiawan,

S


objective Bayesian method, we will get the estimation

parameter p = (p1, p2, p3) = (0,08, 0,88, 0,15) and the MLE of

parameter p = (p1, p2, p3) is (0,07, 0,80, 0,13). The estimate

will minimize intrinsic statistical value. In this case, the

intrinsic statistical value is presented in Figure 1. In other

hand, if we have x = ( x1, x2, x3 ) = (0,2,5) and by using

objective Bayesian method we will get (0,06, 0,29, 0,65) but,

the MLE is (0, 0,29, 0,71). Thus, we can see that p1 will not

be zero eventhough x1 = 0. Figure 2 presents the intrinsic

statistical value for p given data x = ( x1, x2, x3 ) =

(0,2,5).

0 1000 2000 3000 4000

0.0

00

.05

0.1

00

.15

0.2

00

.25

0.3

00

.35

Intrinsic Statistic value

Index

Intr

insi

c S

tatis

tic

Figure 1. The intrinsic statistical value for p given data

x = ( x1, x2, x3 ) = (1,12,2).

III. METHODS

Data consists of 120 sheets of questioner from 9 courses.

Every sheet of questioner contains answers of 16 items or

questions. Based on the answer of questioner for every

respondent, we can determine value of xi = ( xi1, xi2, xi3) i. e.

the number of score i where i = 1, 2, 3 for every courses and

then the parameter p = (p1, p2, p3) is estimated using objective

Bayesian method. We assume that answer of respondent for

every item will be independent each other. To measure the

teaching quality for every course we can use statistic

3/)32(%100 321 pppT

(in percent). The statistic T will be lay between 0 and 100

percent. The statistic T will give the measure of the quality of

lecturer for every course.

0 1000 2000 3000 4000

0.0

00

.05

0.1

00

.15

0.2

00

.25

0.3

0

Intrinsic Statistic value

Index

Intr

insic

Sta

tistic

Figure 2. The intrinsic statistical value for p given data

x = ( x1, x2, x3 ) = (0,2,5).

IV. RESULTS AND DISCUSSION

Based on 120 sheets of questioner form 9 courses, we

analyze the data using multinomial distribution model and

objective Bayesian method. Table 1 presents the result of the

teaching quality for every courses. The analysis of T

statistical value using T based on MLE and objective Bayesian

method are present in Table 2 and Table 3, respectively. We

can see that Course 4 becomes the higest teaching quality and

Corse 9 becomes the lowest teaching quality. Thus, the result

of analysis will be moreless same as the MLE and statistics T

because the number of items times the number of respondent

are large.

Tabel 1. Teaching Quality for every courses based on questioner sheet.

No. Course 16n x = ( x1, x2, x3 )

1 Course 1 352 (60, 175, 117)

2 Course 2 304 (40, 141, 123)

3 Course 3 208 (5, 96, 107)

4 Course 4 192 (2, 55, 135)

5 Course 5 208 (5, 96, 107)

6 Course 6 144 (6, 58, 80)

7 Course 7 176 (7, 94, 75)

8 Course 8 176 (23, 86, 67)

9 Course 9 224 (43, 148, 33)

The methods can be extended for the number of answer for

every item is bigger than three. The research can be continued

to a simulation study based on the model to see the property of


estimation for every value of parameter space.

Tabel 2. Teaching Quality for every courses based on MLE.

No. Course 16n p T

1 Course 1 352 (0,17, 0,5, 0,33) 72,06 %

2 Course 2 304 (0,13, 0,46, 0,41) 75,77 %

3 Course 3 208 (0,03, 0,46, 0,51) 83,01 %

4 Course 4 192 (0,02, 0,28, 0,70) 89,76 %

5 Course 5 209 (0,02, 0,46, 0,51) 83,01 %

6 Course 6 144 (0,04, 0,40, 0,56) 83,79 %

7 Course 7 176 (0.04, 0.53, 0.43) 79 ,55%

8 Course 8 176 (0,13, 0,49, 0,38) 75 %

9 Course 9 224 (0,19, 0,66, 0,15) 65,18%

Tabel 3. Teaching Quality for every courses based on objective Bayesian

method.

No. Course 16n p T

1 Course 1 352 (0,17, 0,5, 0,33) 72 %

2 Course 2 304 (0,14, 0,46, 0,40) 75,33 %

3 Course 3 208 (0,02, 0,46, 0,52) 83,33 %

4 Course 4 192 (0,02, 0,28, 0,70) 89,33 %

5 Course 5 209 (0,10, 0,56, 0,34) 74,67 %

6 Course 6 144 (0,04, 0,40, 0,56) 84 %

7 Course 7 176 (0.04, 0.54, 0.42) 79,33 %

8 Course 8 176 (0,14, 0,48, 0,38) 74,67 %

9 Course 9 224 (0,18, 0,66, 0,16) 66 %

REFERENCES

[1] Ahmed, I, M. M. Nawaz, Z. Ahmad, Zafar Ahmad, M. Z,

Shaukat, A. Usman, Wasim-ul-Rehman, N. Ahmed,

(2010), Does service quality affect student’s

performance? Evidence from institutes of higher learing,

African Journal of Bussiness M anagement Vol. 4 (12)

[2] Barone, S and E. L. Franco, 2010, TESF Methodology for

Statistics Education Improvement, Journal of Statistics

Education, Vol. 18 (3)

[3] H. A. Parhusip, H. A., & A. Setiawan (2011) Modelling

on Lecturer’s Performance with Hotteling-Harmonic-

Fuzzy, The 6th SEAMS GMU 2011 July 12-15.

[4] Setiawan, Adi & Hanna Arini Parhusip (2011)

Pengukuran Kualitas Pengajaran Dosen Berdasarkan

Kuesioner dengan Menggunakan Hotelling, Prosiding

SemNas Statistika Undip 2011.

[5] Setiawan, A., & Hanna A Parhusip (2011) Determine

Teaching Quality of Lecturer Based on Questioner Using

T Statistics, ICREM 5, Bandung, 22-24 October 2011.

[6] Setiawan, A. (2011) Penggunaan Metode Bayesian

Obyektif dalam Analisis Pengukuran Tingkat Kepuasan

Pelanggan berdasarkan Kuesioner, Prosiding Seminar

Nasional Matematika dan Pendidikan Matematika, UNY

Yogyakarta 3 Desember 2011.


PSM14-1

Abstract— The coal mining sector that is the mainstay

products of interest to investors in Kalimantan Selatan,

contributes about 17.56% of the Gross Domestic Product

of South Kalimantan. This paper described the application

of the spatial statistical technique, Inverse Distance

Weighting (IDW) and Ordinary Kriging (OK), to estimate

the mineral reserve such coal deposit in Kabupaten Hulu

Sungai Utara. Ordinary kriging and Inverse Distance

Weighting are linear interpolators as the methods in

mining grade control and mine resource estimation.

Kriging, that is commonly described as minimum variance

estimator, would give the best estimation when the

neighbourhood is properly defined. Kriging can be a very

effective statistical method for limiting the number of

samples needed to spatially characterize objects while still

insuring adequate data quality. The result indicate that

IDW and OK performed equally well in estimating the

thickness of coal deposit.

Index Terms— Inverse Distance Weighting, Ordinary

Kriging, A Coal Deposit.

I. INTRODUCTION

nterpolation is an estimation of a variable at an unmeasured

location from observed values at surrounding locations. All

interpolation algorithms (inverse distance squared, splines,

radial basis functions, triangulation, etc.) estimate the value at a

given location as a weighted sum of data values at surrounding

locations. Almost all assign weights according to functions that

give a decreasing weight with increasing separation distance.

Kriging assigns weights according to a (moderately) data-

driven weighting function, rather than an arbitrary function, but

it is still just an interpolation algorithm and will give very

similar results to others in many cases [1]. The estimates will

be fairly good if the data locations are fairly dense and

uniformly distributed throughout the study area regardless of

interpolation algorithm. The estimates will be unreliable if the

data locations fall in a few clusters with large gaps in between

regardless of interpolation algorithm. Almost all interpolation

algorithms will underestimate the highs and overestimate the

Dewi Sri Susanti is lecturer of MIPA Faculty, Lambung Mangkurat

University Banjarmasin (corresponding author to provide phone:

08152149700; e-mail: dew_oqi@ yahoo.com).

lows; this is inherent to averaging and if an interpolation

algorithm didn’t average we wouldn’t consider it reasonable.

Kriging is a geostatistical method of spatial data interpolation

that can be used to estimate mine resource. In 1963 G.

Matheron named Kriging after D.G. Krige, a South African

mining engineer, who used the technique to more accurately

predict the extent of gold deposits in unsampled areas [1].

Kriging is an interpolation method that optimally predicts data

values by using data taken at known nearby locations. Kriging

can be either two-dimensional or three-dimensional.

Kriging is a set of linear regression routines which minimize

estimation variance from a predefined covariance model.

Kriging is based on the assumption that the parameter being

interpolated at a site is a regionalized variable. A regionalized

variable varies in a continuous manner spatially so that data

values from points nearer each other are more correlated. Data

values from widely separated points are statistically

independent in kriging. [2].

There are some advantages of kriging i.e: helps to compensate

for the effects of data clustering, assigning individual points

within a cluster less weight than isolated data points, gives

estimate of estimation error (kriging variance), along with

estimate of the variable, Z, itself. Availability of estimation

error provides basis for stochastic simulation of possible

realizations of Z(u).

II. LINEAR SPATIAL INTERPOLATION

A. Inverse Distance Weighting

Inverse Distance Weighting (IDW) is one of the linear

interpolators to estimate spatial data, as is Ordinary Kriging

(OK). A relatively non-mathematical understanding of linear

weighted averaging can be gained from thinking about linear

regression. In linear regression, the relationship between two

variables, x and y, is considered to be a straight line (i.e.

linear). The formula for this straight line is simple: y = ax + b.

Where a is the slope of the line and b is the value of y when x

equals zero (i.e. the y-intercept). If we specify a particular

value of x we can therefore conveniently determine the

expected y value corresponding to this x. It doesn’t matter

whether we specify an x value which is very small or very

large, or anywhere in-between: the relationship between x and

y is always the same as the specified straight line. In other

words, the formula used to estimate y does not alter as the

Spatial Interpolation Comparison in Estimating A Coal

Deposit in Kabupaten Hulu Sungai Utara, South

Kalimantan, Indonesia

Dewi Sri Susanti

I


PSM14-2

magnitude of the x value changes [3].

A linear interpolator has this property: the weights we assign

to each of the N sample locations inside our estimation

neighbourhood are independent of the specific data values at

these locations. Think about the simplest kind of linear

interpolator, IDW. An IDW estimate assigns the weight to a

sample located within the estimation neighbourhood as:.

N

j j

ii

d

d

i

1

1

Where λ are the weights, d are the distances from each

sample location to the centroid of the block to be estimated

and α is the power. Once the power to be used is specified, the

ith

sample is assigned a weight that depends solely upon its

location (distance di to the centroid). Whether the sample at

this location had an average or extreme value does not have

any impact whatsoever on the assignment of di λ [4].

OK is a more sophisticated linear interpolator proposed by

Matheron (1962). OK’s advantage over IDW as a linear

estimator is that it ensures minimum estimation variance given:

a specified model spatial variability (i.e. variogram or other

characterisation of spatial covariance/correlation), and a

specified data/block configuration. The second criterion

involves knowing the block dimensions and geometry, the

location and support of the informing samples, and the search

(or “Kriging neighbourhood”) employed. Minimum estimation

variance simply means that the estimation error is minimised by

OK. Given an appropriate variogram model, OK will

outperform IDW because the estimate will be smoothed in a

manner conditioned by the spatial variability of the data

(known from the variogram).

B. Variogram

In ordinary kriging [5], a variogram is first constructed using

a spatial set of soil or sediment data, for example, from a site.

A variogram has two parts: an experimental data and a model

variogram. An experimental variogram is constructed by first

calculating the variance of each point in a dataset with respect

to each of the other points. The experimental variogram

consists of the plotted variances versus the distance between

each data point at the site. The typical variogram was

calculated using the following formulae:

hN

i

ii szhszhN

h1

2

2

1

The model variogram is a curved line through the experimental

variogram points. The model variogram represents a simple

mathematical function modeling the trend in the points of the

experimental variogram. The variogram in kriging can be used

to calculate the expected error of estimation at each target

interpolation point since the estimation error is a function of

the distance to surrounding data points. There are four types

of model functions that support for building model

variograms. Each of the functions are characterized by a

nugget, contribution and range. The four model supported are:

spherical, exponential, gaussian and power [6].

The expected estimation error is minimized in a least squares

sense in kriging by using the variogram to compute weights in

the kriging equations. For this reason, kriging is said to

produce the best linear unbiased estimate. In most mapping

software manuals, kriging is recommended as the best

interpolation method.

III. STATISTICAL ANALYSIS AND DATA

SUBDIVISION

The study was conducted on a coal deposit. The deposit

extends over an area of about 16 km2 in Hulu Sungai Utara,

South Kalimantan. The thickness anf the depth of coal deposit

was observed to estimate the value of unobserved area. Prior

to modeling, detailed statistical analyses of the composite data

were carried out, because these data are the basis for the ore

grade estimation. Table 1 presents the descriptive statistics of

the data sets containing all the values [6]. The table shows that

the distribution of data variable were not skewed, ( value of

kurtosis and skewness between -1 and 1) respectively.

Table 1. Basic statistics of the observed data set

Statistics X Y Thickness Depth

Mean 295922.12 9779851.44 1.13 14.68

N 112.00 112.00 112.00 112.0

0

Std. Deviation 61.92 68.72 0.39 8.02

Variance 3834.50 4723.08 0.15 64.38

Kurtosis -0.66 -0.91 -0.11 -0.81

Skewness 0.17 -0.32 1.00 0.30

Minimum 295756.00 9779715.00 0.68 1.55

Figure 1 presents the normal Q-Q plots of thickness and

depth of coaldata. From these plots it can be seen that

thickness and depth are normally distributed. However, K-S

tests conducted on the dataof these variables indicated that the

data follow a normal distribution and it was statistically

significant at 5% level of significance.


PSM14-3

Figure 1. Normal Q-Q Plots of Thickness & Depth of coal

deposit.

Since the data meet the assumption of normally distributed

and stationary then IDW and OK was applied to estimate the

coal data [7]. The spherical and Gaussian variogram performed

the best fitting for data covariance (Figure 2). The spherical

variogram characterized with nugget of 0.07, a sill of 0.175,

and a range of 20 m. The gaussian variogram characterized

with nugget of 0.07, a sill of 0.175, and a range of 30 m.

Figure 2. The spherical and Gaussian variogram

To derive an effective measure of model performance, the

data available for this study were divided into two sets: training

and testing. The model was trained using training data, and its

performance was validated using testing data. It is worth

pointing out that these two data sets should have similar

statistical characteristics: there is no point training the model

with data that has no relevance to the testing data [8]. This

would also lead to biased model performance This study

followed the conventional practice of randomly dividing the

data into training and testing sets. Instead of simple random

data division, the data were randomly divided in two groups.

Both mean and standard deviation values are close for all the

attributes. Further, the statistical similarity of the two data sets

was checked using F test. The F test result confirmed that both

the data sets are statistically similar at 0.05 level of

significance.

Table 2 Statistics of training and testing data

Statistics Data set X Y Thickness Depth

Mean Training 295922.12 9779851.44 1.13 14.68

Testing 296112.44 9779899.01 1.25 13.86

Std.

Deviation

Training 61.92 68.72 0.39 8.02

Testing 60.09 71.20 0.44 7.75

The validity of the OK model was established through a

comparative evaluation between IDW and OK. To derive a

legitimate model comparison, the same data set which was

used to train the OK model was used to developing the kriging

model. Finally, the effectiveness of the two models was

examined using the testing data set. For comparison of the

result, three statistical indices, mean error, R2 and mean

squared error were used. Table 3 shows the statistical summary

of the comparative results of the OK and IDW techniques for

both attributes. It is apparent from Table 3 that both IDW and

OK methods have performed equally well.

Table 3 Error statistics of IDW and OK based estimation of

testing data

Statistics Method Thickness Depth

Mean

Squared Error

IDW 0.000104 15.6632

OK 0.000088 11.0628

R2 IDW 0.774 0.651

OK 0.882 0.843

Mean Error IDW -0.001572 5.025

OK 0.002451 6.027

The mean squared error as well as R2 (coefficient of

determination) values indicate that the OK model works

slightly better than the IDW model for both variables

(thickness and depth of coal deposit. Further, the R2 values of

the OK model for both attributes are reasonably high, which

indicates that a reliable grade model can be constructed for the

deposit. All the modeling approaches had low prediction bias.

Figures 3 presents the contour plot of mining area for observed

value and estimating value using OK model.


PSM14-4

IV. SUMMARY

This paper used two techniques - Inverse Distance

Weighting (IDW) and Ordinary Kriging (OK) – to model the

thickness and depth of coal deposit in Hulu Sungai Utara,

South Kalimantan. The sample set was carefully divided into

two groups as modeling and testing sets to ensure that

performance evaluation was valid. Both approaches, IDW and

OK, performed equally (in term of mean error (bias) and mean

squared error) on both variables, thickness and depth of coal

deposit. Since the R2 values of OK model are higher than IDW

model, it apparent that prediction of OK model was slightly

better than IDW technique.

A. References

[1] Armstrong, M, Basic Linear Geostatistics, Springer,

Berlin, 1998.

[2] Krige, D. G, A basic persprective on the Roles of

Classical Statistics, Data Search Routines, Conditional

Biases and Information and Smoothing Effects in Ore

Block Evaluations. Proceedings Conferenceon Mining

Geostatistics. Kruger National Park. South Africa. pp: 1-

10, 1996.

[3] Cressie, N. Statistic for Spatial Data, Revised Edition.

New York: Willey. 1993.

[4] Matheron, G. Principles of Geostatistics. Economic

Geology. 58:1246-1266. 1963.

[5] Abdullah, Arik. Effects of Search Parameters on Kriged

Reserve Estimation. International Journal of Mining and

Geological Engineering. 8:319-331. 1990.

[6] David, M. Geostatistical Ore Reserve Estimation

(Developments in Geomathematics 2). Elsevier.

Amsterdam. 1977.

[7] Vann, J. and Guibal, D. Beyond Ordinary Kriging – An

Overview of Non-Linear Estimation. In Mineral

Resource and Ore Reserve Estimation. The AusIMM

Guide to Good Practice. Monograph 23. pp: 249-256.

2000.

[8] Samanta, B, Ganguli, R. and Bandopadhyay. Comparing

The Predictive of Neural Networks with Ordinary Kriging

in Bauxite Deposit. Mining Technology (Trans. Inst. Min.

Metall. A). Vol. 114:A129-A139. September 2005.

The Third Basic Science International Conference - 2013 AU-1

NAME Institute COUNTRY E-Mail

Dann Mallet Queensland University of

Technology Australia [email protected]

Hideo Tsuboi Nagoya University Japan [email protected]

Kwang-Ryeol

Lee

Korea Institute of Science and

Technology South of Korea [email protected]

Lidia Morawska Queensland University of

Technology Australia [email protected]

M. Nurhuda Brawijaya University Indonesia [email protected]

Nurul T.

Rochman

Indonesian Institute of

Sciences Indonesia [email protected]

Petr Solich Charles University Czech

Republic [email protected]

S.K. Lai National Central University Taiwan [email protected]

Agus Z. Arifin Sepuluh Nopember Institute

of Technology Indonesia [email protected]

Adi Setiawan Satya Wacana Christian

University Indonesia [email protected]

Amran Sepuluh Nopember Institute

of Technology Indonesia amranihsani@ gmail.com

Ani Budi Astuti Brawijaya University Indonesia [email protected]

Anik Djuraidah Bogor Agricultural University Indonesia [email protected]

Ari Suparwanto Gadjah Mada University Indonesia

Arif Rahman

Hakim University of Indonesia Indonesia

Arman Gadjah Mada University Indonesia [email protected]

Asep Saefuddin Bogor Agricultural University Indonesia [email protected]

Brodjol S. S.

Ulama

Sepuluh Nopember Institute


Ch. Rini Indrati Gadjah Mada University Indonesia

Dewi Sri

Susanti

Lambung Mangkurat

University Indonesia dew_oqi@ yahoo.com

Endang

Widiyastuti University of Indonesia Indonesia

Eprina Eksa

Gutami Yogyakarta State University Indonesia [email protected]

Erma Suwastika Bandung Institute of

Technology Indonesia [email protected]

Erni Tri Astuti Sepuluh Nopember Institute


Hardinsyah Bogor Agricultural University Indonesia [email protected]

Heri Kuswanto Sepuluh Nopember Institute


Herlina Hanum Sriwijaya University Indonesia linhanum@ yahoo.com.au


Hossein

Mohammadikia

Universiti Teknologi

Malaysia Malaysia

I Nyoman

Budiantara



Ida Mariati

Hutabarat Cenderawasih University Indonesia [email protected]

Intan Muchtadi-

Alamsyah

Bandung Institute of

Technology Indonesia

Irhamah Sepuluh Nopember Institute


Ismaini Zain Sepuluh Nopember Institute


J. K. Wororomi Sepuluh Nopember Institute


Kartika

Fithriasari



Lisa Nesti Akademi Teknologi Industri

Padang Indonesia [email protected]

M. Mashuri Sepuluh Nopember Institute


Md Nor bin

Bakar

Universiti Teknologi

Malaysia Malaysia

Moch. Aruman

Imron Brawijaya University Indonesia [email protected]

Mohamad

Dokhi Sekolah Tinggi Ilmu Statistik Indonesia [email protected]

Muhammad

Rifki Taufik Yogyakarta State University Indonesia [email protected]

Muhammad

Syifa’ul Mufid



Mukhsar Sepuluh Nopember Institute


Nelly Oktavia

Adiwijaya Jember University Indonesia [email protected]

Nur Iriawan Sepuluh Nopember Institute


Preatin Sepuluh Nopember Institute


Purhadi Sepuluh Nopember Institute


Rahmawati

Pane


of Technology Indonesia

[email protected]

d

Rara Sugiarti Sebelas Maret University Indonesia

Rita Diana Sepuluh Nopember Institute


Salmah Gadjah Mada University Indonesia

Satwiko

Darmesto

National Institute of Public

Administration Indonesia [email protected]


Scott McCue Queensland University of

Technology Australia

Sony Sunaryo Sepuluh Nopember Institute

of Technology Indonesia sonny_s@ statistika.its.ac.id

Sri Subanti Sebelas Maret University Indonesia [email protected]

Subiono Sepuluh Nopember Institute

of Technology Indonesia

Sutikno Sepuluh Nopember Institute


Tony Karnain Universiti Teknologi

Malaysia Malaysia [email protected]

Trisilowati Brawijaya University Indonesia [email protected]

Wendy Hartanto

Deputy for Population

Management National Family

Planning Coordination Board

(BKKBN)

Indonesia [email protected]

Widodo Gadjah Mada University Indonesia

The Third Basic Science International Conference - 2013 ACK01

Acknowledgement The Program Committee would like to thank the followings for their supports:

Universitas Brawijaya

PT. Semen Gresik

PT. PLN (Persero)

preface - universitas brawijaya...13.00 - 13.30 invited a/prof. dann mallet investigating chlamydia...

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