abstracts - university of new south wales...ashish goyal 21exchangeability and g-measures louise...

Wednesday 1st October, 9:30am-5pmColombo Theatres B & C

2014 School Postgraduate Conference

Abstracts

09:30-‐09:40

10:10-‐10:15Parallel Session 1 (Chair: Anna Tomskova) Parallel Session 2 (Chair: Thais Rodrigues)

Stefan Riha Boris BerangerThe Construction of a 3-‐d Neutral Density Variable for Arbitrary Data Sets

Likelihood based estimation method for Extreme Dependence Models

Benoit Pasquier Kylie-‐Anne RichardsPlumbing of the biological pump Heavy-‐tailed features and dependence in limit order book

volume profiles in futures marketsBryce Kerr Damien WeeLower bounds for the Riemann zeta function on short intervals of the critical line

Parameter Estimation in the COGARCH(1,1) model using Incomplete Data Algorithms

11:00-‐11:20

11:50-‐11:55Parallel Session 3 (Chair: Bryce Kerr) Parallel Session 3 (Chair: Boris Beranger)

Guilherme Souza Rodrigues Sabarina Binti ShafieFunctional regression ABC for non-‐parametric density estimation

A posteriori error estimates for semidiscrete and fully discrete finite element methods for initial-‐boundary value problems

Wei Wu Mengzhe ZhangA New Class of Singular Stochastic Optimal Control Problems

Asymptotics of the Europe option with regime-‐switching model

Xin Gao Juan Ignacio Ortega PiwonkaHermite functions and Hardy's uncertainty principle Stochastic resonance and bias to cyclic motion in

overdamped stochastic systemsNguyen Hong Le Carlos Enrique Aya MorenoIncenter Circles, chromogeometry, and the Omega triangle

Wavelet density estimation with applications to image registration / New wavelet-‐based density estimation in higher dimensions

12:55-‐13:40

14:10-‐14:15Parallel Session 5 (Chair: Yuehua Li) Parallel Session 6 (Chair: Benoît Pasquier)

Eric Kwok Bo WangSpectral Partitions of Dynamical Networks Modelling Insurance Claim DevelopmentAshish Goyal Louise WilkinsonMathematical modelling of hepatitis D and hepatitis B virus

Exchangeability and G-‐measures

Austen Erickson Wanchuang ZhuSubdiffusion and Early Stage HIV Infection An unified bayesian approach to kinetic model estimation

in dynamic Positron Emission TomographyCatheryn Gray Gordana PopovicThe Akt Switch Covariance modelling of discrete data

15:15-‐15:35

Parallel Session 7 (Chair: Ashish Goyal) Parallel Session 8 (Chair: Austen Erickson)Xin Zhang Yu-‐Heing TingApproximation Bayesian computation methods using Composite Likelihood

Decadal changes in Southern-‐Ocean ventilation inferred using a maximum entropy approach

Thais Carvalho Valadares Rodrigues Yuehua LiNoncrossing Bayesian quantile regression Double Diffusive Interleaving: Properties of the Steady

State (Finite Prandtl Number)Xin Lei Nina RibbatDynamic Non-‐parametric Bayesian Mixture Models Dynamics of the estuary-‐shelf exchange off Sydney and

the impact on a purpose buit Offshore Artifical Reef

17:00-‐19:00

Time

09:40-‐10:10

10:15-‐10:10

10:30-‐10:45

10:45-‐11:00

11:20-‐11:50

11:55-‐12:10

12:10-‐12:25

12:25-‐12:40

12:40-‐12:55

A discrete time random walk model for anomalous diffusion with reactions and forcing

Morning Tea

Isaac DonnellyWelcome

Theatre 1 Theatre 2

Lunch

Tuning Penalized Regression Models using ERICFrancis Hui

After Party -‐ White House

13:40-‐14:10

14:15-‐14:30

14:30-‐14:45

14:45-‐15:00

15:00-‐15:15

15:35-‐15:50

15:50-‐16:05

16:05-‐16:20

Anna TomskovaSchur multipliers and applications

Afternoon Tea

Jieyi HeTesting for Serial Dependence in Binomial Time Series RegressionYuguang Wang

16:20-‐16:35

16:35-‐16:55Computation of isotropic random fields on spheres via needlet decomposition

Conference Program

Oral Sessions 11 A discrete time random walk model for anomalous diffusion with reactions and forcing

Isaac Donnelly

2 The Construction of a 3-d Neutral Density Variable for Arbitrary Data SetsStefan Riha

3 Likelihood based estimation method for Extreme Dependence ModelsBoris Beranger

4 Plumbing of the biological pumpbenoit pasquier

5 Heavy-tailed features and dependence in limit order book volume profiles in futures marketsKylie-Anne Richards

6 Lower bounds for the Riemann zeta function on short intervals of the critical lineBryce Kerr

7 Parameter Estimation in the COGARCH(1,1) model using Incomplete Data AlgorithmsDamien Wee

8 Tuning Penalized Regression Models using ERICFrancis Hui

9 Functional regression ABC for non-parametric density estimationGuilherme Souza Rodrigues

10 A posteriori error estimates for semidiscrete and fully discrete finite element methods for initial-boundary valueproblemsSabarina binti shafie

11 A New Class of Singular Stochastic Optimal Control ProblemWei Wu

12 Asymptotics of the Europe option with regime-switching modelMengzhe zhang

13 Hermite functions and Hardy’s uncertainty principleXin Gao

14 Stochastic resonance and bias to cyclic motion in overdamped stochastic systemsIgnacio Ortega

15 Incenter Circles, chromogeometry, and the Omega triangleNguyen Hong Le

16 Wavelet density estimation with applications to image registration / New wavelet-based density estimation inhigher dimensionsCarlos Enrique Aya Moreno

17 Schur multipliers and applicationsAnna Tomskova

18 Spectral Partitions of Dynamical NetworksEric Kwok

19 Modelling Insurance Claim DevelopmentBo Wang

20 Mathematical modelling of hepatitis D and hepatitis B virusAshish Goyal

21 Exchangeability and G-measuresLouise Wilkinson

22 Subdiffusion and Early Stage HIV InfectionAusten Erickson

23 An unified bayesian approach to kinetic model estimation in dynamic Positron Emission TomographyWanchuang Zhu

24 The Akt SwitchCatheryn Gray

25 Covariance modelling of discrete dataGordana Popovic

26 Approximation Bayesian computation methods using Composite LikelihoodXin Zhang

27 Decadal changes in Southern-Ocean ventilation inferred using a maximum entropy approachYu-Heing Ting

28 Noncrossing Bayesian quantile regressionThais Carvalho Valadares Rodrigues

29 Double Diffusive Interleaving: Properties of the Steady State (Finite Prandtl Number)Yuehua Li

30 Dynamic Non-parametric Bayesian Mixture ModelsXin Lei

31 Dynamics of the estuary-shelf exchange off Sydney and the impact on a purpose buit Offshore Artifical ReefNina Ribbat

32 Testing for Serial Dependence in Binomial Time Series RegressionJieyi He

33 Computation of isotropic random fields on spheres via needlet decompositionYuguang Wang

Index of Authors 35

Postgrad Conference, October 1, 2014

A DISCRETE TIME RANDOM WALK MODEL FOR ANOMALOUSDIFFUSION WITH REACTIONS AND FORCING

Isaac Donnelly

School of Mathematics and Statistics, UNSW

ABSTRACT

The continuous time random walk, introduced in the physics literature by Montroll and Weiss, has been widelyused to model anomalous diffusion in external force fields. One of the features of this model is that the governingequations for the evolution of the probability density function, in the diffusion limit, can generally be simplifiedusing fractional calculus. This has in turn led to intensive research efforts over the past decade to develop robustnumerical methods for the governing equations, represented as fractional partial differential equations. Here weintroduce a discrete time random walk that can also be used to model anomalous diffusion in an external forcefield and with non-linear reactions. The governing evolution equations for the probability density function sharethe continuous time random walk diffusion limit. Thus the discrete time random walk provides a novel numericalmethod for solving anomalous diffusion equations in the diffusion limit, including the fractional Fokker-Planckequation. This method has the clear advantage that the discretization of the diffusion limit equation, which isnecessary for numerical analysis, is itself a well-defined physical process. Some examples using the discretetime random walk to provide numerical solutions of the probability density function for anomalous subdiffusion,including forcing and reactions, are provided.

Biography

I am a third year applied maths PhD student working under the supervision of Prof. Bruce Henry. I am interestedin complex phenomena including anomalous diffusion and transport on networks.

1


THE CONSTRUCTION OF A 3-D NEUTRAL DENSITY VARIABLE FORARBITRARY DATA SETS

Stefan Riha


ABSTRACT

The Neutral Density variable allows inference of water pathways from thermodynamic properties in the globalocean, and is therefore an essential component of global ocean circulation analysis. The widely used algorithm forthe computation of Neutral Density yields accurate results for data sets which are close to the observed climatolog-ical ocean. Long-term numerical climate simulations, however, often generate a significant drift from present-dayclimate, which renders the existing algorithm inaccurate. To remedy this problem, new algorithms which operateon arbitrary data have been developed, which may potentially be used to compute Neutral Density during runtimeof a numerical model. We review existing approaches for the construction of Neutral Density in arbitrary datasets, detail their algorithmic structure, and present an analysis of the computational cost for implementations on asingle-CPU computer. We discuss possible strategies for the implementation in state-of-the-art numerical models,with a focus on distributed computing environments.

Biography

I’m doing a PhD in physical oceanography, and it’s my second year. Originally I’m from Austria. I suffer fromspecific social phobia related to all forms of public speaking, and I’m grateful for this opportunity to practice.

2


LIKELIHOOD BASED ESTIMATION METHOD FOR EXTREMEDEPENDENCE MODELS

Boris Beranger


ABSTRACT

The study of Multivariate Extremes is a very challenging topic and covers a wide range of applications includingenvironmental phenomena, financial indexes or insurance losses. For decision making purposes, experts in thesefields wish to answer questions about the joint behaviour of a set of variables when above some high thresholdor about the maximum values that some variables may reach within the next 10, 20 50 years. Classical resultsfrom univariate extreme value theory provide a well-established framework for modelling the marginal behaviour.When dealing with several variables it is crucial to be able to model the extremal dependence structure.

Multivariate extreme value theory provides an approximate distribution for vectors of component-wise maximawhich can be useful for describing the probabilities that at least one component exceed a high threshold or all thecomponents exceed some high thresholds, since in both cases these are modelled through the spectral measure.Several inferential methods have been explored for inferring the extremal dependence and we will focus here onthe parametric approach.

Both likelihood based and Bayesian methods have been investigated for estimating the parameters of extremaldependence models. Examples of methods based on the likelihood approach are the approximate likelihood andthe composite likelihood. The former approach will be considered here to fit the most commonly used models.Original questions will be answered in an analysis of several air pollutants recorded in the city of Leeds, UK.

Biography

I am at the start of the third year of my PhD done in cotutelle between the School of Mathematics and Statisticshere at UNSW and the Theoretical and Applied Statistics Laboratory (LSTA) at Universit Pierre and Marie Curie(UPMC), Paris. My supervisors are A.Prof Scott Sisson (UNSW) and Prof Michel Broniatowski (LSTA). I amalso co-supervised by Dr Simone Padoan (Bocconi University of Milan). My main area of research is ExtremeValue Theory which I like to apply to environmental phenonmena.

3


PLUMBING OF THE BIOLOGICAL PUMP

Benoit Pasquier


ABSTRACT

Nutrient transport and biological teleconnections of Ocean surface regions are diagnosed in a data-assimilatedcirculation model coupled to a jointly optimized simple phosphorus cycling model. These teleconnections paintthe plumbing of the biological pump: phytoplankton takes up phosphate (PO4) in the euphotic layer, ”pumps” it asdissolved organic phosphorus (DOP) through the whole water column, until it is remineralized in the ocean depthsand ultimately transported to the surface where it is available again for uptake. The biological pump efficiency(39%) is redefined and computed. Ocean surface regions where biological production takes its origin are defined,out of which major contributors as well as biological leaks are determined: The high latitude ocean regions providea large quantity of phosphate to other oceans, but contribute very lightly themselves to the biological pump. Whilethe easternmost part of the tropical oceans produce large quantities of utilized phosphorus which is pumped for longaverage transit times. Using Green functions and adjoint techniques, flow rates, masses in transit, and timescalesof biologically utilized nutrients between surface regions of interest are computed: the easternmost part of tropicalocean basins provide the majority of the biology, which reemerges predominantly in the high latitudes. Time-dependent path densities of major teleconnections are then computed, which paint a very detailed and quantitativepicture of the phosphorus cycle within the ocean interior: paths associated with long transit times (>1000 yrs)spread through the entire ocean, but are concentrated in the deep Northernmost Pacific, while paths associatedwith short transit times (<500 yrs) are more localised, and restricted mostly to the surface currents.

Biography

I am a mathematics enthusiast. I studied pure mathematics in Ecole Polytechnique in France, then turned tofinancial mathematics in Paris-Dauphine University, and ended studying environmental sciences at UNSW in 2010which is why I arrived in Australia. I have now been putting my mathematical skills to use in studying tracers inthe oceans through this PhD since early 2013, and have yet to submit my first article.

4


HEAVY-TAILED FEATURES AND DEPENDENCE IN LIMIT ORDER BOOKVOLUME PROFILES IN FUTURES MARKETS

Kylie-Anne Richards


ABSTRACT

This paper investigates attributes of the stochastic structures of the volume profiles in each level of the LimitOrder Book (LOB). The analysis is performed via statistically rigorous methods carried out to examine futuresmarket Limit Order Book data. In particular, we investigate empirically three families of models: alpha-stable,Generalized Pareto distribution (GPD) and Generalized Extreme Value (GEV) and find that there is statisticalevidence that heavy-tailed sub-exponential volume profiles occur on the LOB bid and ask and on both intra-dayand inter-day time scales. In futures exchanges, the heavy tail features are not asset class dependent and theyoccur on ultra or mid-range high frequency data. Of the distributions and estimation methods considered, the GPDMLE provided the best fit for all assets. We demonstrate the impact of the appropriate modeling of the heavytailed volume profiles on a commonly used liquidity measure, XLM. In addition, we demonstrate that utilizing theGPD distribution to model LOB volume profiles allows one to avoid over-estimating the round trip cost of tradingand also avoids erroneous estimations of volume leading to significant LOB imbalances in low count assets. Weconclude that the building blocks for a volume forecasting model should account for heavy tails, time varyingparameters and long memory present in the data.

Biography

I’ve worked in banking since 2004 and Im now a co-director of QuantTrade Research, a private proprietary tradingcompany (aka hedge fund). I started my PhD in Stats at UNSW in 2011. My study utilizes high frequency financialmarket data and the research is on dynamic models of the limit order book. Recently my 4 year old Thomas askedwhat I did at ’school’, I told him I built an Extremogram. He thought that was cool and it is now the name of hisnew transformer.

5


LOWER BOUNDS FOR THE RIEMANN ZETA FUNCTION ON SHORTINTERVALS OF THE CRITICAL LINE

Bryce Kerr


ABSTRACT

We consider a problem first studied by Karatsuba, of giving lower bounds for the Riemann zeta function on shortintervals of the critical line. Karatsuba conjectured that there exists some function ∆ = ∆(T ) → 0 as T → ∞such that for some fixed A > 0 we have

maxt∈[T,T+∆]

|ζ(1/2 + it)| > T−A,

where ζ(s) is the Riemann zeta function. Some progress towards this conjecture has been made, although it stillseems out of reach given the current state of knowledge about the vertical distribution of the zeros of ζ(s). Weshow Karatsuba’s conjecture holds for almost all T , in the sense of measure.

Biography

I did my undergraduate and honours at the University of Sydney and spent the first year of my PhD at MacquarieUniversity before I transferred to UNSW and have been here for about one year. My main interests are in numbertheory and most of my work has revolved around exponential and character sums.

6


PARAMETER ESTIMATION IN THE COGARCH(1,1) MODEL USINGINCOMPLETE DATA ALGORITHMS

Damien Wee


ABSTRACT

Discrete time GARCH models (Bollerslev [1986]) have become popular in financial econometrics as they arecapable of capturing certain stylized features usually exhibited from financial returns data such as heavy tails,non-constant volatility and being uncorrelated but not independent. However, much of the theory for these discretetime GARCH models was developed at a time when computational resources were limited and as such, much ofthe analysis has been based on the assumption that the data is observed at equally spaced time points. Nowadayswith the increasing availability of high frequency intraday data, this has spurred interest in analyzing financialdata sets with observations that are irregularly spaced in time. One way to proceed is to take these observationsas irregularly spaced realizations of an underlying continuous time process. A continuous time analogue to theGARCH model, dubbed the COGARCH, which retains the desirable features of its discrete time counterpart, wasdeveloped in Kluppelberg [2004]. Since its inception there have been several methods developed for parameterestimation in the COGARCH model, however each with their own limitations. Ive been looking at developingnew parameter estimation methods for this model. Currently Im attempting to employ the use of simulation basedmethods associated with incomplete data problems such as the Monte Carlo Expectation Maximization and MonteCarlo Newton Rapson.

Biography

Im roughly one and a half years into my project. My supervisors are William Dunsmuir and Feng Chen. I am quiteinterested in most things related to Quantitative Finance, however specifically my research so far has been focusedon looking at the modelling of high frequency financial data.

7


TUNING PENALIZED REGRESSION MODELS USING ERIC

Francis Hui


ABSTRACT

Penalized likelihood methods are a powerful approach for variable selection in regression modeling, with wide-ranging applications in ecology, epidemiology, and bioinformatics amongst other fields. A well-known and com-monly applied penalty is the adaptive lasso, although like all penalties, its asymptotic and finite sample perfor-mance depends critically on the choice of tuning parameter. A popular method for choosing the tuning parameteris via information criteria, notably those based on AIC and BIC. Their use however lacks motivation given theywere derived for the unpenalized maximum likelihood framework.

In this talk, I propose the Extended Regularized Information Criterion (ERIC) for choosing the tuning parame-ter in adaptive Lasso regression. ERIC is derived by directly considering the effects of applying the adaptive lassopenalty (or equivalently, the Laplace prior) on the bias-variance tradeoff inherent in regression modeling. In thesetting where the number of covariates increases with sample size, ERIC is shown to asymptotically identify thetrue model. Furthermore, simulation studies demonstrate ERIC can wipe the floor with criteria like BIC currentlyused to choose the tuning parameter. As an illustration, ERIC is applied to construct a penalized logistic regressionfor modeling species distributions along the Great Barrier Reef.

Biography

In my spare time, I like long walks on the beach, getting caught in the rain, and statistics. Actually scrap that...inmy spare time I like statistics.

8


FUNCTIONAL REGRESSION ABC FOR NON-PARAMETRIC DENSITYESTIMATION

Guilherme Souza Rodrigues


ABSTRACT

In this work we propose a new non-parametric procedure for modelling a set of associated density functions, eachof which relates to a different group. This recurrent statistical challenge arises, for example, in the managementcontext when one wants to compare the density of the daily profit of different branches of a given company. As thedensities are affected by common factors, and thus might have similar traits, the estimation can be substantiallyenhanced by sharing strength across the existing groups.

In a Bayesian approach, we introduce a hierarchically structured prior, defined over functions, using convenienttransformations of Gaussian processes. With this formulation, each observation from the prior corresponds to aset of density functions, rather than a vector of finite dimension. Inference is performed through a combinationof Approximate Bayesian Computation (ABC) and functional regression adjustment. The well-known Kernelestimator (computed for each group) plays the role of the summary statistic in the ABC mechanics. This work isunderstood to be the first to use ABC to estimate infinite-dimensional parameters. By avoiding MCMC methods,the proposed technique provides approximate posterior samples at a considerable lower computational cost. Weillustrate some interesting properties and give further insight of the method through an instructive example. Thisis joint work with David Nott and Scott Sisson.

Biography

Guilherme Rodrigues is a PhD candidate at University of New South Wales under supervision of A/Prof. ScottSisson, being particularly engaged in the development of Approximate Bayesian Computation (ABC) methods.He obtained his bachelor and master’s degrees in Statistics at the Universidade de Brasilia Brazil. Before pursuinghis PhD, Guilherme worked for four years as statistical analyst for the Brazilian government at the Federal DistrictCourt of Justice.

9


A POSTERIORI ERROR ESTIMATES FOR SEMIDISCRETE AND FULLYDISCRETE FINITE ELEMENT METHODS FOR INITIAL-BOUNDARY

VALUE PROBLEMS

Sabarina Binti Shafie


ABSTRACT

This study is devoted to a posteriori error estimation of finite element methods for initial-boundary value problems.A posteriori error estimates are known as a fundamental component in the design of efficient adaptive algorithmsfor solving initial-boundary value problems and a tool to evaluate the effectiveness of the approximate solutions.This approach of a posteriori error estimates has successfully been employed for nonlinear parabolic and Sobolevequations. The error estimates are computed locally on each element, which allows the flexibility on controllingthe error estimates to satisfy certain accuracy. Due to this, we are able to reduce the cost of computation foradaptive scheme by improving the estimates only on the necessary elements, instead of computing on the wholeinterval of the problem. The overall aim of this study is to produce a complete a posteriori error estimations ofsemidiscrete and fully discrete finite elements methods for Burgers’ equation.

Firstly, we target to produce an alternative method for the time discretization in the fully discrete version ofthe finite element methods. Then, we focus on a posteriori error estimations of semidiscrete and fully discrete H1-Galerkin Mixed Finite Element Methods. Finally, we aim to generate an adaptive scheme for the finite elementmethod.

Biography

• Third year PhD student in School of Mathematics and Statistics

• Malaysian, sponsored by Malaysia Ministry of Higher Education.

• Academic trainee / tutor in Sultan Idris Education University (UPSI), Malaysia.

10


A NEW CLASS OF SINGULAR STOCHASTIC OPTIMAL CONTROLPROBLEM

Wei Wu


ABSTRACT

In a market with multiple agents, information available to different agents need not be the same. In this case, theinformed agent chooses a strategy based on his private information, the noise agent chooses his strategy randomly,and the market maker sets the price and clears the market. In a market of this form, the existence of marketequilibrium is an important question in mathematical finance, since it allows us to test how quickly the informationis incorporated into the price of an asset. Our aim is to investigate the existence of market equilibrium if everyagent optimizes their own performance. In order to formulate the model, we have to study a new class of singularstochastic optimal control problems that cannot be solved by using the classical Hamilton-Jacobi-Bellman (HJB)equation. This new class of control problems was proposed by Larsy and Lions who make the assumption that thestate process of the control problem follows a stochastic differential equation driven by Brownian noise. We willgeneralize their results by assuming the state process is driven by Lvy type noise, and show that the similar resultshold.

Biography

After obtaining the Bachelor of Science (Advanced Mathematics) from UNSW, I started my PhD and continue mystudy at UNSW. I am currently in the third year of my research program, and working in the area of stochasticoptimal control and its applications in finance. My primary interest is in financial mathematics, and in particularin the applications of control theory in finance.

11


ASYMPTOTICS OF THE EUROPE OPTION WITH REGIME-SWITCHINGMODEL

Mengzhe Zhang


ABSTRACT

In a regime-switching model, we assume the price movement has multi-state and a state variable is introducedto model the underlying state. The model could capture new features than usual model. As the state variable ismodel by a Markov Chain, to calculate the exact solution of the option prices is time consuming and the explicitsolution is also complicated. My research interest is to use asymptotic methods to approximate the option priceswith regime-switching model, which cost less time and have a reasonable accuracy level.

In the past 12 months, I spend first few months in finding short-maturity asymptotics for Europe call optionswith regime-switching model using the asymptotic theory of Amel Bentata and Rama Cont (2012). In my results,the occupation time distribution function is approximated by a power series of the exact function. I also comparedto distribution functions in matlab. The figure shows that if the maturity time is short the approximated function hasa reasonable error and the shape of the function is sensitive to the value of transaction parameter. Currently, I amtrying to use the saddlepoint approximation method (Paul Glasserman,2008) to approximate the price distributionfunction of the two state regime-swithching models. First, we find the moment generating function of the assetprice. Then we apply Lugannani-Rice formular (1980) or Liebermans approximation (1994) to approximate theprobability distribution function of the asset price. At last, we use these results to calculate the option prices.

Biography

My name is Mengzhe Zhang and I come form China mainland. I completed my undergraduate study at theUniversity of Auckland. This year is my second year in researching my topic. My research interest is to useasymptotic methods to approximate the option prices with regime-switching model, which cost less time and havea reasonable accuracy level.

12


HERMITE FUNCTIONS AND HARDY’S UNCERTAINTY PRINCIPLE

Xin Gao


ABSTRACT

The uncertainty principles states that a function and its Fourier transform cannot both decay very quickly at infinity.There are, in fact, many ways to make the above statement precise. Here we are going to talk about the uncertaintyprinciple in Hardy’s form and its initial proof and why we are interested in finding other proofs instead of the initialone and what has (has not) been done.

Biography

I am doing harmonic analysis under supervisor Michael Cowling. I have started my third year in PHD. My maininterest is uncertainty principle and its applications.

13


STOCHASTIC RESONANCE AND BIAS TO CYCLIC MOTION INOVERDAMPED STOCHASTIC SYSTEMS

Ignacio Ortega


ABSTRACT

Optical tweezers are scientific instruments based on highly focused LASER beams able to hold and move micro-scopic dielectric objects.

This project proposes a theoretical approach for an experiment involving optical tweezers manipulating indiumphosphide nanowires. These nanowires exhibit phenomenon associated to stochastic resonance such as peak fre-quencies in the power spectral densities and bias to cyclic motion. Numerical simulations already rendered predictuncoupled dynamics in the planes parallel to the optical beam propagation and the electric and magnetic field,respectively. These simulations also predict the emergence of cyclic motion when the stiffness matrix associatedto the optical force is non-symmetric. A simple theoretical model has been developed to understand this problem.This model describes both the peaks in the spectral densities and the bias to cyclic motion on the qualitative basis.

Further steps of research in this project include:1. - describe the resonance phenomenon on the physical basis, i.e., how the characteristic frequencies change

in terms of the physical parameters such as the trap width, the trap power and the nanowire dimensions.2. - study the evolution of the three-dimensional angular velocity of the nanowire, as a stochastic variable,

qualitative and quantitatively.3. - understand the relationship between the different characteristic frequencies involved in the system: the

spectral frequencies, the deterministic frequency and the cyclic motion frequency.

Biography

My name is Ignacio Ortega and I am a Chilean student coursing the second year of my PhD in Mathematics. Ifollowed my undergrad studies at the University of Chile, where I coursed a Bachelors degree and a Masters degreein Physics, graduated with maximum distinction.

My area of research is Nonlinear Dynamics and Complex Systems. My main academic interests includestochastic differential equations, random processes and pattern formation, also as education in Science.

14


INCENTER CIRCLES, CHROMOGEOMETRY, AND THE OMEGATRIANGLE

Nguyen Hong Le


ABSTRACT

Chromogeometry brings together planar Euclidean geometry, here called blue geometry, and two relativistic ge-ometries, called red and green. We show that it a triangle has four blue Incenters and four red Incenters, then theseeight points lie on a green circle, whose center is the green Orthocenter of the triangle, and similarly for the othercolours. Tangents to the incenter circles yield interesting additional standard quadrangles and concurrencies. Theproofs use the framework of rational trigonometry together with standard coordinates for triangle geometry, whilea dilation argument allows us to extend the results also to Nagel and Speiker points.

We investigate a surprising connection between three closely related Incenter hierarchies of a fixed planar tri-angle. The framework here is that of Rational Trigonometry which allows a consistent universal triangle geometryvalid for any symmetric bilinear form together with the three-fold symmetry for chromogeometry, which connectsthe familiar Euclidean (blue) geometry based on the symmetric bilinear form x1x2+y1y2, and two relativistic ge-ometries (red and green) based respectively on the bilinear forms x1x2-y1y2 and x1y2+y1x2. By working withthe rational notions of quadrance and spread instead of the transcendental notions of distance and angle, the mainlaws of Rational Trigonometry allow metrical geometry, and so triangle geometry, to be developed in each of thesethree geometries in a parallel fashion, with mostly identical formulas and theorems.

Biography

Nguyen Le is from Vietnam. She has studied at San Francisco State University for her Master degree, and iscurrently third year Phd student at UNSW in Pure Math. Her main research areas are triangle geometry andChromogeometry. She has also done work in number theory and combinatorics during her time at SFSU.

15


WAVELET DENSITY ESTIMATION WITH APPLICATIONS TO IMAGEREGISTRATION / NEW WAVELET-BASED DENSITY ESTIMATION IN

HIGHER DIMENSIONS

Carlos Enrique Aya Moreno


ABSTRACT

Density estimation is a core problem in statistics with many areas of applications. In particular, gray level imagescan be seen as two-dimensional densities. More over, we think that the problem of image recognition, that haslately attracted much attention, can effectively be tackled via bivariate density discrimination in combination withwavelets. In this talk, we will present a wavelet-based method aiming at estimating

√f in the bivariate setting.

Targeting√f in the first place instead of f is motivated by two elements: first, the resulting density estimate

(

√f)2 is guaranteed to be positive, a basic property that other methods often fail to fulfil, and second,

√f has

always unit L2-norm by definition, which makes it a point in the unit hyper-sphere. This last property will enableus to use geodesic paths and related machinery to tackle density discrimination and ultimately image registration.The construction we will outline is an extension to a 1-D algorithm but that departs from a different statisticalfoundation and is therefore not straightforward. Finally, we will close by discussing briefly some issues aroundwavelet density estimation as thresholding, coarse and detail resolution, and consistency.

Biography

Carlos Aya, mathematician and software engineer, has been working in the software industry for over 20 years andis currently applying some statistical and signal processing methods in his day to day work. He has been interestedin studying the mathematical foundations behind image processing algorithms, particularly in those based onwavelets and so called multi-resolution analysis that have been applied to image registration and morphing.

16


SCHUR MULTIPLIERS AND APPLICATIONS

Anna Tomskova


ABSTRACT

For two given symmetric sequence spaces E and F we study the (E; F)- Schur multiplier space, that is, the spaceof all matrices M for which the Schur product M * A maps E into F boundedly whenever A does. We obtainseveral results asserting continuous embedding of the (E; F)- Schur multiplier space into the classical (p; q)- Schurmultiplier space (that is, when E = lp, F = lq). We extend classical results of S. Kwapien and A. Peczynski (1970)and of G. Bennett (1976, 1977) for the case when E = lp, F = lq.

Biography

My name is Anna. I have just started my second year PhD in Pure Math. I am from Uzbekistan. My supervisoris Prof. Sukochev. He has been worked with me for three years. We study very interesting questions in operatoralgebras and noncommutative Lp spaces. Our technique is based on the operator integration theory.

17


SPECTRAL PARTITIONS OF DYNAMICAL NETWORKS

Eric Kwok


ABSTRACT

A fundamental characteriser of network structure are clusters: regions on a network where the number of vertexto vertex connections are high within a cluster compare to the number of connections between the clusters. Inthis talk, we explore the complex interaction of dynamics and clusters on a network, and present a new method offinding clusters that persist when the network is subjected to a general vertex permutation. Our approach is basedon extending the classical spectral method for graph partitioning, we construct a new dynamic Laplacian matrix,and show that its eigenvectors are used to identify persistent clusters in a network.

Biography

I am a research student, currently interested in the geometry of coherent sets in time-dependent dynamical systems.

18


MODELLING INSURANCE CLAIM DEVELOPMENT

Bo Wang


ABSTRACT

A hierarchical approach is used to model claims developments for long tailed insurance products. A long tailedinsurance claim may take years to finalise and the estimate of the claim cost may take multiple revisions before itis ultimately finalised.

The claim development process is decomposed into its component processes and GLARMA (GeneralisedLinear Autoregressive Moving Average) models are being used to represent these component processes. This pre-sentation concentrates on the Delay Component process which measures the time elapsed between claim revisions.Due to the heterogeneity found in insurance claims, an alternate model structure incorporating a random effects(RE) structure is also discussed.

These models are being applied to the NSW CTP Claims dataset and the results are discussed.

Biography

Bo Wang is a qualified actuary with 10 years of general insurance experience. He currently works at Zurich Insur-ance Australia as a Senior Pricing Actuary. Bo is undertaking further research to develop his statistical knowledgeand stay abreast of the current research and techniques. His research interests include applying advanced regressionand data mining techniques to insurance data modelling problems.

19


MATHEMATICAL MODELLING OF HEPATITIS D AND HEPATITIS BVIRUS

Ashish Goyal


ABSTRACT

The major cause of liver cancer around the globe is hepatitis B virus (HBV) which also contributes to a largenumber of deaths due to liver failure alone. Hepatitis delta virus (HDV) is as potentially alarming as HBV sincelife threatening cases are 10 times more likely with HBV-HDV dual infection as compared to HBV monoinfection.Very little is known about HDV and its interaction with HBV. A way to better understanding of the HDV viraldynamics and its epidemiology is through quantitative modelling.

Since HBV is a satellite virus of HDV, study of HBV is absolutely necessary in order to study HDV. The pro-gression of acute hepatitis B virus (HBV) to chronic infection or clearance is highly dependent on the host immuneresponse composed of cytolytic (CTL) and non-cytolytic (non-CTL) effects. Cytolytic processes induce hepatocytekilling while non-CTL processes inhibit intracellular replication. Both effects are widely recognized and accepted.However, there are uncertainties about the assistance provided by either the loss of covalently circular closed DNA(cccDNA) during cell proliferation or the emergence of refractory cells to immune mediated clearance. Therefore,we develop an agent based mathematical model and test the relative roles of different mechanisms of the immunesystem in the clearance of acute HBV infection.

Biography

I am a second year PhD student in the department of applied maths working under the supervision of Prof. JohnMurray. Apart from research, I frequently enjoy traveling and being thoughtless.

20


EXCHANGEABILITY AND G-MEASURES

Louise Wilkinson


ABSTRACT

Exchanegeability lies at the heart of the Bayesian school of thought in statistics. A sequence of random variablesis exchangeable if its distribution is unchanged if their order is permuted.

It is easy to see that every sequence of independent and identically distributed (i.i.d.) random variables isexchangeable, but there are exchangeable sequences which do not arise in this way. The standard example is givenby an experiment where one has two coins, one fair and one two-headed. You choose one coin at random andrepeatedly toss it with Xi being the random variable giving the result of the ith toss. In this case the distribution ofthe sequence (Xi) is an averaging of the distributions for two sequences which are i.i.d., the one for the fair coinand the one for the biased one. de Finetti’s Theorem says that every infinite exchangeable sequence of randomvariables arises from this sort of averaging process.

We prove a generalisation of de Finetti’s Theorem using the concept of a G-measure. This only requiresthe weaker condition of a quasi-invariant measure. Note that a measure is quasi-invariant if the transformationpreserves sets of measure zero.

Biography

I have two first class honours degrees, one in economics (with the university medal) at Newcastle University andthe other in pure mathematics at UNSW. I worked as an economist for the Reserve Bank of Australia for fiveyears. I’m in my sixth year of my PhD in mathematics. My main research interest in mathematics is ergodictheory. Ergodic theory is the study of ergodic measures or ergodic systems.

21


SUBDIFFUSION AND EARLY STAGE HIV INFECTION

Austen Erickson


ABSTRACT

Human Immunodeficiency Virus (HIV), infects more than 35 million people worldwide, killing more than 1.5million annually. Due to the rapid advance of the virus from an initial founder population to a systemic steadystate, understanding the early stages of infection is of great importance.

Mathematical modelling of early stage HIV infection provides insight into the body’s natural defences, butcare must be taken to account for the complexities of motion through biological media. For a successful vaginalsexual infection event to occur, HIV virions must contend with the vaginal mucosa.

HIV virions are trapped as they travel through mucus, making their motion subdiffusive. Simplistic modelsof Brownian motion are therefore insufficient, with a continuous time random walk (CTRW) model most likelyto correctly model the system, and a scaled Brownian motion model potentially serving as an approximation. Wepresent a model of virion transport across the vaginal mucosa including the effects of trapping-based subdiffusion,mucus clearance, and virion death. Approximations by traditional Brownian motion and scaled Brownian motionare contrasted with a CTRW solution, demonstrating both the need for picking the correct model, and the efficacyof even a thin mucus layer at preventing the crossing of HIV virions.

Biography

Austen Erickson is finishing up the second year of his PhD in Applied Mathematics. He Holds an MSc in AppliedMathematics from Northwestern University, and a triple BSc in Mathematics, Physics, and Environmental Sciencefrom the University of Rochester. He is currently investigating the mathematics of the earliest stages of HIVinfection. His past research projects include studying the paleomagnetic properties of pallasite meteorites anddeveloping a model of the human visual accommodation apparatus.

22


AN UNIFIED BAYESIAN APPROACH TO KINETIC MODEL ESTIMATIONIN DYNAMIC POSITRON EMISSION TOMOGRAPHY

Wanchuang Zhu


ABSTRACT

We present a fully Bayesian statistical approach to the problem of compartmental modelling in the context ofPositron Emission Tomography. We perform kinetic parameter estimation and clustering homogeneous region ofinterest simultaneously. A mixture modelling approach is adopted, incorporating both spatial and temporal infor-mation based on reconstructed dynamic PET image. Our modelling approach is flexible, and provides uncertaintyestimates for the estimated kinetic parameters. Crucially, the proposed method allows us to determine the unknownnumber of clusters, which has a great impact on resulting cluster and parameter estimates. We demonstrate ourmethod on simulated dynamic Myocardial PET data, and show that our method is superior to standard curve-fittingapproach.

Biography

I am a PhD candidate of Statistics. My research areas are Bayesian inference, spatial statistics, medical imageprocessing.

23


THE AKT SWITCH

Catheryn Gray


ABSTRACT

Akt is a cellular component plays a role in a number of important cellular pathways, such as apoptosis and insulinsignalling. Disruption of these pathways can result in cancer or diabetes. In this talk I will discuss mathematicalmodelling of the metabolic role of Akt in insulin signalling.

Biography

I am a part-time PhD student in the Applied Maths department at UNSW studying mathematical modelling of theinsulin signalling pathway. When not working on the PhD, I teach maths in the Learning Centre. I also share mylife with 2 kids, 3 cats and 1 budgerigar.

24


COVARIANCE MODELLING OF DISCRETE DATA

Gordana Popovic


ABSTRACT

A major challenge in multivariate analysis is building a plausible but sufficiently parsimonious model for covari-ance that can be estimated when the number of observations is not large compared to the number of responsevariables. For Gaussian data we can use a number of covariance modelling procedures, such as graphical modelsand factor analysis, however these cannot be directly applied to discrete data. We propose a general algorithm forusing Gaussian copulas to extend existing covariance modelling approaches such that they can now be applied todiscrete data. Our Gaussian copula model can combine any marginal model, including models for over-dispersedcount data, with any likelihood based covariance modelling procedure designed for Gaussian data, such as graph-ical modelling, to carry out covariance modelling on discrete data. Our motivating example comes from ecology,where these models are useful when modelling a community of species, where there are a large number of po-tential species interactions relative to the number of locations where species abundances have been observed.Graphical modelling of these data can find conditional independence relationships between variables, and whenapplied to species counts can distinguish between direct and indirect species interactions. Simulations demonstrateour method can recover conditional independence relationships in count data if we have sufficient observations.We can also estimate covariance matrices efficiently, even when we have fewer observations than the number ofresponse variables. The method is illustrated on example data of hunting spiders.

Biography

I am a PhD student in the Ecological Statistics research group and the School of Mathematics and Statistics,UNSW. My PhD is focused on multivariate modelling of discrete data, with an emphasis on ecological applications.I am currently in the third year of my PhD, final stages of my world domination plan, and am supervised by DavidWarton and William Dunsmuir, as well as external co-supervisors.

25


APPROXIMATION BAYESIAN COMPUTATION METHODS USINGCOMPOSITE LIKELIHOOD

Xin Zhang


ABSTRACT

Approximate Bayesian computation (ABC) methods are a family of likelihood-free inference algorithms forBayesian analysis of intractable models. The application of these algorithms are restricted to models of rela-tively low-dimensions due to the dimensionality issues. In this article, we propose to use composite likelihoods(CL) constructed by summary statistics instead of intractable ones, to avoid comparisons of high-dimensional sum-mary statistics. Further, we utilise the factorisation structure of CL to design a parallel computation frameworkfor ABC. A iterative hierarchical clustering method is also provided for the ecient construction of CL with sum-mary statistics. The performance of our algorithms is evaluated via a simulated example of multivariate Gaussiandistributions with dierent covariance structures and a real example of the inference of foreign exchange rate dailyreturns data set of eight countries based on multivariate g-and-k distributions.

Biography

Xin is a second year PhD student. His research focusees on Bayesian computation methods and symbolic dataanalysis.

26


DECADAL CHANGES IN SOUTHERN-OCEAN VENTILATION INFERREDUSING A MAXIMUM ENTROPY APPROACH

Yu-Heing Ting


ABSTRACT

We use a maximum-entropy method to infer decadal changes in the locations and timescales of Southern Oceanventilation. Comparing deconvolutions of repeat and original tracer hydrographies, we find older circumpolar deepwater (CDW) and younger subantarctic mode water (SAMW) in the subtropics. Intriguing evidence for increasesin mixing rates is also uncovered. All of these changes are consistent with being driven by strengthened west-erlies. Our estimate of the boundary propagator allows us to infer changes in the anthropogenic carbon (CANT)concentration that are due to changes in oceanic transport.

Biography

Yu-Heng (Ian) is a Masters by Research student in his final year. Originally from Taiwan, Ian found his interest inquantitative science in high school. He finished his BSc Adv (Physical Oceanography) also here in UNSW, withinterest in numerical methods, information theory and oceanography.

27


NONCROSSING BAYESIAN QUANTILE REGRESSION

Thais Carvalho Valadares Rodrigues


ABSTRACT

Quantile regression models provide a wider picture of the conditional distribution of the response variable bydescribing the effect of the covariates at any quantile of interest. However, as they are usually fitted separately, thefinal estimates may not respect the logical ordering of percentiles, violating basic probabilistic rules and resultingin crossing quantile curves. A fully Bayesian two-stage approach to solve this issue is proposed in this talk.The method is very general, handling, on the first stage, both linear and non-linear standard Bayesian quantileregression based on the asymmetric Laplace distribution. The initial estimates are then adjusted by borrowingstrength across nearby quantiles using Gaussian process regression, yielding smoother noncrossing final estimates.Avoiding MCMC on the second stage and controlling the crossing constraint through a single parameter reducescomputational cost giving rise to a simple alternative approach. The theoretical aspects of the proposal will beexplored and the performance demonstrated on simulated and real examples. This is a joint work with Yanan Fan.

Biography

Thais Rodrigues is a statistics PhD candidate at UNSW under supervision of Prof. Yanan Fan. She is on her secondyear and her main research area is Bayesian statistics, including quantile and nonparametric regression models.She has a double degree in Statistics and Electrical Engineering and obtained her master’s degree in Statistics atUniversidade de Brasilia, Brazil, in 2012. She also held a position of statistician for one year at the BrazilianDisaster and Risk Management National Centre.

28


DOUBLE DIFFUSIVE INTERLEAVING: PROPERTIES OF THE STEADYSTATE (FINITE PRANDTL NUMBER)

Yuehua Li


ABSTRACT

Double diffusive convection is driven by two different density gradients that have different rates of diffusion. Alinear stability analysis indicated that it is possible that a steady state is eventually achieved where finite amplitudeinterleaving motions stop growing, and both the temperature and salinity budgets are in balance.

Combining a linear stability analysis with experimental flux laws, we examined double diffusive interleavingas it progresses from a linear instability towards finite amplitude. The interleaving motions were studied from asmall initial perturbation with scales and slopes as found in the linear instability analysis, through three evolvingstages, and steady state conditions were found. It was also found that the strength of the existing experimentalflux law for diffusive interfaces needs to be increased significantly, relative to the corresponding laboratory fingerfluxes. This is valid regardless of the magnitude of the Prandtl number. Some researchers are convinced that thePrandtl number for ocean fluids are smaller than the one was agreed decades ago. My research focuses on thesmall(finite) Prandtl number.

The results of the study have important implications for how we understand the oceans. There are implicationson the magnitudes of fluxes across diffusive and finger interfaces. Besides, there are also implications for howthese interleaving motions could be parameterised in intermediate-scale and large-scale ocean models.

Biography

I am a first year PhD student who got started in this March. I work with Trevor McDougall. My research is onthe development of ocean models, more specifically, Horizontal Residue Mean Theory. As ocean models tends tounderestimate the northward transport in the oceans, my theory aims to add these missed northward heat transportsinto the ocean models, so that they could be more accurate.

29


DYNAMIC NON-PARAMETRIC BAYESIAN MIXTURE MODELS

Xin Lei


ABSTRACT

Mixture models are commonly used for the analysis of data with sub-populations, such as in cluster analysis ordensity estimation. Some applications require that we consider how such mixture models vary dynamically (e.g.through time).

My research is focussed on the specification and subsequent estimation of dynamic mixture models usingBayesian techniques. Some issues that could be explored beyond the current literature include dealing with achanging number of mixtures, more efficient estimation procedures and how to construct dependencies linkingvarious mixture models.

I will begin by going through the various Bayesian approaches to this problem, from finite Bayesian mixturemodels to infinite Bayesian mixture models such as the Dirichlet and Pitman-Yor processes, and their possibleextensions. I will also discuss the progress of my research so far and future research directions.

Biography

I am a Bachelor of Science graduate at UNSW with majors in maths and stats. I worked briefly for the AustralianBureau of Statistics and various consulting agencies before returning to study a PhD.

30


DYNAMICS OF THE ESTUARY-SHELF EXCHANGE OFF SYDNEY ANDTHE IMPACT ON A PURPOSE BUIT OFFSHORE ARTIFICAL REEF

Nina Ribbat


ABSTRACT

Shelf dynamics off Sydney are primarily driven by the East Australian Current, its resulting eddy field and regionalwind regime. This study aims to obtain a new level of understanding of how and to what extent shelf dynamicsinfluence the coastal ocean. In particular, we will focus on the interaction of mesoscale eddies with shelf andcoastal waters, their influence on the exchange flows between the continental shelf, Sydney Harbour Estuary andan Offshore Artificial Reef. This will be accomplished using a combination of observations and Regional OceanModel System (ROMS) simulation outputs to quantify the estuary-shelf exchange and to reveal new insights intothe spatial extent of the East Australian Current into the coastal zone. At this stage of the study, comparisons aremade between nearshore / shelf currents and coastal winds to examine variability in the nearshore circulation anddetermine the correlation between data from buoy-mounted Acoustic Doppler Current Profilers (ADCPs) deployedacross the continental slope, near the Harbour Entrance and the Offshore Artificial Reef. The current record in thenearshore region was taken at 38 and 44 m depth, an area where the influence of shelf dynamics has not been wellstudied yet. The nearshore current flows predominantly southward, current reversals occur as a possible responseto eddy encroachment and/ or to the wind regime near the coast. In addition, a low density estuarine plume capturedafter a heavy rainfall event in the vicinity of the Sydney Harbour Entrance was found to be restricted to the top7 m with the outer extension reaching the northern end of the Entrance and a residence time of 5 days, with noinfluence on the Offshore Artificial Reef.

Biography

I am a Bachelors in Applied Maths, Bachelors in Oceanography, Masters in Applied Physics. I am currently doinga PhD in Coastal Oceanography.

31


TESTING FOR SERIAL DEPENDENCE IN BINOMIAL TIME SERIESREGRESSION

Jieyi He


ABSTRACT

Detection and estimation of serial dependence in binomial response time series is considerably more difficult thanit is in continuous response time series. This talk reviews various methods for detecting serial dependence intime series of binomial observations suitable for the regression setting under two classes of dependence models:observation driven and parameter driven. Methods include the traditional Box-Ljung-Pearce statistic based onauto-correlations of Pearson residuals, optimal score tests, Wald test and likelihood ratio tests in generalized linearauto-regressive moving average models for binomial and binary counts and analogous results for parameter driven(latent process) models are presented. Performance of these methods is based on large sample asymptotic results,which is challenging for parameter driven models since issues of uniqueness of likelihood estimates arise for binaryresponses. Key asymptotic results provide easily implementable consistent and asymptotically normal estimatorsof standard generalized linear mixed modelling based on products of one-dimensional integrals (which ignore theserial dependence in the latent process but not its variability) and a useable finite sample approximation of theprobability of concluding that there is no latent process when in fact one is present. Simulations will also confirmthe proposed theoretical results and describe conditions on the regressors and latent process for identifiability.Examples include modeling binary time series of economic recessions, winners in completing sport events, andmovements in financial series. We also illustrate the methods for screening time series for serial dependence incriminal data.

Biography

I am working on the subject of ”Detecting and Modelling serial dependence in non-Gaussian, non-Linear TimeSeries” with Professor William Dunsmuir, and this is the end of my third year.

32


COMPUTATION OF ISOTROPIC RANDOM FIELDS ON SPHERES VIANEEDLET DECOMPOSITION

Yuguang Wang


ABSTRACT

Isotropic random fields on the sphere have applications in environmental models and astrophysics. The classicKarhunen-Loeve expansion in terms of spherical harmonics has a drawback of requiring full observation of therandom field over the sphere. Attempting to solve this difficulty, we study decomposition by needlets — a highlylocalised basis — of an isotropic random field on the sphere. We prove the L2 convergence of the needlet de-composition of a two-weakly isotropic random field. We use a quadrature rule to construct fully discrete needletsfor computation and show the truncation error of the discrete needlet approximation for smooth isotropic randomfields.

This is a joint work with Quoc T. Le Gia, Ian H. Sloan and Robert S. Womersley.

Biography

I am a third year PhD student in applied mathematics. My supervisors are Prof. Ian H. Sloan, A/Prof. Robert S.Womersley and Prof. Michael Cowling. My research interests include harmonic analysis and approximation onthe sphere and quadrature rules on sphere and manifolds. I recently work on Riemann localisation on sphere andfor Jacobi weights, filtered approximation on the sphere and covering radius of QMC designs.

33

Index of Authors

Beranger, Boris, 3

Donnelly, Issac, 1

Erickson, Austen , 22

Gao, Xin, 13Goyal, Ashish, 20Gray, Catheryn, 24

He, Jieyi, 32Hui, Francis, 8

Kerr, Bryce, 6Kwok, Eric, 18

Le, Nguyen Hong, 15Lei, Xin, 30Li, Yuehua, 29

Moreno, Carlos Enrique Aya , 16

Ortega, Ignacio , 14

Pasquier, Benoit , 4Popovic, Gordana , 25

Ribbat, Nina, 31Richards, Kylie-Anne, 5Riha, Stefan, 2Rodrigues, Guilherme Souza , 9Rodrigues, Thais Carvalho Valadares , 28

Shafie, Sabarina Binti , 10

Ting, Yu-Heing, 27Tomskova, Anna, 17

Wand, Bo, 19Wang, Yuguang Wang , 33Wee, Damien, 7Wilkinson, Louise , 21Wu, Wei, 11

Zhang, Mengzhe, 12Zhang, Xin, 26Zhu, Wanchuang , 23

abstracts - university of new south wales...ashish goyal 21exchangeability and g-measures louise...

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