EXPLORISMontserratVolcano ObservatoryAspinall and Associates
Risk Management Solutions
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An Evidence Science approach to volcano hazard forecasting
Thea Hincks1, Willy Aspinall1,2, Gordon Woo3, Gillian Norton4,5
Evidence science
Evidence-based medicine is the conscientious, explicit and judicious use of current best evidence in making decisions
… the integration of individual expertise with the best available external evidence from systematic research After Sackett et al., 1996
Evidence Based Medicine
Need to model uncertainty and make
forecasts using
• Expert judgment & knowledge of physical system
• Observational evidence
= highly complex system
Bayesian networks
Bayesian belief networks (BBNs)Causal probabilistic network
Directed acyclic graph
Set of variables Xi discrete or continuous
Set of directed linksVariables can represent hidden or observable states of a system
Very useful in volcanology - our observations on internal dynamics of the volcano are indirect
Expert systems
NASA data analysis
MSOffice assistant…
Bayesian Network
applications
Speech recognition
Molecular Biology and Bioinformatics
Medical diagnosis & decision making
VOLCANIC HAZARD
FORECASTING
Building a Bayesian network
Sensor model: Prior and transition models
Probability of observation P(Y|X)
Probability of initial state P(X0)
Transition between states P(X1|X0)
Bayes theorem
€
P(A | B,C) =P(B | A,C)P(A | C)
P(B | C)
Filtering - estimate current state Xt
Prediction - future states Xt+n
Forward pass :
Smoothing- past unobserved statesBackward pass :
Network structure• Judgment, physical models, observations
factors we believe lead to instability
• Structure learning algorithms
purely data driven model
difficult to model unobserved nodes problem is NP-hard algorithms slow to compute(~ few days for 6 x ternary node graph)
BN for dome collapse on Montserrat
rainfall on dome dome collapse
magma flux
ground deformation
stability of edifice
degassing
pressure
Factors that might lead to dome collapse:
BN for dome collapse on Montserrat
rainfall on dome dome collapse
magma flux
ground deformation
degassing
stability of edifice
Can’t measurestate directly
hidden variablespressure
BN for dome collapse on Montserrat
magma flux
deformation
SO2 flux
observed rainfall UEA & MVO rain gauges
degassing
stability
pres
sure
GPS, EDM and tilt
Seismicity: VT earthquakes
Long period earthquakes
Hybrid
Rockfall
LP Rockfall
BN for dome collapse on Montserrat
use sensor models for our observations:
Data
Testing with daily data from July 95 - August 04
• S02 flux
• Ground deformation (4 GPS lines) 4 nodes• Seismic activity (event triggered count & magnitude
data) VT, Hybrid, LP, LPRF, RF 5 nodes• Rainfall• Collapse activity
Time dependence
Structure: how are processes coupled?
What is the order of the process ?
Dynamic system - history is important• Variables tied over several time slices
Time series analysis of monitoring data
Autocorrelation & partial autocorrelation functions, differenced data
Approximate order for time dependent processes
Autocorrelations
Computed autocorrelation function and and partial autocorrelation function for data and first differenced data
check structure is sensible and estimate order of time dependence
Dynamic Bayesian Network
Structural integrity or stability of the dome is dependant on
• previous state• prior rock fall activity• prior collapse activity
(also affects pressurization)
Current model
Prior distribution
• Expert judgment
Sensor model
Transition model
• Expert judgment to set initial distributions• Parameter learning algorithms on monitoring data
P(X0), P(Y0)
for all states X
observations Y
P(Yt|Xt)
P(Xt+1|Xt)
Results so far
Parameter learning using ~9 years of data
transition and sensor models
1. static BN
2. two-slice dynamic model
3. three-slice dynamic model Can estimate probability of collapse given new observations
Smoothing to estimate hidden state probabilities and distributions for missing values of observed nodes
Results so far
Structure learning on a small (5 node) model - observed nodes only
…work still in progress!
Results so far
• High ground deformation
• Consistent, moderate hybrid activity
• No SO2 observations
Further work…
• Model observations with continuous nodes
• More monitoring data - extend network
• Look at full seismic record (not just event triggered data)
• Run structure learning algorithm on larger network
• Investigate second order uncertainties (model uncertainty) and scoring rules to see how well different models perform
• User interface for real time updating of network at MVO real time forecasting probability of collapse
• Longer range forecasting?
Conclusions
All models are wrong (to some degree…)
but some models are better than others
EVIDENCE SCIENCE and BAYESIAN NETWORKS
Robust, defensible procedure for combining observations, physical models and expert judgment
Risk informed decision making
•Can incorporate new observations/phenomena as they occur
•Strictly proper scoring rules - unbiased assessment of performance & model uncertainty
References
Druzdzel, M and van der Gaag, L., 2000. Building Probabilistic Networks: Where do the numbers come from? IEEE Transactions on Knowledge and Data Engineering 12(4):481:486
Jensen, F., 1996. An Introduction to Bayesian Networks. UCL Press.
Matthews, A.J.and Barclay J., 2004 A thermodynamical model for rainfall-triggered volcanic dome collapse. GRL 31(5)
Murphy, K., 2002 Dynamic Bayesian Networks: Representation, Inference and Learning. PhD Thesis, UC Berkeley. www.ai.mit.edu
openPNL (Intel) http://sourceforge.net/projects/openpnl
open source C++ library for probabilistic networks/directed graphs