EXPLORIS

1. An Evidence Science approach to volcano hazard forecasting • Thea Hincks1, Willy Aspinall1,2, Gordon Woo3, Gillian Norton4,5 1 EXPLORIS 4 Montserrat Volcano Observatory 2 Aspinall and Associates 5 3 Risk Management Solutions

2. Evidence science • = highly complex system 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., 1996Evidence Based Medicine • Need to model uncertainty and make • forecasts using • Expert judgment & knowledge of physical system • Observational evidence

3. Bayesian networks • Bayesian belief networks (BBNs) Causal probabilistic network Directed acyclic graph Set of variables Xi discrete or continuous Set of directed links Variables can represent hidden or observable states of a system Very useful in volcanology - our observations on internal dynamics of the volcano are indirect

4. Expert systems NASA data analysis Medical diagnosis & decision making Speech recognition Bayesian Network applications Molecular Biology and Bioinformatics VOLCANIC HAZARD FORECASTING MSOffice assistant…

5. Building a Bayesian network Prior and transition models • Sensor model: Probability of initial state P(X0) Transition between states P(X1|X0) Probability of observation P(Y|X) Forward pass : Bayes theorem Filtering - estimate current state XtPrediction - future states Xt+n Backward pass : Smoothing- past unobserved states

6. BN for dome collapse on Montserrat • 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)

7. BN for dome collapse on Montserrat Factors that might lead to dome collapse: rainfall on dome dome collapse stability of edifice pressure magma flux degassing ground deformation

8. BN for dome collapse on Montserrat rainfall on dome dome collapse stability of edifice Can’t measure state directly  hidden variables pressure magma flux degassing ground deformation

9. BN for dome collapse on Montserrat observed rainfall UEA & MVO rain gauges use sensor models for our observations: Rockfall stability LP Rockfall Long period earthquakes pressure magma flux degassing Hybrid Seismicity: VT earthquakes SO2 flux deformation GPS, EDM and tilt

10. 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

11. Time dependence • Dynamic system- history is important • Variables tied over several time slices Structure: how are processes coupled? What is the order of the process ? • Time series analysis of monitoring data • Autocorrelation & partial autocorrelation functions, differenced data •  Approximate order for time dependent processes

12. 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

13. Dynamic Bayesian Network Rainfall - 1 day autocorrelation  Hidden Markov model O(1)

14. Dynamic Bayesian Network Pressure

15. Dynamic Bayesian Network Magma flux

16. Dynamic Bayesian Network Gas flux

17. Dynamic Bayesian Network Ground deformation

18. 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)

19. Dynamic Bayesian Network

20. Current model Where monitoring time series suggest higher order processes …

21. 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)

22. Results so far • Parameter learning using ~9 years of data •  transition and sensor models • static BN • two-slice dynamic model • 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

23. Results so far • Structure learning on a small (5 node) model - observed nodes only • …work still in progress!

24. Results so far • High ground deformation • Consistent, moderate hybrid activity • No SO2 observations

25. Results so far

26. 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?

27. 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

28. 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., 2004A thermodynamical model for rainfall-triggered volcanic dome collapse. GRL 31(5) • Murphy, K., 2002Dynamic 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