1. COV4 2006

2. outline Case study 1: Model with expert judgment (limited data): Perceived probability of explosive magmatic eruption of La Soufriere, Guadeloupe, 1976 Formal procedure for assessment of risk based on current scientific knowledge Case study 2: Model with data: Forecasting dome collapse activity on Montserrat daily forecasts  alert level or warning system forecast verification Bayesian Belief Networks

3. COV4 2006 Bayesian Belief Networks Causal probabilistic network directed acyclic graph Set of variables X i discrete or continuous hidden or observable states Set of directed links (arcs)

4. COV4 2006 Building a BBN Dynamic BBN P(X t |X t-1 ) Sensor modelTransition model define PDFs P(Y|X) P( Y|X ) Y 1 =0Y 1 =1 X 1 =00.80.2 X 1 =10.960.04

5. COV4 2006 Inference Bayes’ theorem:

6. COV4 2006 Guadeloupe 1976: perceived probability of eruption Construct a simple BBN for La Soufrière Representation of the magmatic system - hidden states Relationships between observational evidence current scientific interpretation of evidence expected behavior and evolution of the system structured decision making

7. COV4 2006 Magmatic eruption imminent? Coupled/competing hidden processes Surface effects & monitoring Inference RISK? evacuation / mitigation

8. COV4 2006

11. Bayesian network for Soufrière Hills forecasting dome collapse Rainfall on the dome

12. COV4 2006 Rainfall on the dome dome volume Bayesian network for Soufrière Hills forecasting dome collapse

13. COV4 2006 Dynamic model - tied over two time- slices

14. COV4 2006 Logical structure (!) Elicited (estimated) prior distributions 9 years daily data (MVO) Testing: Parameter learning with past data Forecasting (1, 3 and 5 days ahead) - probability of collapse? Update with new data does it work? Dome collapse BBN

15. COV4 2006 Known structure: results Dome collapse BBN

16. COV4 2006 Dome collapse BBN: verification ROC curve: Receiver Operating Characteristic measure of forecast skill plot hit rate vs false alarm rate calculated for a range of probability thresholds

17. COV4 2006 Performance over time

18. COV4 2006 Conditional probabilities learned from the data Physically plausible results? How to interpret contradictory evidence? Can we identify strong precursors? How informative are individual observations? How significant is the absence of a trait? BBN results Identify key monitoring parameters calculate marginal distributions P( collapse | observation )

19. COV4 2006 More unstable More stable

20. COV4 2006

21. Real time forecasting update model with new observations Basis for defining alert levels and early warning systems Use hazard forecast and understanding of the uncertainty in the forecast to support decision making in a crisis Robust,transparent and defensible procedure for combining observations, physical models and expert judgment  Risk informed decision making Goals

22. COV4 2006 Jensen, F., 1996. An Introduction to Bayesian Networks. UCL Press. Murphy, K., 2002 Dynamic Bayesian Networks: Representation, Inference and Learning. PhD Thesis, UC Berkeley. www.ai.mit.eduwww.ai.mit.edu 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 openPNL (Intel) http://sourceforge.net/projects/openpnl open source C++ library for probabilistic networks/directed graphs References Summary online soon … http://eis.bris.ac.uk/~gltkh/theahincks