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outline. Bayesian Belief Networks. 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 :

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  1. outline • Bayesian Belief Networks • 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

  2. Bayesian Belief Networks Causal probabilistic network directed acyclic graph Set of variables Xi discrete or continuous hidden or observable states Set of directed links (arcs)

  3. Building a BBN • Dynamic BBN P(Xt|Xt-1) • Sensor model • Transition model • define PDFs P(Y|X)

  4. Inference Bayes’ theorem:

  5. 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

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

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

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

  9. Dynamic model - tied over two time-slices

  10. Dome collapse BBN • 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?

  11. Dome collapse BBN results • Known structure:

  12. 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

  13. Performance over time

  14. BBN results • 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? Identify key monitoring parameters calculate marginal distributions P( collapse | observation )

  15. More unstable More stable

  16. Goals 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

  17. References • Jensen, F., 1996. An Introduction to Bayesian Networks. UCL Press. • Murphy, K., 2002Dynamic Bayesian Networks: Representation, Inference and Learning. PhD Thesis, UC Berkeley. www.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 • Summary online soon … http://eis.bris.ac.uk/~gltkh/theahincks

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