This tutorial introduces the notions of interval-valued probability and imprecisely specified probability distributions and reviews their uses in risk analysis. It will address the approaches of interval probabilities, probability bounds analysis, Dempster-Shafer theory, robust Bayes methods, and the theory of imprecise probabilities.
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This full-day tutorial introduces the notions of interval-valued probabilities and imprecisely specified probability distributions and their uses in risk analysis. It reviews five practical and quantitative approaches based on these elementary notions. The simplest approach uses the idea of interval probability, in which the probability of an event can be specified as an interval of possible values rather than only as a precise one. This idea, dating from George Boole, provides a convenient way to assess the reliability of fault-tree risk analyses. This idea is generalized by probability bounds analysis, which propagates constraints on a distribution function through mathematical operations, and Dempster-Shafer theory which recognizes that uncertainty attending any real-world measurement may not allow an analyst to distinguish between events in empirical evidence. These approaches are related to robust Bayes (aka Bayesian sensitivity) methods, in which an analyst can relax the requirement that the prior distribution and likelihood function must be precisely specified. The most general approach comes from the theory of imprecise probabilities in which uncertainty is represented by closed, convex sets of probability distributions.
These five approaches redress, or comprehensively solve, several major deficiencies of Monte Carlo simulations and of standard probability theory in risk assessments. For instance, it is almost always difficult, if not impossible, to completely characterize dependencies among variables in a risk analysis. As a result, in the practical situations where empirical data are limiting, these difficulties can result in assessments that are arbitrarily over-specified and therefore misleading. More fundamentally, it can be argued that probability theory has an inadequate model of ignorance because it uses equiprobability as a model for incertitude and thus cannot distinguish uniform risk from pure lack of knowledge. In most practical risk assessments, some uncertainty is epistemic rather than aleatory, that is, it is incertitude rather than variability. For example, uncertainty about the shape of a probability distribution and most other instances of model uncertainty are typically epistemic. Treating incertitude as though it were variability is even worse than overspecification because it confounds epistemic and aleatory uncertainty and leads to risk conclusions that are simply wrong. Approaches based on imprecise probabilities allow an analyst to keep these kinds of uncertainty separate and treat them differently as necessary to maintain the interpretation of risk as the frequency of adverse outcomes.
The interval and imprecise probability methods also make backcalculations possible and practicable. Backcalculation is required to compute cleanup goals, remediation targets and performance standards from available knowledge and constraints about uncertain variables. The needed calculations are notoriously difficult with standard probabilistic methods and cannot be done at all with straightforward Monte Carlo simulation.
Although the five approaches arose from distinct scholarly traditions and have many important differences, the tutorial emphasizes that they share a commonality of purpose and employ many of the same ideas and methods. They can be viewed as complementary, and they constitute a single perspective on risk analysis that is sharply different from both traditional worst-case and standard probabilistic approaches. Each approach is illustrated with a numerical case study and summarized by a checklist of reasons to use, and not to use, the approach.
The presentation style will be casual and interactive. Participants will receive a CD of the illustrations used during the tutorial.
Gert de Cooman is Professor in Uncertainty Modelling and Systems Science at Universiteit Gent, Belgium, from which he holds an M.Sc. and Ph.D. degrees in physical engineering. He has held several positions at the Fund for Scientific Research--Flanders and was a Visiting Research Fellow at Binghamton University in New York. He is a member of the SYSTeMS research group of the Universiteit Gent. He is editor of the Imprecise Probabilities Project, editor of several books, and the author of over 70 scholarly papers. He is also actively involved in the organisation of the ISIPTA '99 and ISIPTA '01 conferences. His research interests are in the mathematical representation of uncertainty, imprecision in probability theory and the study of uncertainty in systems. He has worked on the topics of coherence, conditioning and independence, possibility measures, second-order uncertainty models, belief change and combination, imprecise probability models in processes and dynamical systems, and vagueness in expressions of probability.
Scott Ferson is a senior scientist at Applied Biomathematics. His research focuses on developing reliable mathematical and statistical tools for risk assessments and on methods for uncertainty analysis when empirical information is very sparse. Ferson holds a Ph.D. from the State University of New York at Stony Brook. He is author of
The registration fee is $300 USD before 10 June, or 325 euros on site. You do not need to register for the Congress to attend the workshop. Registration will be handled by
The event will be held 9:00 - 17:30 on Sunday, 22 June 2003, at
The room for the event has not yet been determined; check with the concierge. See tourist descriptions of the hotel at http://www.sheraton.com/brussels and http://www.hotels-belgium.com/brussel-bac/brussels-h-sheratonhotel.htm. To reserve a room at the hotel, call +32 2 2243111 by 22 May 2003. Be sure to identify yourself as a SRA World Congress attendee to receive the following group rates (in euros).
More information can be obtained from Scott Ferson scott@ramas.com, telephone 631-751-4350, fax 631-751–3435.
World Congress on Risk (flier and registration) http://sra.org/worldcongress9.pdf
World Congress on Risk (other links) http://sra.org/events.htm#world
The Imprecise Probabilities Project http://www.sipta.org/
Society for Risk Analysis www.sra.org
ISIPTA (International Symposium on Imprecise Probabilities and Their Applications) http://ippserv.rug.ac.be/~isipta03/