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Imprecise probability and decision in civil engineering : Dempster-Shafer theory and application Luo, Wuben

Abstract

Over the last three decades, Bayesian theory has been widely adopted in civil engineering for dealing with uncertainty and for purposes of decision making under uncertainty. However the Bayesian approach is not without criticisms. One major concern has been that information or knowledge, no matter how weak or sparse, must necessarily be represented by conventional, precisely specified, probabilities. This has lead to thedevelopment of statistical methods which allow for more flexible expressions of both information inputs, and inferred results. More recently a general concept, called imprecise probability, which embraces a number of these methods, has been described [Walley, 1991]. Weak information is often encountered in civil engineering. This is especially true in decision making as major decisions are often dominated by random, but infrequent, extreme natural events. For these rare events the sample record is usually short and the relevant subjective knowledge based on human experience is also likely to be very limited. The imprecise probability concept therefore has potential relevance to some important civil engineering decision problems. Among the existing imprecise probability schemes, Dempster-Shafer (D-S) theory is prominent. This theory has attracted considerable attention in the Artificial Intelligence (AI) field, but the applications are different from those considered here. This has largely overshadowed the relevance of the theory to the more conventional inference and decision making types of problems encountered in civil engineering. In this thesis, some applications of the D-S theory primarily to water resources engineering decision problems are developed. The engineering examples presented throughout the thesis provide some indications of the impact of implementing imprecise probabilities on engineering decision analysis. In most instances a closest equivalent Bayesian analysis is performed and the results compared with those obtained from the D-S scheme. The concept of imprecise probability is philosophically important to the research and is briefly reviewed. The theoretical ingredients of D-S theory which are necessary to support engineering applications are then introduced. This is followed by presentation of several different procedures for translating weak sampling information inputs into D-S inference results. The elicitation of subjective prior inputs for the D-S scheme is also discussed and includes representing some typical engineering expressions of subjective knowledge. Two civil engineering models, one in hydrologic design and the other in reliability analysis, are also developed, and they demonstrate how the scheme can be applied in more complex engineering situations. When presented with weak information input, the D-S decision analysis yields upper and lower expected utilities. This reduces the ability to choose between the best decision alternatives, especially when the expected utility intervals for different decisions overlap. But this reduction in resolution is believed to more realistically reflect the true decision making situation. The factors governing the size of the expected utility interval are also discussed.

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