Optimization in the Space of Distribution Functions and Applications in the Bayes Analysis
This paper is stimulated by reliability estimation problems for safety systems of Nuclear Power Plants. A new approach for calculating robust Bayes estimators is considered. Upper and lower bounds for Bayes estimates, provided that a prior distribution satisfies available prior information, are constructed. The problems of calculating lower and upper bounds for Bayes estimates is reduced to optimization on a set of distributions satisfying available prior information. It was demonstrated that Bayes estimates of parameters are sensitive to the type of a prior distribution function. Analysis of the reliability data of a nuclear safety system was conducted using the developed methodology. The robust estimates were compared to Bayes estimates traditionally used in nuclear industry.
KeywordsPrior Distribution Beta Estimate Binomial Sampling Robust Bayesian Analysis Reliability Parameter Estimate
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