(A) study on the systematic prior assignment in bayesian analysis by coupling the mini-max entropy method with the moment-matching method

Abstract

A systematic algorithm is developed for the assignment of the prior in Bayesian analysis by the use of the mini-max entropy method coupled with the moment-matching method. The Bayesian analysis technique currently being used tends to be too much dependent on the judgement of the analyst. A subjective judgement or assumption usually made by the analyst, which is unavoidable in Bayesian analysis, has been recognized as the limitation of the Bayesian method. The algorithm developed in this study is designed to improve the Bayesian analysis technique so that the prior assignment can be made explicitly as well as logically based on the data gathered. The development of the methodology in this study consists of three steps. The first step involves the derivation of the parameters associated with the distributions commonly used in the reliability analysis. The parameters are derived with the constraint that the first and the second moments are the same for the given data. the second stop involves the examination of various aspects of entropy functions for the continuous distributions and the derivation of the equations which relate the entropy values with the parameters derived in the first step. The third stop involves the establishment of the procedure for the assignment of prior in Bayesian analysis in such a way that the population variability can be minimum with the chosen prior out of the considered candidates without losing conservatism. The mini-max entropy method and the moment-matching method are used in this third stop. The methodology is demonstrated through the comparison of the results with the different types of the prior for the several data sets of initiating events taken from performance of nuclear power plants. The identified favorable prior candidates are lognormal and gamma. The lognormal type prior is favoured for the cases of relatively rare events such as steam generator tube rupture and spurious safety injection while the gamma type prior is f...