SYSTEMATIC BAYES PRIOR-ASSIGNMENT BY COUPLING THE MINI-MAX ENTROPY AND MOMENT-MATCHING METHODS

Abstract

The prior is chosen somewhat conservatively, but not arbitrarily, in Bayes analysis for the event whose characteristics are not well understood. It is desirable to get the prior through an objective procedure for the given information. Our approach of assigning the pre-prior is by coupling the principle of maximum entropy with the moment-matching method; ie, to find upper & lower bounds of the population parameter sets - based on upper & lower bounds of the entropy for the given information. The methodology is demonstrated by applying it to the data sets of initiating events taken from the performance of nuclear power plants. The favorable prior candidates (lognormal & gamma) are competitive with respect to the mean & variance of the data. And, one can get the more suitable pre-prior type, depending on the data, by choosing the one whose prior is more conservative than that obtained by the moment-matching method. As uncertainty or variance is decreased, the entropy of each prior candidate converges to the maximum entropy of the normal (Gaussian) distribution. This is similar to the central limit theorem that all distributions converge to the normal distribution as the sample size becomes large. Therefore, no special concern is necessary, conceptually, to select the prior form for the data with a small variance. Consequently, our algorithm provides explicit process-conserving scrutability, thus minimizing the introduction of subjectivity or arbitrariness in Bayes analysis. However, we recommend considering various types of distribution in addition to those examined in this study, as an additional effort to complete our algorithm.