MBR-A Computer Program for Performing Nonparametric Bayesian Analyses of Ordered Binomial Data

摘要

The MBR computer program computes posterior marginal distributions for binomial response probabilities associated with a set of M-ordered stresses or stimuli. Exact solutions are achieved of the posterior marginal distribution functions, first published by Disch, which was based on Ramsey s M-variate ordered Dirichlet joint prior. MBR assumes a related joint prior that is a mixture of Dirichlet distributions to obtain a class capable of representing arbitrary and quite general forms. The joint prior distribution is reconstructed from three percentile curves, such as the 10th, 50th, and 90th percentiles, of the prior marginal distributions as assigned by an expert. The code then calculates the posterior marginal distributions (mixtures of beta distributions) and constructs new percentile curves that reflect the effect of the data upon the priors in accordance with Bayes s law. Rapid and exact solutions are obtained by means of a recursive theory developed by the author.