NCJ Number
95230
Date Published
1983
Length
40 pages
Annotation
Distribution theory is given for Bayesian inference from multinomial (or multiple Bernoulli) sampling with missing category distinctions, such as a contingency table with supplemental purely marginal counts.
Abstract
A new conjugate family generalizes the usual Dirichlet prior distributions. The posterior moments and predictive probabilities are found to be proportional to ratios of Carlson's hypergeometric functions of matrix argument. Dimension-reducing integral identities and expansions are given for statistical use. Closed-form expressions are developed for cases of nested missing distinctions. Two examples are given, including an analysis of data from two sample surveys of attitudes toward the death penalty. A simple method for the assessment of a Dirichlet subjective prior distribution is appended. Twenty-three references are listed. (Author abstract modified)