Bayesian Methods for Multinomial Sampling With Missing Data Using Multiple Hypergeometric Functions

• NCJ Number: 95230
• Date Published: 1983
• Author(s): J M Dickey; J Jiang; J B Kadane
• Length: 40 pages
• Grant Number(s): MCS-8301335; 81-IJ-CX-0087
• Agencies: NIJ-Sponsored
• Publication Type: Statistics

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)