Using Gibbs Sampling for Bayesian Inference in Multidimensional Contingency Tables

Abstract

This paper discusses a method suggested by Epstein and Fienberg (1991) for the Bayesian analysis of multidimensional contingency tables in connection with the Gibbs sampler to calculate posterior densities. The method consists of a two-stage hierarchical prior. The first stage is a Dirichlet distribution with a loglinear reparametrization for its means. The second stage is a multivariate normal distribution on the loglinear parameters. However, other distributions can be used if the Dirichlet-normal combination is not flexible enough to accommodate one's prior beliefs. These prior distributions are useful when one believes, with uncertainty, in a given loglinear structure for the cell probabilities. Contingency tables; Bayesian estimation; Dirichlet prior distribution; Gibbs sampler; Loglinear model; Maximum likelihood estimation of Dirichlet distributions.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1992
Accession Number
ADP007137

Entities

People

  • Leonardo D. Epstein
  • Stephen E. Fienberg

Organizations

  • Johns Hopkins University

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Bayesian Inference
  • Bayesian Networks
  • Computer Science
  • Data Science
  • Equations
  • Estimators
  • Information Science
  • Maximum Likelihood Estimation
  • Models
  • Monte Carlo Method
  • Probability
  • Random Variables
  • Sampling
  • Statistical Algorithms
  • Statistics
  • Universities

Fields of Study

  • Mathematics

Readers

  • Regression Analysis.
  • Statistical inference.

Technology Areas

  • AI & ML
  • AI & ML - Bayesian Inference
  • AI & ML - Information Retrieval