An automatic and proper Bayesian estimation analysis of 2×2 contingency tables with one and two fixed margins

摘要

The Bayesian analysis of a 2×2 contigency table with one or two fixed margins is presented as an estimation problem when using Exponential Family likelihoods with two or one free parameters, respectively. The computation of the Jeffreys priors for one or two fixed marginals is then straightforward for the canonical parameter. Jeffreys priors are proper distributions, despite of the fact that the parameter spaces are unbounded. Coupling the Jeffreys prior with exponential likelihoods thus yields a proper and automatic Bayesian analysis. Two contingency tables with one and two fixed margins are then analysed