Equivalence of posteriors in the Bayesian analysis of the multinomial-Poisson transformation

摘要

The multinomial-Poisson (MP) transformation simplifies maximum likelihood estimation in a wide variety of models for multinomial data. On the basis of the MP transformation, we present a general result which shows that the posterior inference for the parameters from a multinomial likelihood is exactly equivalent to that from the corresponding Poisson likelihood with an arbitrary proper prior for the parameters of interest and independent uniform priors for the latent parameters. The result is then extended to prove the equivalence of posterior inference for the odds ratio parameter based on prospective and retrospective likelihoods in stratified case-control studies where some of the exposure variables could potentially be missing completely at random.