Data-dependent posterior propriety of a Bayesian beta-binomial-logit model

Hyungsuk Tak, Carl N. Morris

Research output: Contribution to journalArticle

5 Scopus citations

Abstract

A Beta-Binomial-Logit model is a Beta-Binomial model with covariate information incorporated via a logistic regression. Posterior propriety of a Bayesian Beta-Binomial-Logit model can be data-dependent for improper hyper-prior distributions. Various researchers in the literature have unknowingly used improper posterior distributions or have given incorrect statements about posterior propriety because checking posterior propriety can be challenging due to the complicated functional form of a Beta-Binomial-Logit model. We derive datadependent necessary and sufficient conditions for posterior propriety within a class of hyper-prior distributions that encompass those used in previous studies. When a posterior is improper due to improper hyper-prior distributions, we suggest using proper hyper-prior distributions that can mimic the behaviors of improper choices.

Original languageEnglish (US)
Pages (from-to)533-555
Number of pages23
JournalBayesian Analysis
Volume12
Issue number2
DOIs
StatePublished - Jun 1 2017

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Applied Mathematics

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