Data-Dependent Posterior Propriety of a Bayesian Beta-Binomial-Logit Model
Year: 2016
Type: article
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 data-dependent 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.
Source: Bayesian Analysis
DOI: 10.1214/16-ba1012
Authors: Hyungsuk Tak, Carl N. Morris
Language: Spanish
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W2221087461