Bayesian Analysis

Data-Dependent Posterior Propriety of a Bayesian Beta-Binomial-Logit Model

Hyungsuk Tak and Carl N. Morris

Full-text: Open access

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.

Article information

Source
Bayesian Anal., Volume 12, Number 2 (2017), 533-555.

Dates
First available in Project Euclid: 20 July 2016

Permanent link to this document
https://projecteuclid.org/euclid.ba/1469021382

Digital Object Identifier
doi:10.1214/16-BA1012

Mathematical Reviews number (MathSciNet)
MR3620744

Zentralblatt MATH identifier
1384.62272

Keywords
objective Bayes hierarchical models random effects overdispersion logistic regression beta-binomial uniform shrinkage prior

Rights
Creative Commons Attribution 4.0 International License.

Citation

Tak, Hyungsuk; Morris, Carl N. Data-Dependent Posterior Propriety of a Bayesian Beta-Binomial-Logit Model. Bayesian Anal. 12 (2017), no. 2, 533--555. doi:10.1214/16-BA1012. https://projecteuclid.org/euclid.ba/1469021382


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