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June 2017 Data-Dependent Posterior Propriety of a Bayesian Beta-Binomial-Logit Model
Hyungsuk Tak, Carl N. Morris
Bayesian Anal. 12(2): 533-555 (June 2017). DOI: 10.1214/16-BA1012

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.

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Hyungsuk Tak. Carl N. Morris. "Data-Dependent Posterior Propriety of a Bayesian Beta-Binomial-Logit Model." Bayesian Anal. 12 (2) 533 - 555, June 2017. https://doi.org/10.1214/16-BA1012

Information

Published: June 2017
First available in Project Euclid: 20 July 2016

zbMATH: 1384.62272
MathSciNet: MR3620744
Digital Object Identifier: 10.1214/16-BA1012

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Vol.12 • No. 2 • June 2017
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