On the propriety of the posterior of hierarchical linear mixed models with flexible random effects distributions

TL;DR

This paper investigates the conditions under which the posterior distribution remains proper in Bayesian hierarchical linear mixed models when using flexible random effects distributions and general improper priors.

Contribution

It extends the analysis of posterior propriety to models with more flexible random effects distributions and broader improper prior structures.

Findings

Established conditions for posterior propriety with flexible random effects

Generalized prior structures under which the posterior remains proper

Provides theoretical foundations for Bayesian hierarchical models with non-normal random effects

Abstract

The use of improper priors in the context of Bayesian hierarchical linear mixed models has been studied under the assumption of normality of the random effects. We study the propriety of the posterior under more flexible distributional assumptions and general improper prior structures.