Bayes Factor Consistency for One-way Random Effects Model

TL;DR

This paper develops a Bayesian hypothesis testing method for one-way random effects models, providing a closed-form Bayes factor and analyzing its consistency under various asymptotic conditions, supported by simulations.

Contribution

It introduces a specific prior for variance ratios that yields an explicit Bayes factor and studies its consistency in different asymptotic regimes.

Findings

Explicit closed-form Bayes factor derived

Bayes factor shown to be consistent under multiple asymptotic scenarios

Simulation studies validate theoretical results

Abstract

In this paper, we consider Bayesian hypothesis testing for the balanced one-way random effects model. A special choice of the prior formulation for the ratio of variance components is shown to yield an explicit closed-form Bayes factor without integral representation. Furthermore, we study the consistency issue of the resulting Bayes factor under three asymptotic scenarios: either the number of units goes to infinity, the number of observations per unit goes to infinity, or both go to infinity. Finally, the behavior of the proposed approach is illustrated by simulation studies.