Bayes factors for longitudinal model assessment via power posteriors

TL;DR

This paper investigates the use of power posteriors to compute Bayes factors efficiently for model assessment in linear mixed models, addressing computational challenges in marginal likelihood estimation.

Contribution

It introduces a novel application of power posteriors for Bayesian model comparison in LMMs, supported by simulation studies and real data analysis.

Findings

Power posteriors facilitate marginal likelihood computation in LMMs.

The method performs well in simulation studies.

Application to sardine landings data demonstrates practical utility.

Abstract

Bayes factor, defined as the ratio of the marginal likelihood functions of two competing models, is the natural Bayesian procedure for model selection. Marginal likelihoods are usually computationally demanding and complex. This scenario is particularly cumbersome in linear mixed models (LMMs) because marginal likelihood functions involve integrals of large dimensions determined by the number of parameters and the number of random effects, which in turn increase with the number of individuals in the sample. The power posterior is an attractive proposal in the context of the Markov chain Monte Carlo algorithms that allows expressing marginal likelihoods as one-dimensional integrals over the unit range. This paper explores the use of power posteriors in LMMs and discusses their behaviour through two simulation studies and a real data set on European sardine landings in the Mediterranean Sea.