Mode jumping MCMC for Bayesian variable selection in GLMM

TL;DR

This paper introduces a novel mode jumping MCMC algorithm for Bayesian variable selection in GLMMs, efficiently exploring complex model spaces with multiple local optima, demonstrated on various datasets.

Contribution

The paper presents a new MCMC method that improves Bayesian variable selection in GLMMs by enabling efficient mode jumping in complex model spaces.

Findings

Effective exploration of model space demonstrated on multiple datasets

Outperforms existing methods in model selection accuracy

Efficient marginal likelihood computation enhances algorithm performance

Abstract

Generalized linear mixed models (GLMM) are used for inference and prediction in a wide range of different applications providing a powerful scientific tool. An increasing number of sources of data are becoming available, introducing a variety of candidate explanatory variables for these models. Selection of an optimal combination of variables is thus becoming crucial. In a Bayesian setting, the posterior distribution of the models, based on the observed data, can be viewed as a relevant measure for the model evidence. The number of possible models increases exponentially in the number of candidate variables. Moreover, the space of models has numerous local extrema in terms of posterior model probabilities. To resolve these issues a novel MCMC algorithm for the search through the model space via efficient mode jumping for GLMMs is introduced. The algorithm is based on that marginal likelihoods can be efficiently calculated within each model. It is recommended that either exact expressions or precise approximations of marginal likelihoods are applied. The suggested algorithm is applied to simulated data, the famous U.S. crime data, protein activity data and epigenetic data and is compared to several existing approaches.