Mode jumping MCMC for Bayesian variable selection in GLMM

Aliaksandr Hubin and Geir Storvik

Computational Statistics & Data Analysis, 2018, vol. 127, issue C, 281-297

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.

Keywords: Bayesian variable selection; Bayesian model averaging; Generalized linear mixed models; Auxiliary variables MCMC; Combinatorial optimization; High performance computations (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:127:y:2018:i:c:p:281-297

DOI: 10.1016/j.csda.2018.05.020

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