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Accurate Computation of Marginal Data Densities Using Variational Bayes

T Wozniak, Gholamreza Hajarghasht

arXiv.org | Published : 2018

Abstract

Bayesian model selection and model averaging rely on estimates of marginal data densities (MDDs) also known as marginal likelihoods. Estimation of MDDs is often nontrivial and requires elaborate numerical integration methods. We propose using the variational Bayes posterior density as a weighting density within the class of reciprocal importance sampling MDD estimators. This proposal is computationally convenient, is based on variational Bayes posterior densities that are available for many models, only requires simulated draws from the posterior distribution, and provides accurate estimates with a moderate number of posterior draws. We show that this estimator is theoretically well-justifie..

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