Title: Accurate Computation of Marginal Data Densities Using Variational Bayes,
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-justified, has finite variance, provides a minimum variance
candidate for the class of reciprocal importance sampling MDD estimators, and
that its reciprocal is consistent, asymptotically normally distributed and
unbiased. We also investigate the performance of the variational Bayes
approximate density as a weighting density within the class of bridge sampling
estimators. Using several examples, we show that our proposed estimators are at
least as good as the best existing estimators and outperform many MDD
estimators in terms of bias and numerical standard errors.