Accurate Computation of Marginal Data Densities Using Variational Bayes
share
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.
READ FULL TEXT
