Fast and Accurate Computation of Marginal Likelihood

Dr Reza Hajargasht | University of Melbourne

Bayesian model selection and model averaging require estimation of Marginal Likelihood also known as Marginal Data Density (MDD). Estimation of marginal likelihood relies on numerical integration methods but the problem is still nontrivial for many statistical and econometric models. In the present paper two new MDD estimators are proposed. The first, belongs to the class of Generalized Harmonic Mean estimators, and the second to the class of Bridge Sampling estimators. Both proposals use approximate posterior density from variational Bayes estimation procedure as a candidate density. Such a density approximates the posterior well and its features make it a good candidate for reciprocal importance sampling based techniques. The two new MDD estimators are computed using the sample from the MCMC simulation of the posterior density and the output from variational Bayes estimation. Several examples including Vector Autoregression, Nonparametric Regression, and Stochastic Frontier Models are considered and the accuracy of their MDD estimator is compared to those from the common techniques.