Mean-field variational approximate Bayesian inference for latent variable models

Authors:
Guido Consonni;Jean-Michel Marin
Affiliations:
Department of Economics and Quantitative Methods, University of Pavia, Pavia, Italy;INRIA FUTURS Projet SELECT, Laboratoire de Mathématiques (Bít. 425), Université d'Orsay, 91405 Orsay, France
Venue:
Computational Statistics & Data Analysis
Year:
2007

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Abstract

The ill-posed nature of missing variable models offers a challenging testing ground for new computational techniques. This is the case for the mean-field variational Bayesian inference. The behavior of this approach in the setting of the Bayesian probit model is illustrated. It is shown that the mean-field variational method always underestimates the posterior variance and, that, for small sample sizes, the mean-field variational approximation to the posterior location could be poor.