Lack of Consistency of Mean Field and Variational break Bayes Approximations for State Space Models

Authors:
Bo Wang;D. M. Titterington
Affiliations:
Department of Statistics, University of Glasgow, Glasgow, UK G12 8QQ;Department of Statistics, University of Glasgow, Glasgow, UK G12 8QQ
Venue:
Neural Processing Letters
Year:
2004

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Abstract

The consistency problem of both mean field and variational Bayes estimators in the context of linear state space models is investigated. We prove that the mean field approximation is asymptotically consistent when the variances of the noise variables in the system are sufficiently small, but neither the mean field estimator nor the variational Bayes estimator is always asymptotically consistent as the 'sample size' becomes large. The 'gap' between the estimators and the true values is roughly estimated.