On the adequacy of variational lower bound functions for likelihood‐based inference in Markovian models with missing values

Peter Hall, K. Humphreys and D. M. Titterington

Journal of the Royal Statistical Society Series B, 2002, vol. 64, issue 3, 549-564

Abstract: Summary. Variational methods have been proposed for obtaining deterministic lower bounds for log‐likelihoods within missing data problems, but with little formal justification or investigation of the worth of the lower bound surfaces as tools for inference. We provide, within a general Markovian context, sufficient conditions under which estimators from the variational approximations are asymptotically equivalent to maximum likelihood estimators, and we show empirically, for the simple example of a first‐order autoregressive model with missing values, that the lower bound surface can be very similar in shape to the true log‐likelihood in non‐asymptotic situations.

Date: 2002
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