On the adequacy of variational lower bound functions for likelihood-based inference in Markovian models with missing values
Peter Hall, K. Humphreys, D. M. Titterington
Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 2002 · Volume 64 · Issue 3
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.
Keywords
Autoregressive model, Gaussian random field, Markovian model, Maximum likelihood, Missing values, Variational approximation
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