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

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  • Peter Hall
  • K. Humphreys
  • D. M. Titterington

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.

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  • Peter Hall & K. Humphreys & D. M. Titterington, 2002. "On the adequacy of variational lower bound functions for likelihood‐based inference in Markovian models with missing values," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 549-564, August.
    • Handle: RePEc:bla:jorssb:v:64:y:2002:i:3:p:549-564
    DOI: 10.1111/1467-9868.00350
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    Cited by:

    1. K. Humphreys & D. Titterington, 2003. "Variational approximations for categorical causal modeling with latent variables," Psychometrika, Springer;The Psychometric Society, vol. 68(3), pages 391-412, September.
    2. Ormerod, John T., 2011. "Grid based variational approximations," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 45-56, January.

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