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On asymptotic validity of naive inference with an approximate likelihood

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  • H. E. Ogden

Abstract

SUMMARY Many statistical models have likelihoods which are intractable: it is impossible or too expensive to compute the likelihood exactly. In such settings, a common approach is to replace the likelihood with an approximation, and proceed with inference as if the approximate likelihood were the true likelihood. In this paper, we describe conditions which guarantee that such naive inference with an approximate likelihood has the same first-order asymptotic properties as inference with the true likelihood. We investigate the implications of these results for inference using a Laplace approximation to the likelihood in a simple two-level latent variable model and using reduced dependence approximations to the likelihood in an Ising model.

Suggested Citation

  • H. E. Ogden, 2017. "On asymptotic validity of naive inference with an approximate likelihood," Biometrika, Biometrika Trust, vol. 104(1), pages 153-164.
    • Handle: RePEc:oup:biomet:v:104:y:2017:i:1:p:153-164.
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    File URL: http://hdl.handle.net/10.1093/biomet/asx002
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    Cited by:

    1. Ruggero Bellio & Nicola Soriani, 2021. "Maximum likelihood estimation based on the Laplace approximation for p2 network regression models," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 75(1), pages 24-41, February.
    2. Han, Jeongseop & Lee, Youngjo, 2024. "Enhanced Laplace approximation," Journal of Multivariate Analysis, Elsevier, vol. 202(C).
    3. Matti Vihola & Jouni Helske & Jordan Franks, 2020. "Importance sampling type estimators based on approximate marginal Markov chain Monte Carlo," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(4), pages 1339-1376, December.

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