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Grid based variational approximations

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  • Ormerod, John T.

Abstract

Variational methods for approximate Bayesian inference provide fast, flexible, deterministic alternatives to Monte Carlo methods. Unfortunately, unlike Monte Carlo methods, variational approximations cannot, in general, be made to be arbitrarily accurate. This paper develops grid-based variational approximations which endeavor to approximate marginal posterior densities in a spirit similar to the Integrated Nested Laplace Approximation (INLA) of Rue et al. (2009)but which may be applied in situations where INLA cannot be used. The method can greatly increase the accuracy of a base variational approximation, although not in general to arbitrary accuracy. The methodology developed is at least reasonably accurate on all of the examples considered in the paper.

Suggested Citation

  • Ormerod, John T., 2011. "Grid based variational approximations," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 45-56, January.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:1:p:45-56
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    References listed on IDEAS

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    1. Håvard Rue & Sara Martino & Nicolas Chopin, 2009. "Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 319-392, April.
    2. Consonni, Guido & Marin, Jean-Michel, 2007. "Mean-field variational approximate Bayesian inference for latent variable models," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 790-798, October.
    3. 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.
    4. Ormerod, J. T. & Wand, M. P., 2010. "Explaining Variational Approximations," The American Statistician, American Statistical Association, vol. 64(2), pages 140-153.
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    1. Brown, Paul T. & Joshi, Chaitanya & Joe, Stephen & Rue, Håvard, 2021. "A novel method of marginalisation using low discrepancy sequences for integrated nested Laplace approximations," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).
    2. Minjeong Jeon & Frank Rijmen & Sophia Rabe-Hesketh, 2017. "A Variational Maximization–Maximization Algorithm for Generalized Linear Mixed Models with Crossed Random Effects," Psychometrika, Springer;The Psychometric Society, vol. 82(3), pages 693-716, September.

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