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Recursive computing and simulation-free inference for general factorizable models

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  • Nial Friel
  • Håvard Rue

Abstract

We illustrate how the recursive algorithm of Reeves & Pettitt (2004) for general factorizable models can be extended to allow exact sampling, maximization of distributions and computation of marginal distributions. All of the methods we describe apply to discrete-valued Markov random fields with nearest neighbour integrations defined on regular lattices; in particular we illustrate that exact inference can be performed for hidden autologistic models defined on moderately sized lattices. In this context we offer an extension of this methodology which allows approximate inference to be carried out for larger lattices without resorting to simulation techniques such as Markov chain Monte Carlo. In particular our work offers the basis for an automatic inference machine for such models. Copyright 2007, Oxford University Press.

Suggested Citation

  • Nial Friel & Håvard Rue, 2007. "Recursive computing and simulation-free inference for general factorizable models," Biometrika, Biometrika Trust, vol. 94(3), pages 661-672.
    • Handle: RePEc:oup:biomet:v:94:y:2007:i:3:p:661-672
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    File URL: http://hdl.handle.net/10.1093/biomet/asm052
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    References listed on IDEAS

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    1. Håvard Rue & Ingelin Steinsland & Sveinung Erland, 2004. "Approximating hidden Gaussian Markov random fields," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(4), pages 877-892, November.
    2. R. Reeves, 2004. "Efficient recursions for general factorisable models," Biometrika, Biometrika Trust, vol. 91(3), pages 751-757, September.
    3. Scott S. L., 2002. "Bayesian Methods for Hidden Markov Models: Recursive Computing in the 21st Century," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 337-351, March.
    4. Julian Besag & Jeremy York & Annie Mollié, 1991. "Bayesian image restoration, with two applications in spatial statistics," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 43(1), pages 1-20, March.
    5. C. P. Robert & T. Rydén & D. M. Titterington, 2000. "Bayesian inference in hidden Markov models through the reversible jump Markov chain Monte Carlo method," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(1), pages 57-75.
    6. Ming Gao Gu & Hong‐Tu Zhu, 2001. "Maximum likelihood estimation for spatial models by Markov chain Monte Carlo stochastic approximation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 339-355.
    7. Francesco Bartolucci, 2002. "A recursive algorithm for Markov random fields," Biometrika, Biometrika Trust, vol. 89(3), pages 724-730, August.
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    Cited by:

    1. Jin, Ick Hoon & Liang, Faming, 2014. "Use of SAMC for Bayesian analysis of statistical models with intractable normalizing constants," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 402-416.

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