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Model comparison for Gibbs random fields using noisy reversible jump Markov chain Monte Carlo

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  • Bouranis, Lampros
  • Friel, Nial
  • Maire, Florian

Abstract

The reversible jump Markov chain Monte Carlo (RJMCMC) method offers an across-model simulation approach for Bayesian estimation and model comparison, by exploring the sampling space that consists of several models of possibly varying dimensions. A naive implementation of RJMCMC to models like Gibbs random fields suffers from computational difficulties: the posterior distribution for each model is termed doubly-intractable since computation of the likelihood function is rarely available. Consequently, it is simply impossible to simulate a transition of the Markov chain in the presence of likelihood intractability. A variant of RJMCMC is presented, called noisy RJMCMC, where the underlying transition kernel is replaced with an approximation based on unbiased estimators. Based on previous theoretical developments, convergence guarantees for the noisy RJMCMC algorithm are provided. The experiments show that the noisy RJMCMC algorithm can be much more efficient than other exact methods, provided that an estimator with controlled Monte Carlo variance is used, a fact which is in agreement with the theoretical analysis.

Suggested Citation

  • Bouranis, Lampros & Friel, Nial & Maire, Florian, 2018. "Model comparison for Gibbs random fields using noisy reversible jump Markov chain Monte Carlo," Computational Statistics & Data Analysis, Elsevier, vol. 128(C), pages 221-241.
    • Handle: RePEc:eee:csdana:v:128:y:2018:i:c:p:221-241
    DOI: 10.1016/j.csda.2018.07.005
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    References listed on IDEAS

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    Cited by:

    1. Alexander Y. Mitrophanov, 2024. "The Arsenal of Perturbation Bounds for Finite Continuous-Time Markov Chains: A Perspective," Mathematics, MDPI, vol. 12(11), pages 1-15, May.

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