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Block-Wise Pseudo-Marginal Metropolis-Hastings


  • Kohn, R.
  • Quiroz, M.
  • Tran, M.-N.
  • Villani, M.


The pseudo-marginal Metropolis-Hastings approach is increasingly used for Bayesian inference in statistical models where the likelihood is analytically intractable but can be estimated unbiasedly, such as random effects models and state-space models, or for data subsampling in big data settings. In a seminal paper, Deligiannidis et al. (2015) show how the pseudo-marginal Metropolis-Hastings (PMMH) approach can be made much more e cient by correlating the underlying random numbers used to form the estimate of the likelihood at the current and proposed values of the unknown parameters. Their proposed approach greatly speeds up the standard PMMH algorithm, as it requires a much smaller number of particles to form the optimal likelihood estimate. We present a closely related alternative PMMH approach that divides the underlying random numbers mentioned above into blocks so that the likelihood estimates for the proposed and current values of the likelihood only di er by the random numbers in one block. Our approach is less general than that of Deligiannidis et al. (2015), but has the following advantages. First, it provides a more direct way to control the correlation between the logarithms of the estimates of the likelihood at the current and proposed values of the parameters. Second, the mathematical properties of the method are simplified and made more transparent compared to the treatment in Deligiannidis et al. (2015). Third, blocking is shown to be a natural way to carry out PMMH in, for example, panel data models and subsampling problems. We obtain theory and guidelines for selecting the optimal number of particles, and document large speed-ups in a panel data example and a subsampling problem.

Suggested Citation

  • Kohn, R. & Quiroz, M. & Tran, M.-N. & Villani, M., 2016. "Block-Wise Pseudo-Marginal Metropolis-Hastings," Working Papers 2016-03, University of Sydney Business School, Discipline of Business Analytics.
  • Handle: RePEc:syb:wpbsba:2123/14595

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    Cited by:

    1. Golightly, Andrew & Bradley, Emma & Lowe, Tom & Gillespie, Colin S., 2019. "Correlated pseudo-marginal schemes for time-discretised stochastic kinetic models," Computational Statistics & Data Analysis, Elsevier, vol. 136(C), pages 92-107.
    2. Kohn, Robert & Nguyen, Nghia & Nott, David & Tran, Minh-Ngoc, 2017. "Random Effects Models with Deep Neural Network Basis Functions: Methodology and Computation," Working Papers 2123/17877, University of Sydney Business School, Discipline of Business Analytics.

    More about this item


    Intractable likelihood; Data subsampling; Panel data; Unbiasedness;
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