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Optimal Scaling for the Pseudo-Marginal Random Walk Metropolis: Insensitivity to the Noise Generating Mechanism

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  • Chris Sherlock

    (Lancaster University)

Abstract

We examine the optimal scaling and the efficiency of the pseudo-marginal random walk Metropolis algorithm using a recently-derived result on the limiting efficiency as the dimension, d → ∞ $d\rightarrow \infty $ . We prove that the optimal scaling for a given target varies by less than 20 % across a wide range of distributions for the noise in the estimate of the target, and that any scaling that is within 20 % of the optimal one will be at least 70 % efficient. We demonstrate that this phenomenon occurs even outside the range of noise distributions for which we rigorously prove it. We then conduct a simulation study on an example with d = 10 where importance sampling is used to estimate the target density; we also examine results available from an existing simulation study with d = 5 and where a particle filter was used. Our key conclusions are found to hold in these examples also.

Suggested Citation

  • Chris Sherlock, 2016. "Optimal Scaling for the Pseudo-Marginal Random Walk Metropolis: Insensitivity to the Noise Generating Mechanism," Methodology and Computing in Applied Probability, Springer, vol. 18(3), pages 869-884, September.
    • Handle: RePEc:spr:metcap:v:18:y:2016:i:3:d:10.1007_s11009-015-9471-6
    DOI: 10.1007/s11009-015-9471-6
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    References listed on IDEAS

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    1. Christophe Andrieu & Arnaud Doucet & Roman Holenstein, 2010. "Particle Markov chain Monte Carlo methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(3), pages 269-342, June.
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    3. Emanuele Giorgi & Sanie S. S. Sesay & Dianne J. Terlouw & Peter J. Diggle, 2015. "Combining data from multiple spatially referenced prevalence surveys using generalized linear geostatistical models," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 178(2), pages 445-464, February.
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