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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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