Optimal scaling for the pseudo-marginal random walk Metropolis : insensitivity to the noise generating mechanism

Sherlock, Christopher (2016) Optimal scaling for the pseudo-marginal random walk Metropolis : insensitivity to the noise generating mechanism. Methodology and Computing in Applied Probability, 18 (3). pp. 869-884. ISSN 1387-5841

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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→∞. 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.