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

Chris Sherlock ()
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Chris Sherlock: Lancaster University

Methodology and Computing in Applied Probability, 2016, vol. 18, issue 3, 869-884

Abstract: 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.

Keywords: Pseudo marginal Markov chain Monte Carlo; Random walk Metropolis; Optimal scaling; Particle MCMC; Robustness; 65C05; 65C40 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s11009-015-9471-6

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