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Methodology and Computing in Applied Probability

, Volume 18, Issue 3, pp 869–884 | Cite as

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

  • Chris SherlockEmail author
Article
  • 96 Downloads

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, \(d\rightarrow \infty \). 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 

Mathematics Subject Classification (2010)

65C05 65C40 

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsLancaster UniversityLancasterUK

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