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

Research output: Contribution to Journal/Magazine › Journal article › peer-review

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Optimal scaling for the pseudo-marginal random walk Metropolis: insensitivity to the noise generating mechanism. / Sherlock, Christopher.
In: Methodology and Computing in Applied Probability, Vol. 18, No. 3, 09.2016, p. 869-884.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Sherlock, C 2016, 'Optimal scaling for the pseudo-marginal random walk Metropolis: insensitivity to the noise generating mechanism', Methodology and Computing in Applied Probability, vol. 18, no. 3, pp. 869-884. https://doi.org/10.1007/s11009-015-9471-6

APA

Sherlock, C. (2016). Optimal scaling for the pseudo-marginal random walk Metropolis: insensitivity to the noise generating mechanism. Methodology and Computing in Applied Probability, 18(3), 869-884. https://doi.org/10.1007/s11009-015-9471-6

Vancouver

Sherlock C. Optimal scaling for the pseudo-marginal random walk Metropolis: insensitivity to the noise generating mechanism. Methodology and Computing in Applied Probability. 2016 Sept;18(3):869-884. Epub 2015 Oct 30. doi: 10.1007/s11009-015-9471-6

Author

Sherlock, Christopher. / Optimal scaling for the pseudo-marginal random walk Metropolis : insensitivity to the noise generating mechanism. In: Methodology and Computing in Applied Probability. 2016 ; Vol. 18, No. 3. pp. 869-884.

Bibtex

@article{19984c001890403da9576a3144798863,
title = "Optimal scaling for the pseudo-marginal random walk Metropolis: insensitivity to the noise generating mechanism",
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.",
keywords = "Pseudo marginal Markov chain Monte Carlo, Random walk Metropolis, Optimal scaling, Particle MCMC, Robustness, 65C05, 65C40",
author = "Christopher Sherlock",
note = "The final publication is available at Springer via http://dx.doi.org/10.1007/s11009-015-9471-6 ",
year = "2016",
month = sep,
doi = "10.1007/s11009-015-9471-6",
language = "English",
volume = "18",
pages = "869--884",
journal = "Methodology and Computing in Applied Probability",
issn = "1387-5841",
publisher = "Springer Netherlands",
number = "3",

}

RIS

TY - JOUR

T1 - Optimal scaling for the pseudo-marginal random walk Metropolis

T2 - insensitivity to the noise generating mechanism

AU - Sherlock, Christopher

N1 - The final publication is available at Springer via http://dx.doi.org/10.1007/s11009-015-9471-6

PY - 2016/9

Y1 - 2016/9

N2 - 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.

AB - 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.

KW - Pseudo marginal Markov chain Monte Carlo

KW - Random walk Metropolis

KW - Optimal scaling

KW - Particle MCMC

KW - Robustness

KW - 65C05

KW - 65C40

U2 - 10.1007/s11009-015-9471-6

DO - 10.1007/s11009-015-9471-6

M3 - Journal article

VL - 18

SP - 869

EP - 884

JO - Methodology and Computing in Applied Probability

JF - Methodology and Computing in Applied Probability

SN - 1387-5841

IS - 3

ER -