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Optimal scaling of random walk metropolis algorithms with non-Gaussian proposals

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Optimal scaling of random walk metropolis algorithms with non-Gaussian proposals. / Neal, Peter John; Roberts, Gareth.
In: Methodology and Computing in Applied Probability, Vol. 13, No. 3, 09.2011, p. 583-601.

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

Harvard

Neal, PJ & Roberts, G 2011, 'Optimal scaling of random walk metropolis algorithms with non-Gaussian proposals', Methodology and Computing in Applied Probability, vol. 13, no. 3, pp. 583-601. https://doi.org/10.1007/s11009-010-9176-9

APA

Neal, P. J., & Roberts, G. (2011). Optimal scaling of random walk metropolis algorithms with non-Gaussian proposals. Methodology and Computing in Applied Probability, 13(3), 583-601. https://doi.org/10.1007/s11009-010-9176-9

Vancouver

Neal PJ, Roberts G. Optimal scaling of random walk metropolis algorithms with non-Gaussian proposals. Methodology and Computing in Applied Probability. 2011 Sept;13(3):583-601. doi: 10.1007/s11009-010-9176-9

Author

Neal, Peter John ; Roberts, Gareth. / Optimal scaling of random walk metropolis algorithms with non-Gaussian proposals. In: Methodology and Computing in Applied Probability. 2011 ; Vol. 13, No. 3. pp. 583-601.

Bibtex

@article{cb25734031704bc0a761440ee3b0af67,
title = "Optimal scaling of random walk metropolis algorithms with non-Gaussian proposals",
abstract = "The asymptotic optimal scaling of random walk Metropolis (RWM) algorithms with Gaussian proposal distributions is well understood for certain specific classes of target distributions. These asymptotic results easily extend to any light tailed proposal distribution with finite fourth moment. However, heavy tailed proposal distributions such as the Cauchy distribution are known to have a number of desirable properties, and in many situations are preferable to light tailed proposal distributions. Therefore we consider the question of scaling for Cauchy distributed proposals for a wide range of independent and identically distributed (iid) product densities. The results are somewhat surprising as to when and when not Cauchy distributed proposals are preferable to Gaussian proposal distributions. This provides motivation for finding proposal distributions which improve on both Gaussian and Cauchy proposals, both for finite dimensional target distributions and asymptotically as the dimension of the target density, d → ∞. Throughout we seek the scaling of the proposal distribution which maximizes the expected squared jumping distance (ESJD).",
keywords = "MCMC, Cauchy distribution, Spherical distributions, Heavy tailed distributions, Random walk metropolis, Optimal scaling",
author = "Neal, {Peter John} and Gareth Roberts",
year = "2011",
month = sep,
doi = "10.1007/s11009-010-9176-9",
language = "English",
volume = "13",
pages = "583--601",
journal = "Methodology and Computing in Applied Probability",
issn = "1387-5841",
publisher = "Springer Netherlands",
number = "3",

}

RIS

TY - JOUR

T1 - Optimal scaling of random walk metropolis algorithms with non-Gaussian proposals

AU - Neal, Peter John

AU - Roberts, Gareth

PY - 2011/9

Y1 - 2011/9

N2 - The asymptotic optimal scaling of random walk Metropolis (RWM) algorithms with Gaussian proposal distributions is well understood for certain specific classes of target distributions. These asymptotic results easily extend to any light tailed proposal distribution with finite fourth moment. However, heavy tailed proposal distributions such as the Cauchy distribution are known to have a number of desirable properties, and in many situations are preferable to light tailed proposal distributions. Therefore we consider the question of scaling for Cauchy distributed proposals for a wide range of independent and identically distributed (iid) product densities. The results are somewhat surprising as to when and when not Cauchy distributed proposals are preferable to Gaussian proposal distributions. This provides motivation for finding proposal distributions which improve on both Gaussian and Cauchy proposals, both for finite dimensional target distributions and asymptotically as the dimension of the target density, d → ∞. Throughout we seek the scaling of the proposal distribution which maximizes the expected squared jumping distance (ESJD).

AB - The asymptotic optimal scaling of random walk Metropolis (RWM) algorithms with Gaussian proposal distributions is well understood for certain specific classes of target distributions. These asymptotic results easily extend to any light tailed proposal distribution with finite fourth moment. However, heavy tailed proposal distributions such as the Cauchy distribution are known to have a number of desirable properties, and in many situations are preferable to light tailed proposal distributions. Therefore we consider the question of scaling for Cauchy distributed proposals for a wide range of independent and identically distributed (iid) product densities. The results are somewhat surprising as to when and when not Cauchy distributed proposals are preferable to Gaussian proposal distributions. This provides motivation for finding proposal distributions which improve on both Gaussian and Cauchy proposals, both for finite dimensional target distributions and asymptotically as the dimension of the target density, d → ∞. Throughout we seek the scaling of the proposal distribution which maximizes the expected squared jumping distance (ESJD).

KW - MCMC

KW - Cauchy distribution

KW - Spherical distributions

KW - Heavy tailed distributions

KW - Random walk metropolis

KW - Optimal scaling

U2 - 10.1007/s11009-010-9176-9

DO - 10.1007/s11009-010-9176-9

M3 - Journal article

VL - 13

SP - 583

EP - 601

JO - Methodology and Computing in Applied Probability

JF - Methodology and Computing in Applied Probability

SN - 1387-5841

IS - 3

ER -