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Optimal scaling for random walk metropolis on spherically constrained target densities

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Optimal scaling for random walk metropolis on spherically constrained target densities. / Neal, Peter John; Roberts, Gareth.
In: Methodology and Computing in Applied Probability, Vol. 10, No. 2, 06.2008, p. 277-297.

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

Harvard

Neal, PJ & Roberts, G 2008, 'Optimal scaling for random walk metropolis on spherically constrained target densities', Methodology and Computing in Applied Probability, vol. 10, no. 2, pp. 277-297. https://doi.org/10.1007/s11009-007-9046-2

APA

Neal, P. J., & Roberts, G. (2008). Optimal scaling for random walk metropolis on spherically constrained target densities. Methodology and Computing in Applied Probability, 10(2), 277-297. https://doi.org/10.1007/s11009-007-9046-2

Vancouver

Neal PJ, Roberts G. Optimal scaling for random walk metropolis on spherically constrained target densities. Methodology and Computing in Applied Probability. 2008 Jun;10(2):277-297. doi: 10.1007/s11009-007-9046-2

Author

Neal, Peter John ; Roberts, Gareth. / Optimal scaling for random walk metropolis on spherically constrained target densities. In: Methodology and Computing in Applied Probability. 2008 ; Vol. 10, No. 2. pp. 277-297.

Bibtex

@article{52c4d5ea3f514d5195d72cb81b5bd1aa,
title = "Optimal scaling for random walk metropolis on spherically constrained target densities",
abstract = "We consider the problem of optimal scaling of the proposal variance for multidimensional random walk Metropolis algorithms. It is well known, for a wide range of continuous target densities, that the optimal scaling of the proposal variance leads to an average acceptance rate of 0.234. Therefore a natural question is, do similar results hold for target densities which have discontinuities? In the current work, we answer in the affirmative for a class of spherically constrained target densities. Even though the acceptance probability is more complicated than for continuous target densities, the optimal scaling of the proposal variance again leads to an average acceptance rate of 0.234.",
keywords = "Random walk Metropolis algorithm, Markov chain Monte Carlo, Optimal scaling, Spherical distributions, Primary 60F05; Seconadary 65C05",
author = "Neal, {Peter John} and Gareth Roberts",
year = "2008",
month = jun,
doi = "10.1007/s11009-007-9046-2",
language = "English",
volume = "10",
pages = "277--297",
journal = "Methodology and Computing in Applied Probability",
issn = "1387-5841",
publisher = "Springer Netherlands",
number = "2",

}

RIS

TY - JOUR

T1 - Optimal scaling for random walk metropolis on spherically constrained target densities

AU - Neal, Peter John

AU - Roberts, Gareth

PY - 2008/6

Y1 - 2008/6

N2 - We consider the problem of optimal scaling of the proposal variance for multidimensional random walk Metropolis algorithms. It is well known, for a wide range of continuous target densities, that the optimal scaling of the proposal variance leads to an average acceptance rate of 0.234. Therefore a natural question is, do similar results hold for target densities which have discontinuities? In the current work, we answer in the affirmative for a class of spherically constrained target densities. Even though the acceptance probability is more complicated than for continuous target densities, the optimal scaling of the proposal variance again leads to an average acceptance rate of 0.234.

AB - We consider the problem of optimal scaling of the proposal variance for multidimensional random walk Metropolis algorithms. It is well known, for a wide range of continuous target densities, that the optimal scaling of the proposal variance leads to an average acceptance rate of 0.234. Therefore a natural question is, do similar results hold for target densities which have discontinuities? In the current work, we answer in the affirmative for a class of spherically constrained target densities. Even though the acceptance probability is more complicated than for continuous target densities, the optimal scaling of the proposal variance again leads to an average acceptance rate of 0.234.

KW - Random walk Metropolis algorithm

KW - Markov chain Monte Carlo

KW - Optimal scaling

KW - Spherical distributions

KW - Primary 60F05; Seconadary 65C05

U2 - 10.1007/s11009-007-9046-2

DO - 10.1007/s11009-007-9046-2

M3 - Journal article

VL - 10

SP - 277

EP - 297

JO - Methodology and Computing in Applied Probability

JF - Methodology and Computing in Applied Probability

SN - 1387-5841

IS - 2

ER -