Optimal scaling of random-walk Metropolis algorithms on general target distributions

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Standard

Optimal scaling of random-walk Metropolis algorithms on general target distributions. / Yang, Jun; Roberts, Gareth O.; Rosenthal, Jeffrey S.

I: Stochastic Processes and Their Applications, Bind 30, Nr. 10, 10.2020, s. 6094-6132.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Yang, J, Roberts, GO & Rosenthal, JS 2020, 'Optimal scaling of random-walk Metropolis algorithms on general target distributions', Stochastic Processes and Their Applications, bind 30, nr. 10, s. 6094-6132. https://doi.org/10.1016/j.spa.2020.05.004

APA

Yang, J., Roberts, G. O., & Rosenthal, J. S. (2020). Optimal scaling of random-walk Metropolis algorithms on general target distributions. Stochastic Processes and Their Applications, 30(10), 6094-6132. https://doi.org/10.1016/j.spa.2020.05.004

Vancouver

Yang J, Roberts GO, Rosenthal JS. Optimal scaling of random-walk Metropolis algorithms on general target distributions. Stochastic Processes and Their Applications. 2020 okt.;30(10):6094-6132. https://doi.org/10.1016/j.spa.2020.05.004

Author

Yang, Jun ; Roberts, Gareth O. ; Rosenthal, Jeffrey S. / Optimal scaling of random-walk Metropolis algorithms on general target distributions. I: Stochastic Processes and Their Applications. 2020 ; Bind 30, Nr. 10. s. 6094-6132.

Bibtex

@article{cacb0278880d44e78cca330694c950c2,
title = "Optimal scaling of random-walk Metropolis algorithms on general target distributions",
abstract = "One main limitation of the existing optimal scaling results for Metropolis–Hastings algorithms is that the assumptions on the target distribution are unrealistic. In this paper, we consider optimal scaling of random-walk Metropolis algorithms on general target distributions in high dimensions arising from practical MCMC models from Bayesian statistics. For optimal scaling by maximizing expected squared jumping distance (ESJD), we show the asymptotically optimal acceptance rate 0.234 can be obtained under general realistic sufficient conditions on the target distribution. The new sufficient conditions are easy to be verified and may hold for some general classes of MCMC models arising from Bayesian statistics applications, which substantially generalize the product i.i.d. condition required in most existing literature of optimal scaling. Furthermore, we show one-dimensional diffusion limits can be obtained under slightly stronger conditions, which still allow dependent coordinates of the target distribution. We also connect the new diffusion limit results to complexity bounds of Metropolis algorithms in high dimensions.",
author = "Jun Yang and Roberts, {Gareth O.} and Rosenthal, {Jeffrey S.}",
year = "2020",
month = oct,
doi = "10.1016/j.spa.2020.05.004",
language = "English",
volume = "30",
pages = "6094--6132",
journal = "Stochastic Processes and their Applications",
issn = "0304-4149",
publisher = "Elsevier BV * North-Holland",
number = "10",

}

RIS

TY - JOUR

T1 - Optimal scaling of random-walk Metropolis algorithms on general target distributions

AU - Yang, Jun

AU - Roberts, Gareth O.

AU - Rosenthal, Jeffrey S.

PY - 2020/10

Y1 - 2020/10

N2 - One main limitation of the existing optimal scaling results for Metropolis–Hastings algorithms is that the assumptions on the target distribution are unrealistic. In this paper, we consider optimal scaling of random-walk Metropolis algorithms on general target distributions in high dimensions arising from practical MCMC models from Bayesian statistics. For optimal scaling by maximizing expected squared jumping distance (ESJD), we show the asymptotically optimal acceptance rate 0.234 can be obtained under general realistic sufficient conditions on the target distribution. The new sufficient conditions are easy to be verified and may hold for some general classes of MCMC models arising from Bayesian statistics applications, which substantially generalize the product i.i.d. condition required in most existing literature of optimal scaling. Furthermore, we show one-dimensional diffusion limits can be obtained under slightly stronger conditions, which still allow dependent coordinates of the target distribution. We also connect the new diffusion limit results to complexity bounds of Metropolis algorithms in high dimensions.

AB - One main limitation of the existing optimal scaling results for Metropolis–Hastings algorithms is that the assumptions on the target distribution are unrealistic. In this paper, we consider optimal scaling of random-walk Metropolis algorithms on general target distributions in high dimensions arising from practical MCMC models from Bayesian statistics. For optimal scaling by maximizing expected squared jumping distance (ESJD), we show the asymptotically optimal acceptance rate 0.234 can be obtained under general realistic sufficient conditions on the target distribution. The new sufficient conditions are easy to be verified and may hold for some general classes of MCMC models arising from Bayesian statistics applications, which substantially generalize the product i.i.d. condition required in most existing literature of optimal scaling. Furthermore, we show one-dimensional diffusion limits can be obtained under slightly stronger conditions, which still allow dependent coordinates of the target distribution. We also connect the new diffusion limit results to complexity bounds of Metropolis algorithms in high dimensions.

UR - http://dx.doi.org/10.1016/j.spa.2020.05.004

U2 - 10.1016/j.spa.2020.05.004

DO - 10.1016/j.spa.2020.05.004

M3 - Journal article

VL - 30

SP - 6094

EP - 6132

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

SN - 0304-4149

IS - 10

ER -

ID: 361385644