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Optimal scaling of MCMC beyond Metropolis
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Agrawal, Sanket, Vats, Dootika, Łatuszyński, Krzysztof and Roberts, Gareth O. (2023) Optimal scaling of MCMC beyond Metropolis. Advances in Applied Probability, 55 (2). pp. 492-509. doi:10.1017/apr.2022.37 ISSN 0001-8678.
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Official URL: http://doi.org/10.1017/apr.2022.37
Abstract
The problem of optimally scaling the proposal distribution in a Markov chain Monte Carlo algorithm is critical to the quality of the generated samples. Much work has gone into obtaining such results for various Metropolis–Hastings (MH) algorithms. Recently, acceptance probabilities other than MH are being employed in problems with intractable target distributions. There are few resources available on tuning the Gaussian proposal distributions for this situation. We obtain optimal scaling results for a general class of acceptance functions, which includes Barker’s and lazy MH. In particular, optimal values for Barker’s algorithm are derived and found to be significantly different from that obtained for the MH algorithm. Our theoretical conclusions are supported by numerical simulations indicating that when the optimal proposal variance is unknown, tuning to the optimal acceptance probability remains an effective strategy.
| Item Type: | Journal Article | ||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics Faculty of Science, Engineering and Medicine > Science > Statistics |
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| Library of Congress Subject Headings (LCSH): | Markov processes, Monte Carlo method, Gaussian processes, Probabilities, Stochastic processes | ||||||||
| Journal or Publication Title: | Advances in Applied Probability | ||||||||
| Publisher: | Applied Probability Trust | ||||||||
| ISSN: | 0001-8678 | ||||||||
| Official Date: | June 2023 | ||||||||
| Dates: |
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| Volume: | 55 | ||||||||
| Number: | 2 | ||||||||
| Page Range: | pp. 492-509 | ||||||||
| DOI: | 10.1017/apr.2022.37 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||
| Date of first compliant deposit: | 15 June 2023 | ||||||||
| Date of first compliant Open Access: | 15 June 2023 |
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