{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T21:06:27Z","timestamp":1785618387884,"version":"3.56.0"},"reference-count":19,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2022,10,20]],"date-time":"2022-10-20T00:00:00Z","timestamp":1666224000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023,8,14]]},"abstract":"<jats:title>Summary<\/jats:title>\n               <jats:p>We study the class of first-order locally balanced Metropolis\u2013Hastings algorithms introduced in Livingstone &amp; Zanella (2022). To choose a specific algorithm within the class, the user must select a balancing function $g:{\\mathbb{R}}_+ \\to {\\mathbb{R}}_+$ satisfying $g(t) = tg(1\/t)$ and a noise distribution for the proposal increment. Popular choices within the class are the Metropolis-adjusted Langevin algorithm and the recently introduced Barker proposal. We first establish a general limiting optimal acceptance rate of 57$\\%$ and scaling of $n^{-1\/3}$, as the dimension $n$ tends to infinity among all members of the class under mild smoothness assumptions on $g$ and when the target distribution for the algorithm is of product form. In particular, we obtain an explicit expression for the asymptotic efficiency of an arbitrary algorithm in the class, as measured by expected squared jumping distance. We then consider how to optimize this expression under various constraints. We derive an optimal choice of noise distribution for the Barker proposal, an optimal choice of balancing function under a Gaussian noise distribution, and an optimal choice of first-order locally balanced algorithm among the entire class, which turns out to depend on the specific target distribution. Numerical simulations confirm our theoretical findings, and in particular, show that a bimodal choice of noise distribution in the Barker proposal gives rise to a practical algorithm that is consistently more efficient than the original Gaussian version.<\/jats:p>","DOI":"10.1093\/biomet\/asac056","type":"journal-article","created":{"date-parts":[[2022,10,20]],"date-time":"2022-10-20T17:35:31Z","timestamp":1666287331000},"page":"579-595","source":"Crossref","is-referenced-by-count":8,"title":["Optimal design of the Barker proposal and other locally balanced Metropolis\u2013Hastings algorithms"],"prefix":"10.1093","volume":"110","author":[{"given":"Jure","family":"Vogrinc","sequence":"first","affiliation":[{"name":"Department of Statistics, University of Warwick , Coventry CV4 7AL, U.K"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Samuel","family":"Livingstone","sequence":"additional","affiliation":[{"name":"Department of Statistical Science, University College London , Gower Street, London WC1E 6BT, U.K"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Giacomo","family":"Zanella","sequence":"additional","affiliation":[{"name":"Department of Decision Sciences, Bocconi University , via Roentgen 1, Milan 20136, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2022,10,20]]},"reference":[{"key":"2023081612375177700_B1","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1007\/s11222-008-9110-y","article-title":"A tutorial on adaptive MCMC","volume":"18","author":"Andrieu,","year":"2008","journal-title":"Statist. Comp."},{"key":"2023081612375177700_B2","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1071\/PH650119","article-title":"Monte Carlo calculations of the radial distribution functions for a proton-electron plasma","volume":"18","author":"Barker,","year":"1965","journal-title":"Aust. J. Phys."},{"key":"2023081612375177700_B3","doi-asserted-by":"crossref","first-page":"1501","DOI":"10.3150\/12-BEJ414","article-title":"Optimal tuning of the hybrid Monte Carlo algorithm","volume":"19","author":"Beskos,","year":"2013","journal-title":"Bernoulli"},{"key":"2023081612375177700_B4","doi-asserted-by":"crossref","first-page":"1041","DOI":"10.1016\/j.spa.2019.04.006","article-title":"Metropolis\u2013Hastings reversiblizations of non-reversible Markov chains","volume":"130","author":"Choi,","year":"2020","journal-title":"Stoch. Proces. Appl."},{"key":"2023081612375177700_B5","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1007\/978-3-030-98319-2_8","article-title":"A fresh take on \u2018 Barker dynamics\u2019 for MCMC","volume-title":"International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing (MCQMC 2020)","author":"Hird,","year":"2022"},{"key":"2023081612375177700_B6","doi-asserted-by":"crossref","first-page":"496","DOI":"10.1111\/rssb.12482","article-title":"The Barker proposal: Combining robustness and efficiency in gradient based MCMC","volume":"84","author":"Livingstone,","year":"2022","journal-title":"J. R. Statist. Soc. B"},{"key":"2023081612375177700_B7","doi-asserted-by":"crossref","first-page":"583","DOI":"10.1007\/s11009-010-9176-9","article-title":"Optimal scaling of random walk Metropolis algorithms with non-Gaussian proposals","volume":"13","author":"Neal,","year":"2011","journal-title":"Methodol. Comp. Appl. Prob."},{"key":"2023081612375177700_B8","article-title":"Accelerated sampling on discrete spaces with non-reversible Markov processes","author":"Power,","year":"2019"},{"key":"2023081612375177700_B9","first-page":"110","article-title":"Weak convergence and optimal scaling of random walk Metropolis algorithms","volume":"7","author":"Roberts,","year":"1997","journal-title":"Ann. Appl. Prob."},{"key":"2023081612375177700_B10","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1111\/1467-9868.00123","article-title":"Optimal scaling of discrete approximations to Langevin diffusions","volume":"60","author":"Roberts,","year":"1998","journal-title":"J. R. Statist. Soc. B"},{"key":"2023081612375177700_B11","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1214\/ss\/1015346320","article-title":"Optimal scaling for various Metropolis-Hastings algorithms","volume":"16","author":"Roberts,","year":"2001","journal-title":"Statist. Sci."},{"key":"2023081612375177700_B12","doi-asserted-by":"crossref","first-page":"341","DOI":"10.2307\/3318418","article-title":"Exponential convergence of Langevin distributions and their discrete approximations","volume":"2","author":"Roberts,","year":"1996","journal-title":"Bernoulli"},{"key":"2023081612375177700_B13","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1239\/jap\/1363784420","article-title":"Optimal scaling of the random walk Metropolis: General criteria for the 0.234 acceptance rule","volume":"50","author":"Sherlock,","year":"2013","journal-title":"J. Appl. Prob."},{"key":"2023081612375177700_B14","doi-asserted-by":"crossref","first-page":"172","DOI":"10.1214\/10-STS327","article-title":"The random walk Metropolis: Linking theory and practice through a case study","volume":"25","author":"Sherlock,","year":"2010","journal-title":"Statist. Sci."},{"key":"2023081612375177700_B15","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1214\/aoap\/1027961031","article-title":"A note on Metropolis-Hastings kernels for general state spaces","volume":"8","author":"Tierney,","year":"1998","journal-title":"Ann. Appl. Prob."},{"key":"2023081612375177700_B16","doi-asserted-by":"crossref","first-page":"972","DOI":"10.1214\/20-AAP1612","article-title":"Counterexamples for optimal scaling of Metropolis\u2013Hastings chains with rough target densities","volume":"31","author":"Vogrinc,","year":"2021","journal-title":"Ann. Appl. Prob."},{"key":"2023081612375177700_B17","doi-asserted-by":"crossref","first-page":"19307","DOI":"10.1073\/pnas.1311790110","article-title":"Searching for efficient Markov chain Monte Carlo proposal kernels","volume":"110","author":"Yang,","year":"2013","journal-title":"Proc. Nat. Acad. Sci."},{"key":"2023081612375177700_B18","doi-asserted-by":"crossref","first-page":"852","DOI":"10.1080\/01621459.2019.1585255","article-title":"Informed proposals for local MCMC in discrete spaces","volume":"115","author":"Zanella,","year":"2020","journal-title":"J. Am. Statist. Assoc."},{"key":"2023081612375177700_B19","doi-asserted-by":"crossref","first-page":"4053","DOI":"10.1016\/j.spa.2017.03.021","article-title":"A Dirichlet form approach to MCMC optimal scaling","volume":"127","author":"Zanella,","year":"2017","journal-title":"Stoch. Proces. Appl."}],"container-title":["Biometrika"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/biomet\/advance-article-pdf\/doi\/10.1093\/biomet\/asac056\/47308774\/asac056.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/biomet\/article-pdf\/110\/3\/579\/51115798\/asac056.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/biomet\/article-pdf\/110\/3\/579\/51115798\/asac056.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,16]],"date-time":"2023-08-16T12:51:50Z","timestamp":1692190310000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/biomet\/article\/110\/3\/579\/6764577"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,10,20]]},"references-count":19,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2022,10,20]]},"published-print":{"date-parts":[[2023,8,14]]}},"URL":"https:\/\/doi.org\/10.1093\/biomet\/asac056","relation":{},"ISSN":["0006-3444","1464-3510"],"issn-type":[{"value":"0006-3444","type":"print"},{"value":"1464-3510","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2023,9,1]]},"published":{"date-parts":[[2022,10,20]]}}}