{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T08:49:07Z","timestamp":1778575747546,"version":"3.51.4"},"reference-count":54,"publisher":"Oxford University Press (OUP)","issue":"5","license":[{"start":{"date-parts":[[2022,10,31]],"date-time":"2022-10-31T00:00:00Z","timestamp":1667174400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["EP\/R018561\/1"],"award-info":[{"award-number":["EP\/R018561\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["EP\/R034710\/1"],"award-info":[{"award-number":["EP\/R034710\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"publisher","award":["RGPIN-2019-04142"],"award-info":[{"award-number":["RGPIN-2019-04142"]}],"id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001843","name":"Science and Engineering Research Board","doi-asserted-by":"publisher","award":["SPG\/2021\/001322"],"award-info":[{"award-number":["SPG\/2021\/001322"]}],"id":[{"id":"10.13039\/501100001843","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022,11,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Yang et al. proved that the symmetric random walk Metropolis\u2013Hastings algorithm for Bayesian variable selection is rapidly mixing under mild high-dimensional assumptions. We propose a novel Markov chain Monte Carlo (MCMC) sampler using an informed proposal scheme, which we prove achieves a much faster mixing time that is independent of the number of covariates, under the assumptions of Yang et al. To the best of our knowledge, this is the first high-dimensional result which rigorously shows that the mixing rate of informed MCMC methods can be fast enough to offset the computational cost of local posterior evaluation. Motivated by the theoretical analysis of our sampler, we further propose a new approach called \u2018two-stage drift condition\u2019 to studying convergence rates of Markov chains on general state spaces, which can be useful for obtaining tight complexity bounds in high-dimensional settings. The practical advantages of our algorithm are illustrated by both simulation studies and real data analysis.<\/jats:p>","DOI":"10.1111\/rssb.12546","type":"journal-article","created":{"date-parts":[[2022,10,31]],"date-time":"2022-10-31T23:32:31Z","timestamp":1667259151000},"page":"1751-1784","source":"Crossref","is-referenced-by-count":18,"title":["Dimension-Free Mixing for High-Dimensional Bayesian Variable Selection"],"prefix":"10.1093","volume":"84","author":[{"given":"Quan","family":"Zhou","sequence":"first","affiliation":[{"name":"Department of Statistics , , College Station , Texas , USA"},{"name":"Texas A&M University , , College Station , Texas , USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jun","family":"Yang","sequence":"additional","affiliation":[{"name":"Department of Statistics , , Oxford , UK"},{"name":"University of Oxford , , Oxford , UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dootika","family":"Vats","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics , , Kanpur , India"},{"name":"Indian Institute of Technology Kanpur , , Kanpur , India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gareth O.","family":"Roberts","sequence":"additional","affiliation":[{"name":"Department of Statistics , , Coventry , UK"},{"name":"University of Warwick , , Coventry , UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jeffrey S.","family":"Rosenthal","sequence":"additional","affiliation":[{"name":"Department of Statistical Sciences , , Toronto , Ontario , Canada"},{"name":"University of Toronto , , Toronto , Ontario , Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2022,10,31]]},"reference":[{"key":"2023030906295890400_","volume-title":"Stepwise searching for feature variables in high-dimensional linear regression (Technical report). Department of Statistics, The London School of Economics and Political Science","author":"An","year":"2008"},{"issue":"2","key":"2023030906295890400_","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1038\/ng.3482","article-title":"Genome-wide association analysis identifies TXNRD2, ATXN2 and FOXC1 as susceptibility loci for primary open-angle glaucoma","volume":"48","author":"Bailey","year":"2016","journal-title":"Nature Genetics"},{"issue":"1B","key":"2023030906295890400_","doi-asserted-by":"crossref","first-page":"700","DOI":"10.1214\/105051604000000710","article-title":"Renewal theory and computable convergence rates for geometrically ergodic Markov chains","volume":"15","author":"Baxendale","year":"2005","journal-title":"The Annals of Applied Probability"},{"issue":"6","key":"2023030906295890400_","doi-asserted-by":"crossref","first-page":"1213","DOI":"10.1007\/s11222-015-9598-x","article-title":"Non-reversible metropolis-Hastings","volume":"26","author":"Bierkens","year":"2016","journal-title":"Statistics and Computing"},{"issue":"3","key":"2023030906295890400_","doi-asserted-by":"crossref","first-page":"1288","DOI":"10.1214\/18-AOS1715","article-title":"The ZIG-ZAG process and super-efficient sampling for Bayesian analysis of big data","volume":"47","author":"Bierkens","year":"2019","journal-title":"The Annals of Statistics"},{"issue":"522","key":"2023030906295890400_","doi-asserted-by":"crossref","first-page":"855","DOI":"10.1080\/01621459.2017.1294075","article-title":"The bouncy particle sampler: A nonreversible rejection-free Markov chain Monte Carlo method","volume":"113","author":"Bouchard-C\u00f4t\u00e9","year":"2018","journal-title":"Journal of the American Statistical Association"},{"issue":"3","key":"2023030906295890400_","doi-asserted-by":"crossref","first-page":"627","DOI":"10.1111\/1467-9868.00144","article-title":"Multivariate Bayesian variable selection and prediction","volume":"60","author":"Brown","year":"1998","journal-title":"Journal of the Royal Statistical Society: Series B (Statistical Methodology)"},{"issue":"5","key":"2023030906295890400_","doi-asserted-by":"crossref","first-page":"1986","DOI":"10.1214\/15-AOS1334","article-title":"Bayesian linear regression with sparse priors","volume":"43","author":"Castillo","year":"2015","journal-title":"Annals of Statistics"},{"key":"2023030906295890400_","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1214\/lnms\/1215540964","article-title":"The practical implementation of Bayesian model selection","volume":"38","author":"Chipman","year":"2001","journal-title":"Lecture Notes-Monograph Series"},{"issue":"2","key":"2023030906295890400_","doi-asserted-by":"crossref","first-page":"160","DOI":"10.1038\/s41588-019-0556-y","article-title":"Multitrait analysis of glaucoma identifies new risk loci and enables polygenic prediction of disease susceptibility and progression","volume":"52","author":"Craig","year":"2020","journal-title":"Nature Genetics"},{"key":"2023030906295890400_","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1214\/aoap\/1177005980","article-title":"Geometric bounds for eigenvalues of Markov chains","volume":"1","author":"Diaconis","year":"1991","journal-title":"The Annals of Applied Probability"},{"issue":"5","key":"2023030906295890400_","doi-asserted-by":"crossref","first-page":"849","DOI":"10.1111\/j.1467-9868.2008.00674.x","article-title":"Sure independence screening for ultrahigh dimensional feature space","volume":"70","author":"Fan","year":"2008","journal-title":"Journal of the Royal Statistical Society: Series B (Statistical Methodology)"},{"issue":"3","key":"2023030906295890400_","doi-asserted-by":"crossref","first-page":"386","DOI":"10.1214\/18-STS648","article-title":"Piecewise deterministic Markov processes for continuous-time Monte Carlo","volume":"33","author":"Fearnhead","year":"2018","journal-title":"Statistical Science"},{"key":"2023030906295890400_","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1239\/jap\/1044476831","article-title":"On the geometric ergodicity of hybrid samplers","volume":"40","author":"Fort","year":"2003","journal-title":"Journal of Applied Probability"},{"key":"2023030906295890400_","doi-asserted-by":"crossref","first-page":"312","DOI":"10.1080\/10618600.2020.1826955","article-title":"Nonreversible jump algorithms for Bayesian nested model selection","volume":"30","author":"Gagnon","year":"2020","journal-title":"Journal of Computational and Graphical Statistics"},{"issue":"5","key":"2023030906295890400_","doi-asserted-by":"crossref","first-page":"2848","DOI":"10.1214\/19-AOS1909","article-title":"A general framework for Bayes structured linear models","volume":"48","author":"Gao","year":"2020","journal-title":"Annals of Statistics"},{"issue":"423","key":"2023030906295890400_","doi-asserted-by":"crossref","first-page":"881","DOI":"10.1080\/01621459.1993.10476353","article-title":"Variable selection via Gibbs sampling","volume":"88","author":"George","year":"1993","journal-title":"Journal of the American Statistical Association"},{"key":"2023030906295890400_","first-page":"339","article-title":"Approaches for Bayesian variable selection","volume":"7","author":"George","year":"1997","journal-title":"Statistica Sinica"},{"issue":"1","key":"2023030906295890400_","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1093\/biomet\/asaa055","article-title":"In search of lost mixing time: adaptive Markov chain Monte Carlo schemes for Bayesian variable selection with very large p","volume":"108","author":"Griffin","year":"2021","journal-title":"Biometrika"},{"key":"2023030906295890400_","doi-asserted-by":"crossref","first-page":"1780","DOI":"10.1214\/11-AOAS455","article-title":"Bayesian variable selection regression for genome-wide association studies and other large-scale problems","volume":"5","author":"Guan","year":"2011","journal-title":"The Annals of Applied Statistics"},{"issue":"478","key":"2023030906295890400_","doi-asserted-by":"crossref","first-page":"507","DOI":"10.1198\/016214507000000121","article-title":"Shotgun stochastic search for \u201clarge p\u201d regression","volume":"102","author":"Hans","year":"2007","journal-title":"Journal of the American Statistical Association"},{"issue":"1","key":"2023030906295890400_","doi-asserted-by":"crossref","first-page":"3040","DOI":"10.1214\/21-EJS1855","article-title":"Unified Bayesian theory of sparse linear regression with nuisance parameters","volume":"15","author":"Jeong","year":"2021","journal-title":"Electronic Journal of Statistics"},{"issue":"3","key":"2023030906295890400_","doi-asserted-by":"crossref","first-page":"632","DOI":"10.1080\/10618600.2020.1864383","article-title":"Fast Markov chain Monte Carlo for high-dimensional Bayesian regression models with shrinkage priors","volume":"30","author":"Jin","year":"2021","journal-title":"Journal of Computational and Graphical Statistics"},{"issue":"73","key":"2023030906295890400_","first-page":"1","article-title":"Scalable approximate MCMC algorithms for the horseshoe prior","volume":"21","author":"Johndrow","year":"2020","journal-title":"Journal of Machine Learning Research"},{"issue":"498","key":"2023030906295890400_","doi-asserted-by":"crossref","first-page":"649","DOI":"10.1080\/01621459.2012.682536","article-title":"Bayesian model selection in high-dimensional settings","volume":"107","author":"Johnson","year":"2012","journal-title":"Journal of the American Statistical Association"},{"key":"2023030906295890400_","doi-asserted-by":"crossref","first-page":"312","DOI":"10.1214\/ss\/1015346315","article-title":"Honest exploration of intractable probability distributions via Markov chain Monte Carlo","volume":"16","author":"Jones","year":"2001","journal-title":"Statistical Science"},{"issue":"430","key":"2023030906295890400_","doi-asserted-by":"crossref","first-page":"773","DOI":"10.1080\/01621459.1995.10476572","article-title":"Bayes factors","volume":"90","author":"Kass","year":"1995","journal-title":"Journal of the American Statistical Association"},{"issue":"6","key":"2023030906295890400_","doi-asserted-by":"crossref","first-page":"778","DOI":"10.1038\/s41588-018-0126-8","article-title":"Genome-wide analyses identify 68 new loci associated with intraocular pressure and improve risk prediction for primary open-angle glaucoma","volume":"50","author":"Khawaja","year":"2018","journal-title":"Nature Genetics"},{"issue":"4","key":"2023030906295890400_","doi-asserted-by":"crossref","first-page":"769","DOI":"10.1198\/jcgs.2010.10039","article-title":"On the utility of graphics cards to perform massively parallel simulation of advanced Monte Carlo methods","volume":"19","author":"Lee","year":"2010","journal-title":"Journal of Computational and Graphical Statistics"},{"key":"2023030906295890400_","first-page":"598","article-title":"T-LoHo: a Bayesian regularization model for structured sparsity and smoothness on graphs","volume":"34","author":"Lee","year":"2021","journal-title":"Advances in Neural Information Processing Systems"},{"key":"2023030906295890400_","doi-asserted-by":"crossref","DOI":"10.1090\/mbk\/107","volume-title":"Markov Chains and Mixing Times","author":"Levin","year":"2017"},{"key":"2023030906295890400_","first-page":"1748","article-title":"A Bayesian contiguous partitioning method for learning clustered latent variables","volume":"22","author":"Luo","year":"2021","journal-title":"Journal of Machine Learning Research"},{"issue":"2","key":"2023030906295890400_","doi-asserted-by":"crossref","first-page":"789","DOI":"10.1214\/14-AOS1207","article-title":"Bayesian variable selection with shrinking and diffusing priors","volume":"42","author":"Narisetty","year":"2014","journal-title":"The Annals of Statistics"},{"issue":"1","key":"2023030906295890400_","first-page":"85","article-title":"A review of Bayesian variable selection methods: what, how and which. Bayesian","volume":"4","author":"O'Hara","year":"2009","journal-title":"Analysis"},{"issue":"12","key":"2023030906295890400_","doi-asserted-by":"crossref","first-page":"2836","DOI":"10.1093\/hmg\/dds103","article-title":"A genome-wide association study in the Japanese population confirms 9p21 and 14q23 as susceptibility loci for primary open angle glaucoma","volume":"21","author":"Osman","year":"2012","journal-title":"Human Molecular Genetics"},{"issue":"1","key":"2023030906295890400_","first-page":"7","article-title":"CODA: convergence diagnosis and output analysis for MCMC","volume":"6","author":"Plummer","year":"2006","journal-title":"R News"},{"issue":"4","key":"2023030906295890400_","doi-asserted-by":"crossref","first-page":"2320","DOI":"10.1214\/18-AOS1749","article-title":"Convergence complexity analysis of Albert and Chib's algorithm for Bayesian probit regression","volume":"47","author":"Qin","year":"2019","journal-title":"Annals of Statistics"},{"issue":"1","key":"2023030906295890400_","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":"Journal of the Royal Statistical Society: Series B (Statistical Methodology)"},{"issue":"2","key":"2023030906295890400_","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1016\/S0304-4149(98)00085-4","article-title":"Bounds on regeneration times and convergence rates for Markov chains","volume":"80","author":"Roberts","year":"1999","journal-title":"Stochastic Processes and Their Applications"},{"issue":"430","key":"2023030906295890400_","doi-asserted-by":"crossref","first-page":"558","DOI":"10.1080\/01621459.1995.10476548","article-title":"Minorization conditions and convergence rates for Markov chain Monte Carlo","volume":"90","author":"Rosenthal","year":"1995","journal-title":"Journal of the American Statistical Association"},{"issue":"4","key":"2023030906295890400_","doi-asserted-by":"crossref","first-page":"607","DOI":"10.1111\/j.1467-9868.2007.00602.x","article-title":"Convergence rates and asymptotic standard errors for Markov chain Monte Carlo algorithms for Bayesian probit regression","volume":"69","author":"Roy","year":"2007","journal-title":"Journal of the Royal Statistical Society: Series B (Statistical Methodology)"},{"issue":"2","key":"2023030906295890400_","first-page":"1053","article-title":"Scalable Bayesian variable selection using nonlocal prior densities in ultrahigh-dimensional settings","volume":"28","author":"Shin","year":"2018","journal-title":"Statistica Sinica"},{"issue":"4","key":"2023030906295890400_","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1017\/S0963548300000390","article-title":"Improved bounds for mixing rates of Markov chains and multicommodity flow","volume":"1","author":"Sinclair","year":"1992","journal-title":"Combinatorics, Probability and Computing"},{"issue":"2","key":"2023030906295890400_","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1016\/0304-4076(95)01763-1","article-title":"Nonparametric regression using Bayesian variable selection","volume":"75","author":"Smith","year":"1996","journal-title":"Journal of Econometrics"},{"issue":"1","key":"2023030906295890400_","first-page":"1","article-title":"Meta-analysis of genome-wide association studies identifies novel loci that influence cupping and the glaucomatous process. Nature","volume":"5","author":"Springelkamp","year":"2014","journal-title":"Communications"},{"issue":"10","key":"2023030906295890400_","doi-asserted-by":"crossref","first-page":"681","DOI":"10.1038\/nrg2615","article-title":"Bayesian statistical methods for genetic association studies","volume":"10","author":"Stephens","year":"2009","journal-title":"Nature Reviews Genetics"},{"issue":"520","key":"2023030906295890400_","doi-asserted-by":"crossref","first-page":"1598","DOI":"10.1080\/01621459.2016.1222288","article-title":"The Hamming ball sampler","volume":"112","author":"Titsias","year":"2017","journal-title":"Journal of the American Statistical Association"},{"issue":"2","key":"2023030906295890400_","doi-asserted-by":"crossref","first-page":"4033","DOI":"10.1214\/17-EJS1351","article-title":"Geometric ergodicity of Gibbs samplers in Bayesian penalized regression models","volume":"11","author":"Vats","year":"2017","journal-title":"Electronic Journal of Statistics"},{"issue":"2","key":"2023030906295890400_","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1093\/biomet\/asz002","article-title":"Multivariate output analysis for Markov chain Monte Carlo","volume":"106","author":"Vats","year":"2019","journal-title":"Biometrika"},{"key":"2023030906295890400_","article-title":"Complexity results for MCMC derived from quantitative bounds","author":"Yang","year":"2022","journal-title":"The Annals of Applied Probability"},{"issue":"6","key":"2023030906295890400_","doi-asserted-by":"crossref","first-page":"2497","DOI":"10.1214\/15-AOS1417","article-title":"On the computational complexity of high-dimensional Bayesian variable selection","volume":"44","author":"Yang","year":"2016","journal-title":"The Annals of Statistics"},{"issue":"530","key":"2023030906295890400_","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":"Journal of the American Statistical Association"},{"issue":"3","key":"2023030906295890400_","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1111\/rssb.12316","article-title":"Scalable importance tempering and Bayesian variable selection","volume":"81","author":"Zanella","year":"2019","journal-title":"Journal of the Royal Statistical Society Series B"},{"key":"2023030906295890400_","volume-title":"Complexity analysis of Bayesian learning of high-dimensional DAG models and their equivalence classes","author":"Zhou","year":"2021"}],"container-title":["Journal of the Royal Statistical Society Series B: Statistical Methodology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1111\/rssb.12546","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1111\/rssb.12546","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/84\/5\/1751\/49458965\/jrsssb_84_5_1751.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/84\/5\/1751\/49458965\/jrsssb_84_5_1751.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,10]],"date-time":"2023-03-10T20:52:47Z","timestamp":1678481567000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jrsssb\/article\/84\/5\/1751\/7072929"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,10,31]]},"references-count":54,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2022,10,31]]},"published-print":{"date-parts":[[2022,11,1]]}},"URL":"https:\/\/doi.org\/10.1111\/rssb.12546","relation":{},"ISSN":["1369-7412","1467-9868"],"issn-type":[{"value":"1369-7412","type":"print"},{"value":"1467-9868","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2022,11]]},"published":{"date-parts":[[2022,10,31]]}}}