{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,17]],"date-time":"2026-08-17T23:26:16Z","timestamp":1787009176778,"version":"build-2736575974"},"reference-count":47,"publisher":"Oxford University Press (OUP)","license":[{"start":{"date-parts":[[2026,6,11]],"date-time":"2026-06-11T00:00:00Z","timestamp":1781136000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"funder":[{"name":"Office of Research at the University of Kansas","award":["GRF-2142090"],"award-info":[{"award-number":["GRF-2142090"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Hamiltonian Monte Carlo (HMC) is widely used for sampling from high-dimensional target distributions with densities known up to proportionality. While HMC exhibits favourable scaling properties in high dimensions, it struggles with strongly multimodal distributions. Tempering methods are commonly used to address multimodality, but they can be difficult to tune, especially in high-dimensional settings. In this study, we propose a method that combines tempering with HMC to enable efficient sampling from high-dimensional, strongly multimodal distributions. Our approach simulates the dynamics of a time-varying Hamiltonian in which the temperature increases and then decreases over time. In the first phase, the simulated trajectory gradually explores low-density regions farther from the mode; the second phase guides it back towards a local mode. We develop efficient tuning strategies based on a time-scale transformation under which the Hamiltonian becomes approximately stationary. This leads to a tempered Hamiltonian Monte Carlo (THMC) algorithm with automatic tuning. We demonstrate numerically that our method scales more effectively with dimension than adaptive parallel tempering and tempered sequential Monte Carlo. Finally, we apply our THMC to sample from strongly multimodal posterior distributions arising in Bayesian inference.<\/jats:p>","DOI":"10.1093\/jrsssb\/qkag080","type":"journal-article","created":{"date-parts":[[2026,5,22]],"date-time":"2026-05-22T11:46:14Z","timestamp":1779450374000},"source":"Crossref","is-referenced-by-count":1,"title":["Sampling from high-dimensional, multimodal distributions using automatically tuned, tempered Hamiltonian Monte Carlo"],"prefix":"10.1093","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4493-7730","authenticated-orcid":false,"given":"Joonha","family":"Park","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Kansas , 1460 Jayhawk Blvd., Lawrence, KS 66045 ,","place":["USA"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2026,6,11]]},"reference":[{"key":"2026061113575296800_qkag080-B1","author":"Ahn","year":"2013"},{"issue":"16","key":"2026061113575296800_qkag080-B2","doi-asserted-by":"publisher","first-page":"6994","DOI":"10.1063\/1.1358861","article-title":"Smart darting Monte Carlo","volume":"114","author":"Andricioaei","year":"2001","journal-title":"The Journal of Chemical Physics"},{"issue":"3","key":"2026061113575296800_qkag080-B3","doi-asserted-by":"publisher","first-page":"987","DOI":"10.3150\/10-BEJ307","article-title":"On nonlinear Markov chain Monte Carlo","volume":"17","author":"Andrieu","year":"2011","journal-title":"Bernoulli: Official Journal of the Bernoulli Society for Mathematical Statistics and Probability"},{"key":"2026061113575296800_qkag080-B4","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-2063-1","volume-title":"Mathematical methods of classical mechanics","author":"Arnold","year":"1989"},{"issue":"1","key":"2026061113575296800_qkag080-B5","first-page":"209","article-title":"The Wang-Landau algorithm in general state spaces: Applications and convergence analysis","volume":"20","author":"Atchad\u00e9","year":"2010","journal-title":"Statistica Sinica"},{"key":"2026061113575296800_qkag080-B6","doi-asserted-by":"publisher","first-page":"555","DOI":"10.1007\/s11222-010-9192-1","article-title":"Towards optimal scaling of Metropolis-coupled Markov chain Monte Carlo","volume":"21","author":"Atchad\u00e9","year":"2011","journal-title":"Statistics and Computing"},{"issue":"4","key":"2026061113575296800_qkag080-B7","doi-asserted-by":"publisher","first-page":"1396","DOI":"10.1214\/13-AAP951","article-title":"On the stability of sequential Monte Carlo methods in high dimensions","volume":"24","author":"Beskos","year":"2014","journal-title":"The Annals of Applied Probability: An Official Journal of the Institute of Mathematical Statistics"},{"issue":"5A","key":"2026061113575296800_qkag080-B8","doi-asserted-by":"publisher","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: Official Journal of the Bernoulli Society for Mathematical Statistics and Probability"},{"key":"2026061113575296800_qkag080-B9","doi-asserted-by":"publisher","first-page":"495","DOI":"10.1007\/s10955-016-1526-8","article-title":"Simulated tempering and swapping on mean-field models","volume":"164","author":"Bhatnagar","year":"2016","journal-title":"Journal of Statistical Physics"},{"issue":"522","key":"2026061113575296800_qkag080-B10","doi-asserted-by":"publisher","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":"2026061113575296800_qkag080-B11","doi-asserted-by":"publisher","first-page":"745","DOI":"10.1214\/20-BA1222","article-title":"Adaptive tuning of Hamiltonian Monte Carlo within sequential Monte Carlo","volume":"16","author":"Buchholz","year":"2021","journal-title":"Bayesian Analysis"},{"issue":"4","key":"2026061113575296800_qkag080-B12","doi-asserted-by":"publisher","first-page":"1228","DOI":"10.1103\/PhysRevD.38.1228","article-title":"Global Monte Carlo algorithms for many-fermion systems","volume":"38","author":"Creutz","year":"1988","journal-title":"Physical Review D"},{"issue":"3","key":"2026061113575296800_qkag080-B13","doi-asserted-by":"publisher","first-page":"411","DOI":"10.1111\/j.1467-9868.2006.00553.x","article-title":"Sequential Monte Carlo samplers","volume":"68","author":"Del Moral","year":"2006","journal-title":"Journal of the Royal Statistical Society: Series B, Statistical Methodology"},{"issue":"2","key":"2026061113575296800_qkag080-B14","doi-asserted-by":"publisher","first-page":"216","DOI":"10.1016\/0370-2693(87)91197-X","article-title":"Hybrid Monte Carlo","volume":"195","author":"Duane","year":"1987","journal-title":"Physics Letters B"},{"key":"2026061113575296800_qkag080-B15","doi-asserted-by":"crossref","DOI":"10.1201\/b16018","volume-title":"Bayesian data analysis","author":"Gelman","year":"2013","edition":"3rd ed."},{"issue":"1","key":"2026061113575296800_qkag080-B16","doi-asserted-by":"publisher","first-page":"110","DOI":"10.1214\/aoap\/1034625254","article-title":"Weak convergence and optimal scaling of random walk Metropolis algorithms","volume":"7","author":"Gelman","year":"1997","journal-title":"The Annals of Applied Probability: An Official Journal of the Institute of Mathematical Statistics"},{"key":"2026061113575296800_qkag080-B17","author":"Geyer","year":"1991"},{"issue":"6","key":"2026061113575296800_qkag080-B18","doi-asserted-by":"publisher","first-page":"061301","DOI":"10.1103\/PhysRevE.91.061301","article-title":"Extended Hamiltonian approach to continuous tempering","volume":"91","author":"Gobbo","year":"2015","journal-title":"Physical Review: E"},{"key":"2026061113575296800_qkag080-B19","author":"Graham","year":"2017"},{"key":"2026061113575296800_qkag080-B20","doi-asserted-by":"publisher","first-page":"399","DOI":"10.1017\/S0962492902000144","article-title":"Geometric numerical integration illustrated by the St\u00f6rmer\u2013Verlet method","volume":"12","author":"Hairer","year":"2003","journal-title":"Acta Numerica"},{"issue":"20","key":"2026061113575296800_qkag080-B21","doi-asserted-by":"publisher","first-page":"206101","DOI":"10.1063\/1.1917749","article-title":"Selection of temperature intervals for parallel-tempering simulations","volume":"122","author":"Kone","year":"2005","journal-title":"The Journal of Chemical Physics"},{"issue":"4","key":"2026061113575296800_qkag080-B22","doi-asserted-by":"publisher","first-page":"1581","DOI":"10.1214\/009053606000000515","article-title":"Equi-energy sampler with applications in statistical inference and statistical mechanics","volume":"34","author":"Kou","year":"2006","journal-title":"Annals of Statistics"},{"key":"2026061113575296800_qkag080-B23","doi-asserted-by":"crossref","DOI":"10.1017\/9781108780346","volume-title":"A guide to Monte Carlo simulations in statistical physics","author":"Landau","year":"2021"},{"key":"2026061113575296800_qkag080-B24","volume-title":"Simulating Hamiltonian dynamics","author":"Leimkuhler","year":"2004"},{"issue":"2","key":"2026061113575296800_qkag080-B25","doi-asserted-by":"publisher","first-page":"486","DOI":"10.1021\/acs.jctc.5b00751","article-title":"Continuous tempering molecular dynamics: A deterministic approach to simulated tempering","volume":"12","author":"Lenner","year":"2016","journal-title":"Journal of Chemical Theory and Computation"},{"key":"2026061113575296800_qkag080-B26","volume-title":"Thermostat-assisted continuously-tempered Hamiltonian Monte Carlo for Bayesian learning","author":"Luo","year":"2018"},{"key":"2026061113575296800_qkag080-B27","doi-asserted-by":"publisher","author":"Mangoubi","year":"2018","DOI":"10.48550\/arXiv.1808.03230"},{"issue":"6","key":"2026061113575296800_qkag080-B28","doi-asserted-by":"publisher","first-page":"451","DOI":"10.1209\/0295-5075\/19\/6\/002","article-title":"Simulated tempering: A new Monte Carlo scheme","volume":"19","author":"Marinari","year":"1992","journal-title":"Europhysics Letters"},{"issue":"3","key":"2026061113575296800_qkag080-B29","doi-asserted-by":"publisher","first-page":"649","DOI":"10.1080\/10618600.2013.778779","article-title":"An adaptive parallel tempering algorithm","volume":"22","author":"Miasojedow","year":"2013","journal-title":"Journal of Computational and Graphical Statistics: A Joint Publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America"},{"key":"2026061113575296800_qkag080-B30","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-0745-0","volume-title":"Bayesian learning for neural networks","author":"Neal","year":"1996"},{"key":"2026061113575296800_qkag080-B31","doi-asserted-by":"publisher","first-page":"353","DOI":"10.1007\/BF00143556","article-title":"Sampling from multimodal distributions using tempered transitions","volume":"6","author":"Neal","year":"1996","journal-title":"Statistics and Computing"},{"key":"2026061113575296800_qkag080-B32","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1023\/A:1008923215028","article-title":"Annealed importance sampling","volume":"11","author":"Neal","year":"2001","journal-title":"Statistics and Computing"},{"key":"2026061113575296800_qkag080-B33","first-page":"113","volume-title":"MCMC using Hamiltonian dynamics","author":"Neal","year":"2011"},{"key":"2026061113575296800_qkag080-B34","doi-asserted-by":"publisher","first-page":"1325","DOI":"10.1007\/s11222-020-09948-4","article-title":"Markov chain Monte Carlo algorithms with sequential proposals","volume":"30","author":"Park","year":"2020","journal-title":"Statistics and Computing"},{"key":"2026061113575296800_qkag080-B35","doi-asserted-by":"publisher","author":"Paulin","year":"2017","DOI":"10.3150\/17-BEJ988SUPP"},{"issue":"1","key":"2026061113575296800_qkag080-B36","doi-asserted-by":"publisher","first-page":"310","DOI":"10.3150\/17-BEJ988","article-title":"Error bounds for sequential Monte Carlo samplers for multimodal distributions","volume":"25","author":"Paulin","year":"2019","journal-title":"Bernoulli: Official Journal of the Bernoulli Society for Mathematical Statistics and Probability"},{"issue":"5","key":"2026061113575296800_qkag080-B37","doi-asserted-by":"publisher","first-page":"2930","DOI":"10.1214\/19-AOS1916","article-title":"A framework for adaptive MCMC targeting multimodal distributions","volume":"48","author":"Pompe","year":"2020","journal-title":"Annals of Statistics"},{"issue":"1","key":"2026061113575296800_qkag080-B38","doi-asserted-by":"publisher","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":"10\u201311","key":"2026061113575296800_qkag080-B39","doi-asserted-by":"publisher","first-page":"2738","DOI":"10.1016\/j.patcog.2011.02.006","article-title":"Generalized darting Monte Carlo","volume":"44","author":"Sminchisescu","year":"2011","journal-title":"Pattern Recognition"},{"key":"2026061113575296800_qkag080-B40","author":"Stephens","year":"1997"},{"issue":"21","key":"2026061113575296800_qkag080-B41","doi-asserted-by":"publisher","first-page":"2607","DOI":"10.1103\/PhysRevLett.57.2607","article-title":"Replica Monte Carlo simulation of spin-glasses","volume":"57","author":"Swendsen","year":"1986","journal-title":"Physical Review Letters"},{"issue":"2","key":"2026061113575296800_qkag080-B42","doi-asserted-by":"publisher","first-page":"321","DOI":"10.1111\/rssb.12464","article-title":"Non-reversible parallel tempering: A scalable highly parallel MCMC scheme","volume":"84","author":"Syed","year":"2022","journal-title":"Journal of the Royal Statistical Society: Series B, Statistical Methodology"},{"key":"2026061113575296800_qkag080-B43","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1007\/s11222-019-09863-3","article-title":"Weight-preserving simulated tempering","volume":"30","author":"Tawn","year":"2020","journal-title":"Statistics and Computing"},{"key":"2026061113575296800_qkag080-B44","doi-asserted-by":"publisher","author":"Vanetti","year":"2017","DOI":"10.48550\/arXiv.1707.05296"},{"issue":"10","key":"2026061113575296800_qkag080-B45","doi-asserted-by":"publisher","first-page":"2050","DOI":"10.1103\/PhysRevLett.86.2050","article-title":"Efficient, multiple-range random walk algorithm to calculate the density of states","volume":"86","author":"Wang","year":"2001","journal-title":"Physical Review Letters"},{"key":"2026061113575296800_qkag080-B46","doi-asserted-by":"publisher","first-page":"780","DOI":"10.1214\/EJP.v14-638","article-title":"Sufficient conditions for torpid mixing of parallel and simulated tempering","volume":"14","author":"Woodard","year":"2009","journal-title":"Electronic Journal of Probability"},{"issue":"2","key":"2026061113575296800_qkag080-B47","doi-asserted-by":"publisher","first-page":"617","DOI":"10.1214\/08-AAP555","article-title":"Conditions for rapid mixing of parallel and simulated tempering on multimodal distributions","volume":"19","author":"Woodard","year":"2009","journal-title":"The Annals of Applied Probability: An Official Journal of the Institute of Mathematical Statistics"}],"container-title":["Journal of the Royal Statistical Society Series B: Statistical Methodology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/jrsssb\/advance-article-pdf\/doi\/10.1093\/jrsssb\/qkag080\/68514683\/qkag080.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/advance-article-pdf\/doi\/10.1093\/jrsssb\/qkag080\/68514683\/qkag080.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,6,11]],"date-time":"2026-06-11T17:58:01Z","timestamp":1781200681000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jrsssb\/advance-article\/doi\/10.1093\/jrsssb\/qkag080\/8706557"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,6,11]]},"references-count":47,"URL":"https:\/\/doi.org\/10.1093\/jrsssb\/qkag080","relation":{},"ISSN":["1369-7412","1467-9868"],"issn-type":[{"value":"1369-7412","type":"print"},{"value":"1467-9868","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,6,11]]},"article-number":"qkag080"}}