{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:45:11Z","timestamp":1740123911528,"version":"3.37.3"},"reference-count":43,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2021,9,15]],"date-time":"2021-09-15T00:00:00Z","timestamp":1631664000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2021,9,15]],"date-time":"2021-09-15T00:00:00Z","timestamp":1631664000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100003246","name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","doi-asserted-by":"publisher","award":["680.50.1529"],"award-info":[{"award-number":["680.50.1529"]}],"id":[{"id":"10.13039\/501100003246","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"crossref","award":["EP\/P002625\/1"],"award-info":[{"award-number":["EP\/P002625\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["EP\/N001974\/1"],"award-info":[{"award-number":["EP\/N001974\/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":"crossref","award":["EP\/R022100\/1"],"award-info":[{"award-number":["EP\/R022100\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Stat Comput"],"published-print":{"date-parts":[[2021,11]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We aim to improve upon the exploration of the general-purpose random walk Metropolis algorithm when the target has non-convex support<jats:inline-formula><jats:alternatives><jats:tex-math>$$A\\subset {\\mathbb {R}}^d$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:mi>A<\/mml:mi><mml:mo>\u2282<\/mml:mo><mml:msup><mml:mrow><mml:mi>R<\/mml:mi><\/mml:mrow><mml:mi>d<\/mml:mi><\/mml:msup><\/mml:mrow><\/mml:math><\/jats:alternatives><\/jats:inline-formula>, by reusing proposals in<jats:inline-formula><jats:alternatives><jats:tex-math>$$A^c$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:msup><mml:mi>A<\/mml:mi><mml:mi>c<\/mml:mi><\/mml:msup><\/mml:math><\/jats:alternatives><\/jats:inline-formula>which would otherwise be rejected. The algorithm is Metropolis-class and under standard conditions the chain satisfies a strong law of large numbers and central limit theorem. Theoretical and numerical evidence of improved performance relative to random walk Metropolis are provided. Issues of implementation are discussed and numerical examples, including applications to global optimisation and rare event sampling, are presented.<\/jats:p>","DOI":"10.1007\/s11222-021-10044-4","type":"journal-article","created":{"date-parts":[[2021,9,15]],"date-time":"2021-09-15T12:03:00Z","timestamp":1631707380000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A Metropolis-class sampler for targets with non-convex support"],"prefix":"10.1007","volume":"31","author":[{"given":"John","family":"Moriarty","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jure","family":"Vogrinc","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6585-4785","authenticated-orcid":false,"given":"Alessandro","family":"Zocca","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,9,15]]},"reference":[{"issue":"16","key":"10044_CR1","doi-asserted-by":"publisher","first-page":"6994","DOI":"10.1063\/1.1358861","volume":"114","author":"I Andricioaei","year":"2001","unstructured":"Andricioaei, I., Straub, J., Voter, A.: Smart darting Monte Carlo. J. Chem. Phys. 114(16), 6994\u20137000 (2001)","journal-title":"J. Chem. Phys."},{"key":"10044_CR2","unstructured":"Andrieu, C., Lee, A., Livingstone, S.: A general perspective on the Metropolis-Hastings kernel. arXiv preprint arXiv:2012.14881 (2020)"},{"key":"10044_CR3","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-03311-7","volume-title":"Large Deviations Techniques and Applications","author":"A Dembo","year":"2010","unstructured":"Dembo, A., Zeitouni, O.: Large Deviations Techniques and Applications. Springer, Berlin Heidelberg (2010). https:\/\/doi.org\/10.1007\/978-3-642-03311-7"},{"key":"10044_CR4","first-page":"89","volume":"6","author":"WR Gilks","year":"1996","unstructured":"Gilks, W.R., Roberts, G.O.: Strategies for improving MCMC. Markov chain Monte Carlo in practice 6, 89\u2013114 (1996)","journal-title":"Markov chain Monte Carlo in practice"},{"key":"10044_CR5","doi-asserted-by":"crossref","unstructured":"Goodridge, M., Moriarty, J., Vogrinc, J., Zocca, A.: Hopping between distant basins. arXiv preprint arXiv:2108.05229 (2021)","DOI":"10.1007\/s10898-022-01153-z"},{"issue":"1","key":"10044_CR6","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1093\/biomet\/57.1.97","volume":"57","author":"W Hastings","year":"1970","unstructured":"Hastings, W.: Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57(1), 97\u2013109 (1970). https:\/\/doi.org\/10.1093\/biomet\/57.1.97","journal-title":"Biometrika"},{"issue":"4","key":"10044_CR7","doi-asserted-by":"publisher","first-page":"770","DOI":"10.1115\/1.2919267","volume":"115","author":"P Jain","year":"1993","unstructured":"Jain, P., Agogino, A.M.: Global optimization using the multistart method. J. Mech. Design 115(4), 770\u2013775 (1993). https:\/\/doi.org\/10.1115\/1.2919267","journal-title":"J. Mech. Design"},{"issue":"2","key":"10044_CR8","doi-asserted-by":"publisher","first-page":"150","DOI":"10.1504\/ijmmno.2013.055204","volume":"4","author":"M Jamil","year":"2013","unstructured":"Jamil, M., Yang, X.S.: A literature survey of benchmark functions for global optimisation problems. Int. J. Math. Modell. Numerical Optimisation 4(2), 150 (2013). https:\/\/doi.org\/10.1504\/ijmmno.2013.055204","journal-title":"Int. J. Math. Modell. Numerical Optimisation"},{"issue":"2","key":"10044_CR9","doi-asserted-by":"publisher","first-page":"341","DOI":"10.1016\/S0304-4149(99)00082-4","volume":"85","author":"S Jarner","year":"2000","unstructured":"Jarner, S., Hansen, E.: Geometric ergodicity of metropolis algorithms. Stochastic Process. their Appl. 85(2), 341\u2013361 (2000). https:\/\/doi.org\/10.1016\/S0304-4149(99)00082-4","journal-title":"Stochastic Process. their Appl."},{"issue":"1","key":"10044_CR10","doi-asserted-by":"publisher","first-page":"224","DOI":"10.1214\/aoap\/1015961162","volume":"12","author":"S Jarner","year":"2002","unstructured":"Jarner, S., Roberts, G.: Polynomial convergence rates of Markov chains. Ann. Appl. Probab. 12(1), 224\u2013247 (2002)","journal-title":"Ann. Appl. Probab."},{"issue":"4598","key":"10044_CR11","doi-asserted-by":"publisher","first-page":"671","DOI":"10.1126\/science.220.4598.671","volume":"220","author":"S Kirkpatrick","year":"1983","unstructured":"Kirkpatrick, S., Gelatt, C.D., Vecchi, M.P.: Optimization by simulated annealing. Science 220(4598), 671\u2013680 (1983). https:\/\/doi.org\/10.1126\/science.220.4598.671","journal-title":"Science"},{"key":"10044_CR12","doi-asserted-by":"crossref","unstructured":"Lan, S., Streets, J., Shahbaba, B.: Wormhole Hamiltonian Monte Carlo. In: Proceedings of the 28th AAAI Conference on Artificial Intelligence, pp. 1953\u20131959 (2014)","DOI":"10.1609\/aaai.v28i1.9006"},{"key":"10044_CR13","unstructured":"\u0141atuszy\u0144ski, K., Rudolf, D.: Convergence of hybrid slice sampling via spectral gap (2014)"},{"issue":"4","key":"10044_CR14","doi-asserted-by":"publisher","first-page":"367","DOI":"10.1023\/a:1026500301312","volume":"18","author":"RH Leary","year":"2000","unstructured":"Leary, R.H.: Global Optimization on Funneling Landscapes. J. Glob. Optimiz. 18(4), 367\u2013383 (2000). https:\/\/doi.org\/10.1023\/a:1026500301312","journal-title":"J. Glob. Optimiz."},{"issue":"449","key":"10044_CR15","doi-asserted-by":"publisher","first-page":"121","DOI":"10.1080\/01621459.2000.10473908","volume":"95","author":"J Liu","year":"2000","unstructured":"Liu, J., Liang, F., Wong, W.: The multiple-try method and local optimization in Metropolis sampling. J. Am. Statistical Association 95(449), 121\u2013134 (2000)","journal-title":"J. Am. Statistical Association"},{"key":"10044_CR16","doi-asserted-by":"publisher","unstructured":"Mart\u00ed, R.: Multi-start methods. In: Handbook of Metaheuristics, pp. 355\u2013368. Kluwer Academic Publishers (2003). https:\/\/doi.org\/10.1007\/0-306-48056-5_12","DOI":"10.1007\/0-306-48056-5_12"},{"issue":"1","key":"10044_CR17","doi-asserted-by":"publisher","first-page":"101","DOI":"10.1214\/aos\/1033066201","volume":"24","author":"K Mengersen","year":"1996","unstructured":"Mengersen, K., Tweedie, R.: Rates of convergence of the Hastings and Metropolis algorithms. Ann. Statistics 24(1), 101\u2013121 (1996). https:\/\/doi.org\/10.1214\/aos\/1033066201","journal-title":"Ann. Statistics"},{"issue":"6","key":"10044_CR18","doi-asserted-by":"publisher","first-page":"1087","DOI":"10.1063\/1.1699114","volume":"21","author":"N Metropolis","year":"1953","unstructured":"Metropolis, N., Rosenbluth, A., Rosenbluth, M., Teller, A., Teller, E.: Equation of state calculations by fast computing machines. J. Chem. Phys. 21(6), 1087\u20131092 (1953)","journal-title":"J. Chem. Phys."},{"key":"10044_CR19","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511626630","volume-title":"Markov chains and stochastic stability","author":"S Meyn","year":"2009","unstructured":"Meyn, S., Tweedie, R.: Markov chains and stochastic stability, 2nd edn. Cambridge University Press, Cambridge (2009). https:\/\/doi.org\/10.1017\/CBO9780511626630","edition":"2"},{"key":"10044_CR20","doi-asserted-by":"crossref","unstructured":"Mira, A.: Ordering and improving the performance of Monte Carlo Markov chains. Statistical Science , 340\u2013350 (2001)","DOI":"10.1214\/ss\/1015346319"},{"issue":"2","key":"10044_CR21","first-page":"651","volume":"19","author":"A Mira","year":"2009","unstructured":"Mira, A., Leisen, F.: Covariance ordering for discrete and continuous time Markov chains. Statistica Sinica 19(2), 651\u2013666 (2009)","journal-title":"Statistica Sinica"},{"key":"10044_CR22","doi-asserted-by":"publisher","unstructured":"Moriarty, J., Vogrinc, J., Zocca, A.: Frequency violations from random disturbances: an MCMC approach. In: IEEE Conference on Decision and Control (CDC), pp. 1598\u20131603 (2018). https:\/\/doi.org\/10.1109\/CDC.2018.8619304","DOI":"10.1109\/CDC.2018.8619304"},{"issue":"3","key":"10044_CR23","doi-asserted-by":"publisher","first-page":"705","DOI":"10.1214\/aos\/1056562461","volume":"31","author":"R Neal","year":"2003","unstructured":"Neal, R.: Slice sampling. Ann. Statistics 31(3), 705\u2013767 (2003). https:\/\/doi.org\/10.1214\/aos\/1056562461","journal-title":"Ann. Statistics"},{"issue":"5","key":"10044_CR24","doi-asserted-by":"publisher","first-page":"1325","DOI":"10.1007\/s11222-020-09948-4","volume":"30","author":"J Park","year":"2020","unstructured":"Park, J., Atchad\u00e9, Y.: Markov chain monte carlo algorithms with sequential proposals. Statistics Comput. 30(5), 1325\u20131345 (2020). https:\/\/doi.org\/10.1007\/s11222-020-09948-4","journal-title":"Statistics Comput."},{"issue":"3","key":"10044_CR25","doi-asserted-by":"publisher","first-page":"607","DOI":"10.1093\/biomet\/60.3.607","volume":"60","author":"P Peskun","year":"1973","unstructured":"Peskun, P.: Optimum Monte-carlo sampling using Markov chains. Biometrika 60(3), 607\u2013612 (1973)","journal-title":"Biometrika"},{"key":"10044_CR26","doi-asserted-by":"publisher","unstructured":"Pompe, E., Holmes, C., \u0141atuszy\u0144ski, K.: A framework for adaptive MCMC targeting multimodal distributions. The Annals of Statistics 48(5),(2020). https:\/\/doi.org\/10.1214\/19-aos1916","DOI":"10.1214\/19-aos1916"},{"issue":"2","key":"10044_CR27","doi-asserted-by":"publisher","first-page":"827","DOI":"10.1006\/jcph.2001.6860","volume":"172","author":"Z Qin","year":"2001","unstructured":"Qin, Z., Liu, J.: Multipoint Metropolis method with application to hybrid Monte Carlo. J. Comput. Phys. 172(2), 827\u2013840 (2001)","journal-title":"J. Comput. Phys."},{"key":"10044_CR28","doi-asserted-by":"crossref","unstructured":"Robert, C.P., Elvira, V., Tawn, N., Wu, C.: Accelerating MCMC algorithms. Wiley Interdisciplinary Reviews: Computational Statistics 10(5), e1435 (2018)","DOI":"10.1002\/wics.1435"},{"key":"10044_CR29","doi-asserted-by":"publisher","first-page":"13","DOI":"10.1214\/ECP.v2-981","volume":"2","author":"G Roberts","year":"1997","unstructured":"Roberts, G., Rosenthal, J.: Geometric ergodicity and hybrid Markov chains. Electron. Commun. Probab. 2, 13\u201325 (1997). https:\/\/doi.org\/10.1214\/ECP.v2-981","journal-title":"Electron. Commun. Probab."},{"key":"10044_CR30","doi-asserted-by":"publisher","first-page":"20","DOI":"10.1214\/154957804100000024","volume":"1","author":"G Roberts","year":"2004","unstructured":"Roberts, G., Rosenthal, J.: General state space Markov chains and MCMC algorithms. Probab. Surv. 1, 20\u201371 (2004). https:\/\/doi.org\/10.1214\/154957804100000024","journal-title":"Probab. Surv."},{"issue":"1","key":"10044_CR31","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1093\/biomet\/83.1.95","volume":"83","author":"G Roberts","year":"1996","unstructured":"Roberts, G., Tweedie, R.: Geometric convergence and central limit theorems for multidimensional Hastings and Metropolis algorithms. Biometrika 83(1), 95\u2013110 (1996). https:\/\/doi.org\/10.1093\/biomet\/83.1.95","journal-title":"Biometrika"},{"issue":"4","key":"10044_CR32","doi-asserted-by":"publisher","first-page":"1186","DOI":"10.1017\/jpr.2018.78","volume":"55","author":"D Rudolf","year":"2018","unstructured":"Rudolf, D., Ullrich, M.: Comparison of hit-and-run, slice sampler and random walk metropolis. J. Appl. Probab. 55(4), 1186\u20131202 (2018)","journal-title":"J. Appl. Probab."},{"issue":"3","key":"10044_CR33","doi-asserted-by":"publisher","first-page":"270","DOI":"10.1109\/tac.1968.1098903","volume":"13","author":"M Schumer","year":"1968","unstructured":"Schumer, M., Steiglitz, K.: Adaptive step size random search. IEEE Trans. Automatic Control 13(3), 270\u2013276 (1968). https:\/\/doi.org\/10.1109\/tac.1968.1098903","journal-title":"IEEE Trans. Automatic Control"},{"key":"10044_CR34","unstructured":"Sminchisescu, C., Welling, M.: Generalized Darting Monte Carlo. In: M.\u00a0Meila, X.\u00a0Shen (eds.) Proceedings of the 11th International Conference on Artificial Intelligence and Statistics, vol.\u00a02, pp. 516\u2013523. PMLR (2007)"},{"key":"10044_CR35","unstructured":"Sminchisescu, C., Welling, M., Hinton, G.: A mode-hopping MCMC sampler. Tech. rep., CSRG-478, University of Toronto (2003)"},{"issue":"6","key":"10044_CR36","doi-asserted-by":"publisher","first-page":"1296","DOI":"10.1287\/opre.32.6.1296","volume":"32","author":"RL Smith","year":"1984","unstructured":"Smith, R.L.: Efficient monte carlo procedures for generating points uniformly distributed over bounded regions. Operations Res. 32(6), 1296\u20131308 (1984)","journal-title":"Operations Res."},{"key":"10044_CR37","doi-asserted-by":"publisher","unstructured":"Tak, H., Meng, X.L., van Dyk, D.: A Repelling-Attracting Metropolis Algorithm for Multimodality. Journal of Computational and Graphical Statistics (2018). https:\/\/doi.org\/10.1080\/10618600.2017.1415911","DOI":"10.1080\/10618600.2017.1415911"},{"key":"10044_CR38","doi-asserted-by":"publisher","unstructured":"Tierney, L.: Markov chains for exploring posterior distributions. The Annals of Statistics 22(4), 1701\u20131762 (1994). https:\/\/doi.org\/10.1214\/aos\/1176325750. With discussion and a rejoinder by the author","DOI":"10.1214\/aos\/1176325750"},{"issue":"1","key":"10044_CR39","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1214\/aoap\/1027961031","volume":"8","author":"L Tierney","year":"1998","unstructured":"Tierney, L.: A note on Metropolis-Hastings kernels for general state spaces. Ann. Appl. Probab. 8(1), 1\u20139 (1998). https:\/\/doi.org\/10.1214\/aoap\/1027961031","journal-title":"Ann. Appl. Probab."},{"issue":"1","key":"10044_CR40","doi-asserted-by":"publisher","first-page":"205","DOI":"10.1111\/1467-9469.00232","volume":"28","author":"H Tjelmeland","year":"2001","unstructured":"Tjelmeland, H., Hegstad, B.: Mode jumping proposals in MCMC. Scandinavian J. Statistics 28(1), 205\u2013223 (2001)","journal-title":"Scandinavian J. Statistics"},{"key":"10044_CR41","volume-title":"Data Structures and Algorithms: Concepts","author":"G Vijayalakshmi Pai","year":"2008","unstructured":"Vijayalakshmi Pai, G.: Data Structures and Algorithms: Concepts. Techniques and Applications, McGraw-Hill Education (2008)"},{"issue":"28","key":"10044_CR42","doi-asserted-by":"publisher","first-page":"5111","DOI":"10.1021\/jp970984n","volume":"101","author":"DJ Wales","year":"1997","unstructured":"Wales, D.J., Doye, J.P.K.: Global Optimization by Basin-Hopping and the Lowest Energy Structures of Lennard-Jones Clusters Containing up to 110 Atoms. J. Phys. Chem. A 101(28), 5111\u20135116 (1997). https:\/\/doi.org\/10.1021\/jp970984n","journal-title":"J. Phys. Chem. A"},{"key":"10044_CR43","unstructured":"Zocca, A., Vogrinc, J.: Skipping sampler code. https:\/\/github.com\/alessandrozocca\/skippingsampler (2021)"}],"container-title":["Statistics and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11222-021-10044-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11222-021-10044-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11222-021-10044-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,1,9]],"date-time":"2023-01-09T07:55:20Z","timestamp":1673250920000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11222-021-10044-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,9,15]]},"references-count":43,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2021,11]]}},"alternative-id":["10044"],"URL":"https:\/\/doi.org\/10.1007\/s11222-021-10044-4","relation":{},"ISSN":["0960-3174","1573-1375"],"issn-type":[{"type":"print","value":"0960-3174"},{"type":"electronic","value":"1573-1375"}],"subject":[],"published":{"date-parts":[[2021,9,15]]},"assertion":[{"value":"23 October 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 August 2021","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 September 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"72"}}