{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,11]],"date-time":"2025-09-11T20:21:50Z","timestamp":1757622110362,"version":"3.44.0"},"reference-count":39,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2025,8,7]],"date-time":"2025-08-07T00:00:00Z","timestamp":1754524800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,8,7]],"date-time":"2025-08-07T00:00:00Z","timestamp":1754524800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001665","name":"Agence Nationale de la Recherche","doi-asserted-by":"publisher","award":["Stat4Plant project ANR-20-CE45-0012","Stat4Plant project ANR-20-CE45-0012","Stat4Plant project ANR-20-CE45-0012"],"award-info":[{"award-number":["Stat4Plant project ANR-20-CE45-0012","Stat4Plant project ANR-20-CE45-0012","Stat4Plant project ANR-20-CE45-0012"]}],"id":[{"id":"10.13039\/501100001665","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Stat Comput"],"published-print":{"date-parts":[[2025,10]]},"DOI":"10.1007\/s11222-025-10664-0","type":"journal-article","created":{"date-parts":[[2025,8,7]],"date-time":"2025-08-07T18:34:22Z","timestamp":1754591662000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Estimation of ratios of normalizing constants using stochastic approximation: the SARIS algorithm"],"prefix":"10.1007","volume":"35","author":[{"given":"Tom","family":"Gu\u00e9don","sequence":"first","affiliation":[]},{"given":"Charlotte","family":"Baey","sequence":"additional","affiliation":[]},{"given":"Estelle","family":"Kuhn","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,8,7]]},"reference":[{"key":"10664_CR1","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1016\/j.jmp.2019.01.005","volume":"89","author":"J Annis","year":"2019","unstructured":"Annis, J., Evans, N.J., Miller, B.J., Palmeri, T.J.: Thermodynamic integration and steppingstone sampling methods for estimating Bayes factors: a tutorial. J. Math. Psychol. 89, 67\u201386 (2019)","journal-title":"J. Math. Psychol."},{"key":"10664_CR2","doi-asserted-by":"publisher","first-page":"4","DOI":"10.1016\/j.csda.2015.04.011","volume":"91","author":"S Allassonniere","year":"2015","unstructured":"Allassonniere, S., Kuhn, E.: Convergent Stochastic Expectation Maximization algorithm with efficient sampling in high dimension. App. Deformable Template Model Estimation .Computational Statistics & Data Analysis 91, 4\u201319 (2015)","journal-title":"App. Deformable Template Model Estimation .Computational Statistics & Data Analysis"},{"key":"10664_CR3","unstructured":"Baey, C., Delattre, M., Kuhn, E., Leger, J.-B., Lemler, S.: Efficient preconditioned stochastic gradient descent for estimation in latent variable models. Proceedings of the 40th International Conference on Machine Learning (2023)"},{"issue":"2","key":"10664_CR4","doi-asserted-by":"publisher","first-page":"245","DOI":"10.1016\/0021-9991(76)90078-4","volume":"22","author":"CH Bennett","year":"1976","unstructured":"Bennett, C.H.: Efficient estimation of free energy differences from monte carlo data. J. Comput. Phys. 22(2), 245\u2013268 (1976)","journal-title":"J. Comput. Phys."},{"key":"10664_CR5","unstructured":"Brekelmans, R., Masrani, V., Bui, T., Wood, F., Galstyan, A., Steeg, G.V., Nielsen, F.: Annealed importance sampling with q-paths. arXiv preprint arXiv:2012.07823 (2020)"},{"key":"10664_CR6","volume-title":"Adaptive Algorithms and Stochastic Approximations","author":"A Benveniste","year":"2012","unstructured":"Benveniste, A., M\u00e9tivier, M., Priouret, P.: Adaptive Algorithms and Stochastic Approximations. Springer, Berlin (2012)"},{"key":"10664_CR7","doi-asserted-by":"crossref","unstructured":"Chen, M.-H., Shao, Q.-M.: Estimating ratios of normalizing constants for densities with different dimensions. Statistica Sinica, 607\u2013630 (1997)","DOI":"10.1214\/aos\/1031594732"},{"issue":"4","key":"10664_CR8","doi-asserted-by":"publisher","first-page":"1563","DOI":"10.1214\/aos\/1031594732","volume":"25","author":"M-H Chen","year":"1997","unstructured":"Chen, M.-H., Shao, Q.-M.: On Monte Carlo methods for estimating ratios of normalizing constants. Ann. Stat. 25(4), 1563\u20131594 (1997)","journal-title":"Ann. Stat."},{"key":"10664_CR9","doi-asserted-by":"crossref","unstructured":"Delyon, B., Lavielle, M., Moulines, E.: Convergence of a stochastic approximation version of the EM algorithm. The Annals of Statistics, 94\u2013128 (1999)","DOI":"10.1214\/aos\/1018031103"},{"issue":"3","key":"10664_CR10","doi-asserted-by":"publisher","first-page":"411","DOI":"10.1111\/j.1467-9868.2006.00553.x","volume":"68","author":"P Del Moral","year":"2006","unstructured":"Del Moral, P., Doucet, A., Jasra, A.: Sequential monte carlo samplers. J. Royal Statistical Soc. Series B (Statistical Methodology) 68(3), 411\u2013436 (2006)","journal-title":"J. Royal Statistical Soc. Series B (Statistical Methodology)"},{"key":"10664_CR11","volume-title":"Algorithmes Stochastiques","author":"M Duflo","year":"1996","unstructured":"Duflo, M.: Algorithmes Stochastiques, vol. 23. Springer, Berlin (1996)"},{"key":"10664_CR12","doi-asserted-by":"publisher","first-page":"60","DOI":"10.1051\/ps\/2014013","volume":"19","author":"G Fort","year":"2015","unstructured":"Fort, G.: Central limit theorems for stochastic approximation with controlled markov chain dynamics. ESAIM: Probability and Statistics 19, 60\u201380 (2015)","journal-title":"ESAIM: Probability and Statistics"},{"issue":"1","key":"10664_CR13","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1111\/j.1368-423X.2004.00125.x","volume":"7","author":"S Fr\u00fchwirth-Schnatter","year":"2004","unstructured":"Fr\u00fchwirth-Schnatter, S.: Estimating marginal likelihoods for mixture and markov switching models using bridge sampling techniques. Economet. J. 7(1), 143\u2013167 (2004)","journal-title":"Economet. J."},{"issue":"3","key":"10664_CR14","doi-asserted-by":"publisher","first-page":"288","DOI":"10.1111\/j.1467-9574.2011.00515.x","volume":"66","author":"N Friel","year":"2012","unstructured":"Friel, N., Wyse, J.: Estimating the evidence-a review. Stat. Neerl. 66(3), 288\u2013308 (2012)","journal-title":"Stat. Neerl."},{"issue":"1","key":"10664_CR15","doi-asserted-by":"publisher","first-page":"523","DOI":"10.1093\/molbev\/msq224","volume":"28","author":"Y Fan","year":"2011","unstructured":"Fan, Y., Wu, R., Chen, M.-H., Kuo, L., Lewis, P.O.: Choosing among partition models in bayesian phylogenetics. Mol. Biol. Evol. 28(1), 523\u2013532 (2011)","journal-title":"Mol. Biol. Evol."},{"issue":"3","key":"10664_CR16","doi-asserted-by":"publisher","first-page":"501","DOI":"10.1111\/j.2517-6161.1994.tb01996.x","volume":"56","author":"AE Gelfand","year":"1994","unstructured":"Gelfand, A.E., Dey, D.K.: Bayesian model choice: asymptotics and exact calculations. J. R. Stat. Soc., Series B (Statistical Methodology) 56(3), 501\u2013514 (1994)","journal-title":"J. R. Stat. Soc., Series B (Statistical Methodology)"},{"key":"10664_CR17","unstructured":"Geyer, C.J.: Estimating normalizing constants and reweighting mixtures. Technical Report 568, School of Statistics, University of Minnesota (1994)"},{"key":"10664_CR18","doi-asserted-by":"crossref","unstructured":"Gelman, A., Meng, X.-L.: Simulating normalizing constants: From importance sampling to bridge sampling to path sampling. Statistical Science, 163\u2013185 (1998)","DOI":"10.1214\/ss\/1028905934"},{"key":"10664_CR19","doi-asserted-by":"publisher","first-page":"80","DOI":"10.1016\/j.jmp.2017.09.005","volume":"81","author":"QF Gronau","year":"2017","unstructured":"Gronau, Q.F., Sarafoglou, A., Matzke, D., Ly, A., Boehm, U., Marsman, M., Leslie, D.S., Forster, J.J., Wagenmakers, E.-J., Steingroever, H.: A tutorial on bridge sampling. J. Math. Psychol. 81, 80\u201397 (2017)","journal-title":"J. Math. Psychol."},{"issue":"10","key":"10664_CR20","doi-asserted-by":"publisher","first-page":"1","DOI":"10.18637\/jss.v092.i10","volume":"92","author":"QF Gronau","year":"2020","unstructured":"Gronau, Q.F., Singmann, H., Wagenmakers, E.-J.: bridgesampling: An R Package for Estimating Normalizing Constants. J. Stat. Softw. 92(10), 1\u201329 (2020). https:\/\/doi.org\/10.18637\/jss.v092.i10","journal-title":"J. Stat. Softw."},{"key":"10664_CR21","doi-asserted-by":"publisher","first-page":"115","DOI":"10.1051\/ps:2004007","volume":"8","author":"E Kuhn","year":"2004","unstructured":"Kuhn, E., Lavielle, M.: Coupling a stochastic approximation version of EM with an MCMC procedure. ESAIM: Probability and Statistics 8, 115\u2013131 (2004)","journal-title":"ESAIM: Probability and Statistics"},{"issue":"1","key":"10664_CR22","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1137\/20M1310849","volume":"65","author":"F Llorente","year":"2023","unstructured":"Llorente, F., Martino, L., Delgado, D., Lopez-Santiago, J.: Marginal likelihood computation for model selection and hypothesis testing: an extensive review. SIAM Rev. 65(1), 3\u201358 (2023)","journal-title":"SIAM Rev."},{"issue":"2","key":"10664_CR23","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1080\/10635150500433722","volume":"55","author":"N Lartillot","year":"2006","unstructured":"Lartillot, N., Philippe, H.: Computing Bayes factors using thermodynamic integration. Syst. Biol. 55(2), 195\u2013207 (2006)","journal-title":"Syst. Biol."},{"issue":"3","key":"10664_CR24","doi-asserted-by":"publisher","first-page":"552","DOI":"10.1198\/106186002457","volume":"11","author":"X-L Meng","year":"2002","unstructured":"Meng, X.-L., Schilling, S.: Warp bridge sampling. J. Comput. Graph. Stat. 11(3), 552\u2013586 (2002)","journal-title":"J. Comput. Graph. Stat."},{"key":"10664_CR25","unstructured":"Meng, X.-L., Wong, W.H.: Simulating ratios of normalizing constants via a simple identity: a theoretical exploration. Statistica Sinica, 831\u2013860 (1996)"},{"key":"10664_CR26","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1023\/A:1008923215028","volume":"11","author":"RM Neal","year":"2001","unstructured":"Neal, R.M.: Annealed importance sampling. Stat. Comput. 11, 125\u2013139 (2001)","journal-title":"Stat. Comput."},{"issue":"1","key":"10664_CR27","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1111\/j.2517-6161.1994.tb01956.x","volume":"56","author":"MA Newton","year":"1994","unstructured":"Newton, M.A., Raftery, A.E.: Approximate Bayesian inference with the weighted likelihood bootstrap. J. R. Stat. Soc. Ser. B Stat Methodol. 56(1), 3\u201326 (1994)","journal-title":"J. R. Stat. Soc. Ser. B Stat Methodol."},{"issue":"4","key":"10664_CR28","doi-asserted-by":"publisher","first-page":"838","DOI":"10.1137\/0330046","volume":"30","author":"BT Polyak","year":"1992","unstructured":"Polyak, B.T., Juditsky, A.B.: Acceleration of stochastic approximation by averaging. SIAM J. Control. Optim. 30(4), 838\u2013855 (1992)","journal-title":"SIAM J. Control. Optim."},{"key":"10664_CR29","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-3071-5","volume-title":"Monte Carlo Statistical Methods","author":"CP Robert","year":"1999","unstructured":"Robert, C.P., Casella, G., Casella, G.: Monte Carlo Statistical Methods, vol. 2. Springer, Berlin (1999)"},{"issue":"88","key":"10664_CR30","first-page":"1","volume":"21","author":"T Rainforth","year":"2020","unstructured":"Rainforth, T., Golinski, A., Wood, F., Zaidi, S.: Target-aware bayesian inference: how to beat optimal conventional estimators. J. Mach. Learn. Res. 21(88), 1\u201354 (2020)","journal-title":"J. Mach. Learn. Res."},{"key":"10664_CR31","doi-asserted-by":"crossref","unstructured":"Robbins, H., Monro, S.: A stochastic approximation method. The Annals of Mathematical Statistics, 400\u2013407 (1951)","DOI":"10.1214\/aoms\/1177729586"},{"key":"10664_CR32","unstructured":"Russel, P.M., Meyer, R., Veitch, J., Christensen, N.: The stepping-stone sampling algorithm for calculating the evidence of gravitational wave models. arXiv preprint arXiv:1810.04488 (2018)"},{"issue":"2","key":"10664_CR33","doi-asserted-by":"publisher","first-page":"349","DOI":"10.1198\/jcgs.2009.06134","volume":"18","author":"GO Roberts","year":"2009","unstructured":"Roberts, G.O., Rosenthal, J.S.: Examples of adaptive MCMC. J. Comput. Graph. Stat. 18(2), 349\u2013367 (2009)","journal-title":"J. Comput. Graph. Stat."},{"key":"10664_CR34","unstructured":"Ruppert, D.: Efficient estimations from a slowly convergent Robbins-Monro process. Technical report, Cornell University Operations Research and Industrial Engineering (1988)"},{"key":"10664_CR35","doi-asserted-by":"crossref","unstructured":"Shirts, M.R., Chodera, J.D.: Statistically optimal analysis of samples from multiple equilibrium states. The Journal of chemical physics 129(12) (2008)","DOI":"10.1063\/1.2978177"},{"key":"10664_CR36","doi-asserted-by":"crossref","unstructured":"Torrie, G.M., Valleau, J.P.: Nonphysical sampling distributions in Monte Carlo free-energy estimation: Umbrella sampling. J. Comput. Phys. 23(2), 187\u2013199 (1977)","DOI":"10.1016\/0021-9991(77)90121-8"},{"key":"10664_CR37","volume-title":"Asymptotic Statistics","author":"AW Van der Vaart","year":"2000","unstructured":"Van der Vaart, A.W.: Asymptotic Statistics, vol. 3. Cambridge University Press, Cambridge (2000)"},{"issue":"538","key":"10664_CR38","doi-asserted-by":"publisher","first-page":"835","DOI":"10.1080\/01621459.2020.1825447","volume":"117","author":"L Wang","year":"2022","unstructured":"Wang, L., Jones, D.E., Meng, X.-L.: Warp bridge sampling: The next generation. J. Am. Stat. Assoc. 117(538), 835\u2013851 (2022)","journal-title":"J. Am. Stat. Assoc."},{"issue":"2","key":"10664_CR39","doi-asserted-by":"publisher","first-page":"150","DOI":"10.1093\/sysbio\/syq085","volume":"60","author":"W Xie","year":"2011","unstructured":"Xie, W., Lewis, P.O., Fan, Y., Kuo, L., Chen, M.-H.: Improving marginal likelihood estimation for Bayesian phylogenetic model selection. Syst. Biol. 60(2), 150\u2013160 (2011)","journal-title":"Syst. Biol."}],"container-title":["Statistics and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11222-025-10664-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11222-025-10664-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11222-025-10664-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,8]],"date-time":"2025-09-08T17:31:38Z","timestamp":1757352698000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11222-025-10664-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,8,7]]},"references-count":39,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2025,10]]}},"alternative-id":["10664"],"URL":"https:\/\/doi.org\/10.1007\/s11222-025-10664-0","relation":{},"ISSN":["0960-3174","1573-1375"],"issn-type":[{"type":"print","value":"0960-3174"},{"type":"electronic","value":"1573-1375"}],"subject":[],"published":{"date-parts":[[2025,8,7]]},"assertion":[{"value":"8 November 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 June 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 August 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of Interest"}}],"article-number":"166"}}