{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,14]],"date-time":"2026-04-14T21:21:06Z","timestamp":1776201666917,"version":"3.50.1"},"reference-count":37,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2016,8,30]],"date-time":"2016-08-30T00:00:00Z","timestamp":1472515200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2016,8,30]],"date-time":"2016-08-30T00:00:00Z","timestamp":1472515200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100005246","name":"Institute of Education Sciences","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100005246","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000006","name":"Office of Naval Research","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000006","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Stat Comput"],"published-print":{"date-parts":[[2017,9]]},"DOI":"10.1007\/s11222-016-9696-4","type":"journal-article","created":{"date-parts":[[2016,8,30]],"date-time":"2016-08-30T12:53:35Z","timestamp":1472561615000},"page":"1413-1432","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4211,"title":["Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC"],"prefix":"10.1007","volume":"27","author":[{"given":"Aki","family":"Vehtari","sequence":"first","affiliation":[]},{"given":"Andrew","family":"Gelman","sequence":"additional","affiliation":[]},{"given":"Jonah","family":"Gabry","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2016,8,30]]},"reference":[{"key":"9696_CR1","unstructured":"Akaike, H.: Information theory and an extension of the maximum likelihood principle. In: Petrov, B.N., Csaki, F. (eds.) Proceedings of the Second International Symposium on Information Theory, pp. 267\u2013281. Akademiai Kiado, Budapest (1973)"},{"key":"9696_CR2","doi-asserted-by":"publisher","first-page":"744","DOI":"10.1016\/j.ijforecast.2009.08.001","volume":"26","author":"T Ando","year":"2010","unstructured":"Ando, T., Tsay, R.: Predictive likelihood for Bayesian model selection and averaging. Int. J. Forecast. 26, 744\u2013763 (2010)","journal-title":"Int. J. Forecast."},{"key":"9696_CR3","doi-asserted-by":"publisher","first-page":"40","DOI":"10.1214\/09-SS054","volume":"4","author":"S Arolot","year":"2010","unstructured":"Arolot, S., Celisse, A.: A survey of cross-validation procedures for model selection. Stat. Surv. 4, 40\u201379 (2010)","journal-title":"Stat. Surv."},{"key":"9696_CR4","doi-asserted-by":"crossref","unstructured":"Bernardo, J.M., Smith A.F.M.: Bayesian Theory. Wiley, New York (1994)","DOI":"10.1002\/9780470316870"},{"key":"9696_CR5","doi-asserted-by":"publisher","first-page":"503","DOI":"10.1093\/biomet\/76.3.503","volume":"76","author":"P Burman","year":"1989","unstructured":"Burman, P.: A comparative study of ordinary cross-validation, $$v$$-fold cross-validation and the repeated learning-testing methods. Biometrika 76, 503\u2013514 (1989)","journal-title":"Biometrika"},{"key":"9696_CR6","doi-asserted-by":"publisher","first-page":"774","DOI":"10.1214\/08-EJS259","volume":"2","author":"I Epifani","year":"2008","unstructured":"Epifani, I., MacEachern, S.N., Peruggia, M.: Case-deletion importance sampling estimators: central limit theorems and related results. Electron. J. Stat. 2, 774\u2013806 (2008)","journal-title":"Electron. J. Stat."},{"key":"9696_CR7","doi-asserted-by":"crossref","unstructured":"Gabry, J., Goodrich, B.: rstanarm: Bayesian applied regression modeling via Stan. R package version 2.10.0. (2016). http:\/\/mc-stan.org\/interfaces\/rstanarm","DOI":"10.32614\/CRAN.package.rstanarm"},{"key":"9696_CR8","doi-asserted-by":"publisher","first-page":"153","DOI":"10.1080\/01621459.1979.10481632","volume":"74","author":"S Geisser","year":"1979","unstructured":"Geisser, S., Eddy, W.: A predictive approach to model selection. J. Am. Stat. Assoc. 74, 153\u2013160 (1979)","journal-title":"J. Am. Stat. Assoc."},{"key":"9696_CR9","first-page":"145","volume-title":"Markov Chain Monte Carlo in Practice","author":"AE Gelfand","year":"1996","unstructured":"Gelfand, A.E.: Model determination using sampling-based methods. In: Gilks, W.R., Richardson, S., Spiegelhalter, D.J. (eds.) Markov Chain Monte Carlo in Practice, pp. 145\u2013162. Chapman and Hall, London (1996)"},{"key":"9696_CR10","first-page":"147","volume-title":"Bayesian Statistics","author":"AE Gelfand","year":"1992","unstructured":"Gelfand, A.E., Dey, D.K., Chang, H.: Model determination using predictive distributions with implementation via sampling-based methods. In: Bernardo, J.M., Berger, J.O., Dawid, A.P., Smith, A.F.M. (eds.) Bayesian Statistics, 4th edn, pp. 147\u2013167. Oxford University Press, Oxford (1992)","edition":"4"},{"key":"9696_CR11","doi-asserted-by":"crossref","DOI":"10.1201\/b16018","volume-title":"Bayesian Data Analysis","author":"A Gelman","year":"2013","unstructured":"Gelman, A., Carlin, J.B., Stern, H.S., Dunson, D.B., Vehtari, A., Rubin, D.B.: Bayesian Data Analysis, 3rd edn. CRC Press, London (2013)","edition":"3"},{"key":"9696_CR12","volume-title":"Data Analysis Using Regression and Multilevel\/Hierarchical Models","author":"A Gelman","year":"2007","unstructured":"Gelman, A., Hill, J.: Data Analysis Using Regression and Multilevel\/Hierarchical Models. Cambridge University Press, Cambridge (2007)"},{"key":"9696_CR13","doi-asserted-by":"publisher","first-page":"997","DOI":"10.1007\/s11222-013-9416-2","volume":"24","author":"A Gelman","year":"2014","unstructured":"Gelman, A., Hwang, J., Vehtari, A.: Understanding predictive information criteria for Bayesian models. Stat. Comput. 24, 997\u20131016 (2014)","journal-title":"Stat. Comput."},{"key":"9696_CR14","unstructured":"Gneiting, T., Raftery, A.E.: Strictly proper scoring rules, prediction, and estimation. J. Am. Stat. Assoc. 102, 359\u2013378 (2007)"},{"key":"9696_CR15","doi-asserted-by":"publisher","first-page":"382","DOI":"10.1214\/ss\/1009212519","volume":"14","author":"J Hoeting","year":"1999","unstructured":"Hoeting, J., Madigan, D., Raftery, A.E., Volinsky, C.: Bayesian model averaging. Stat. Sci. 14, 382\u2013417 (1999)","journal-title":"Stat. Sci."},{"key":"9696_CR16","first-page":"1593","volume":"15","author":"MD Hoffman","year":"2014","unstructured":"Hoffman, M.D., Gelman, A.: The no-U-turn sampler: adaptively setting path lengths in Hamiltonian Monte Carlo. J. Mach. Learn. Res. 15, 1593\u20131623 (2014)","journal-title":"J. Mach. Learn. Res."},{"key":"9696_CR17","doi-asserted-by":"publisher","first-page":"295","DOI":"10.1198\/106186008X320456","volume":"17","author":"EL Ionides","year":"2008","unstructured":"Ionides, E.L.: Truncated importance sampling. J. Comput. Graph. Stat. 17, 295\u2013311 (2008)","journal-title":"J. Comput. Graph. Stat."},{"key":"9696_CR18","doi-asserted-by":"publisher","first-page":"2","DOI":"10.1016\/j.jeconom.2008.10.002","volume":"149","author":"SJ Koopman","year":"2009","unstructured":"Koopman, S.J., Shephard, N., Creal, D.: Testing the assumptions behind importance sampling. J. Econom. 149, 2\u201311 (2009)","journal-title":"J. Econom."},{"key":"9696_CR19","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1080\/01621459.1997.10473617","volume":"92","author":"M Peruggia","year":"1997","unstructured":"Peruggia, M.: On the variability of case-deletion importance sampling weights in the Bayesian linear model. J. Am. Stat. Assoc. 92, 199\u2013207 (1997)","journal-title":"J. Am. Stat. Assoc."},{"key":"9696_CR20","doi-asserted-by":"crossref","unstructured":"Piironen, J., Vehtari, A.: Comparison of Bayesian predictive methods for model selection. Stat. Comput. (2016) (In press). http:\/\/link.springer.com\/article\/10.1007\/s11222-016-9649-y","DOI":"10.1007\/s11222-016-9649-y"},{"key":"9696_CR21","doi-asserted-by":"publisher","first-page":"523","DOI":"10.1093\/biostatistics\/kxm049","volume":"9","author":"M Plummer","year":"2008","unstructured":"Plummer, M.: Penalized loss functions for Bayesian model comparison. Biostatistics 9, 523\u2013539 (2008)","journal-title":"Biostatistics"},{"key":"9696_CR22","unstructured":"R Core Team: R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria (2016). https:\/\/www.R-project.org\/"},{"key":"9696_CR23","doi-asserted-by":"crossref","first-page":"377","DOI":"10.3102\/10769986006004377","volume":"6","author":"DB Rubin","year":"1981","unstructured":"Rubin, D.B.: Estimation in parallel randomized experiments. J. Educ. Stat. 6, 377\u2013401 (1981)","journal-title":"J. Educ. Stat."},{"key":"9696_CR24","doi-asserted-by":"publisher","first-page":"583","DOI":"10.1111\/1467-9868.00353","volume":"64","author":"DJ Spiegelhalter","year":"2002","unstructured":"Spiegelhalter, D.J., Best, N.G., Carlin, B.P., van der Linde, A.: Bayesian measures of model complexity and fit. J. R. Stat. Soc. B 64, 583\u2013639 (2002)","journal-title":"J. R. Stat. Soc. B"},{"key":"9696_CR25","unstructured":"Spiegelhalter, D., Thomas, A., Best, N., Gilks, W., Lunn, D.: BUGS: Bayesian inference using Gibbs sampling. MRC Biostatistics Unit, Cambridge, England (1994, 2003). http:\/\/www.mrc-bsu.cam.ac.uk\/bugs\/"},{"key":"9696_CR26","unstructured":"Stan Development Team: The Stan C++ Library, version 2.10.0 (2016a). http:\/\/mc-stan.org\/"},{"key":"9696_CR27","unstructured":"Stan Development Team: RStan: the R interface to Stan, version 2.10.1 (2016b). http:\/\/mc-stan.org\/interfaces\/rstan.html"},{"key":"9696_CR28","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1111\/j.2517-6161.1977.tb01603.x","volume":"36","author":"M Stone","year":"1977","unstructured":"Stone, M.: An asymptotic equivalence of choice of model cross-validation and Akaike\u2019s criterion. J. R. Stat. Soc. B 36, 44\u201347 (1977)","journal-title":"J. R. Stat. Soc. B"},{"key":"9696_CR29","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1111\/j.1467-9574.2005.00278.x","volume":"1","author":"A van der Linde","year":"2005","unstructured":"van der Linde, A.: DIC in variable selection. Stat. Neerl. 1, 45\u201356 (2005)","journal-title":"Stat. Neerl."},{"key":"9696_CR30","unstructured":"Vehtari, A., Gelman, A.: Pareto smoothed importance sampling (2015). arXiv:1507.02646"},{"key":"9696_CR31","doi-asserted-by":"crossref","unstructured":"Vehtari, A., Gelman, A., Gabry, J.: loo: Efficient leave-one-out cross-validation and WAIC for Bayesian models. R package version 0.1.6 (2016a). https:\/\/github.com\/stan-dev\/loo","DOI":"10.32614\/CRAN.package.loo"},{"key":"9696_CR32","unstructured":"Vehtari, A., Mononen, T., Tolvanen, V., Sivula, T., Winther, O.: Bayesian leave-one-out cross-validation approximations for Gaussian latent variable models. J. Mach. Learn. Res. 17, 1\u201338 (2016b)"},{"key":"9696_CR33","doi-asserted-by":"publisher","first-page":"2439","DOI":"10.1162\/08997660260293292","volume":"14","author":"A Vehtari","year":"2002","unstructured":"Vehtari, A., Lampinen, J.: Bayesian model assessment and comparison using cross-validation predictive densities. Neural Comput. 14, 2439\u20132468 (2002)","journal-title":"Neural Comput."},{"key":"9696_CR34","doi-asserted-by":"publisher","first-page":"142","DOI":"10.1214\/12-SS102","volume":"6","author":"A Vehtari","year":"2012","unstructured":"Vehtari, A., Ojanen, J.: A survey of Bayesian predictive methods for model assessment, selection and comparison. Stat. Surv. 6, 142\u2013228 (2012)","journal-title":"Stat. Surv."},{"key":"9696_CR35","doi-asserted-by":"publisher","first-page":"425","DOI":"10.1214\/14-BA872","volume":"9","author":"A Vehtari","year":"2014","unstructured":"Vehtari, A., Riihim\u00e4ki, J.: Laplace approximation for logistic Gaussian process density estimation and regression. Bayesian Anal. 9, 425\u2013448 (2014)","journal-title":"Bayesian Anal."},{"key":"9696_CR36","first-page":"3571","volume":"11","author":"S Watanabe","year":"2010","unstructured":"Watanabe, S.: Asymptotic equivalence of Bayes cross validation and widely applicable information criterion in singular learning theory. J. Mach. Learn. Res. 11, 3571\u20133594 (2010)","journal-title":"J. Mach. Learn. Res."},{"key":"9696_CR37","doi-asserted-by":"publisher","first-page":"316","DOI":"10.1198\/tech.2009.08017","volume":"51","author":"J Zhang","year":"2009","unstructured":"Zhang, J., Stephens, M.A.: A new and efficient estimation method for the generalized Pareto distribution. Technometrics 51, 316\u2013325 (2009)","journal-title":"Technometrics"}],"updated-by":[{"DOI":"10.1007\/s11222-016-9709-3","type":"correction","label":"Correction","source":"publisher","updated":{"date-parts":[[2016,10,18]],"date-time":"2016-10-18T00:00:00Z","timestamp":1476748800000}}],"container-title":["Statistics and Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11222-016-9696-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11222-016-9696-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11222-016-9696-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,18]],"date-time":"2024-06-18T23:55:19Z","timestamp":1718754919000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11222-016-9696-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,8,30]]},"references-count":37,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2017,9]]}},"alternative-id":["9696"],"URL":"https:\/\/doi.org\/10.1007\/s11222-016-9696-4","relation":{"is-referenced-by":[{"id-type":"doi","id":"10.1007\/s11252-024-01632-z","asserted-by":"object"}]},"ISSN":["0960-3174","1573-1375"],"issn-type":[{"value":"0960-3174","type":"print"},{"value":"1573-1375","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,8,30]]},"assertion":[{"value":"23 January 2016","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 August 2016","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"30 August 2016","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}