메뉴 건너뛰기




Volumn 27, Issue 5, 2017, Pages 1413-1432

Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC

Author keywords

Bayesian computation; K fold cross validation; Leave one out cross validation (LOO); Pareto smoothed importance sampling (PSIS); Stan; Widely applicable information criterion (WAIC)

Indexed keywords


EID: 85026299835     PISSN: 09603174     EISSN: 15731375     Source Type: Journal    
DOI: 10.1007/s11222-016-9696-4     Document Type: Article
Times cited : (3503)

References (37)
  • 1
    • 0000501656 scopus 로고
    • Information theory and an extension of the maximum likelihood principle
    • Petrov, B.N., Csaki, F. (eds.), Akademiai Kiado, Budapest
    • 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. 267–281. Akademiai Kiado, Budapest (1973)
    • (1973) Proceedings of the Second International Symposium on Information Theory , pp. 267-281
    • Akaike, H.1
  • 2
    • 77956264822 scopus 로고    scopus 로고
    • Predictive likelihood for Bayesian model selection and averaging
    • Ando, T., Tsay, R.: Predictive likelihood for Bayesian model selection and averaging. Int. J. Forecast. 26, 744–763 (2010)
    • (2010) Int. J. Forecast. , vol.26 , pp. 744-763
    • Ando, T.1    Tsay, R.2
  • 3
    • 77956649096 scopus 로고    scopus 로고
    • A survey of cross-validation procedures for model selection
    • Arolot, S., Celisse, A.: A survey of cross-validation procedures for model selection. Stat. Surv. 4, 40–79 (2010)
    • (2010) Stat. Surv. , vol.4 , pp. 40-79
    • Arolot, S.1    Celisse, A.2
  • 5
    • 0000354976 scopus 로고
    • A comparative study of ordinary cross-validation, v-fold cross-validation and the repeated learning-testing methods
    • Burman, P.: A comparative study of ordinary cross-validation, v-fold cross-validation and the repeated learning-testing methods. Bio-metrika 76, 503–514 (1989)
    • (1989) Bio-Metrika , vol.76 , pp. 503-514
    • Burman, P.1
  • 6
    • 84859838775 scopus 로고    scopus 로고
    • Case-deletion importance sampling estimators: Central limit theorems and related results
    • Epifani, I., MacEachern, S.N., Peruggia, M.: Case-deletion importance sampling estimators: central limit theorems and related results. Electron. J. Stat. 2, 774–806 (2008)
    • (2008) Electron. J. Stat. , vol.2 , pp. 774-806
    • Epifani, I.1    Maceachern, S.N.2    Peruggia, M.3
  • 8
    • 0001526195 scopus 로고
    • A predictive approach to model selection
    • Geisser, S., Eddy, W.: A predictive approach to model selection. J. Am. Stat. Assoc. 74, 153–160 (1979)
    • (1979) J. Am. Stat. Assoc. , vol.74 , pp. 153-160
    • Geisser, S.1    Eddy, W.2
  • 9
    • 0001803816 scopus 로고    scopus 로고
    • Model determination using sampling-based methods
    • Gilks, W.R., Richardson, S., Spiegelhalter, D.J. (eds.), Chapman and Hall, London
    • 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. 145–162. Chapman and Hall, London (1996)
    • (1996) Markov Chain Monte Carlo in Practice , pp. 145-162
    • Gelfand, A.E.1
  • 10
    • 0000079228 scopus 로고
    • Model determination using predictive distributions with implementation via sampling-based methods
    • Bernardo, J.M., Berger, J.O., Dawid, A.P., Smith, A.F.M. (eds.), 4th edn, Oxford University Press, Oxford
    • 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. 147–167. Oxford University Press, Oxford (1992)
    • (1992) Bayesian Statistics , pp. 147-167
    • Gelfand, A.E.1    Dey, D.K.2    Chang, H.3
  • 13
    • 84916213666 scopus 로고    scopus 로고
    • Understanding predictive information criteria for Bayesian models
    • Gelman, A., Hwang, J., Vehtari, A.: Understanding predictive information criteria for Bayesian models. Stat. Comput. 24, 997–1016 (2014)
    • (2014) Stat. Comput. , vol.24 , pp. 997-1016
    • Gelman, A.1    Hwang, J.2    Vehtari, A.3
  • 14
    • 33947274775 scopus 로고    scopus 로고
    • Strictly proper scoring rules, prediction, and estimation
    • Gneiting, T., Raftery, A.E.: Strictly proper scoring rules, prediction, and estimation. J. Am. Stat. Assoc. 102, 359–378 (2007)
    • (2007) J. Am. Stat. Assoc. , vol.102 , pp. 359-378
    • Gneiting, T.1    Raftery, A.E.2
  • 16
    • 84901687683 scopus 로고    scopus 로고
    • The no-U-turn sampler: Adaptively setting path lengths in Hamiltonian Monte Carlo
    • Hoffman, M.D., Gelman, A.: The no-U-turn sampler: adaptively setting path lengths in Hamiltonian Monte Carlo. J. Mach. Learn. Res. 15, 1593–1623 (2014)
    • (2014) J. Mach. Learn. Res. , vol.15 , pp. 1593-1623
    • Hoffman, M.D.1    Gelman, A.2
  • 17
    • 46849112625 scopus 로고    scopus 로고
    • Truncated importance sampling
    • Ionides, E.L.: Truncated importance sampling. J. Comput. Graph. Stat. 17, 295–311 (2008)
    • (2008) J. Comput. Graph. Stat. , vol.17 , pp. 295-311
    • Ionides, E.L.1
  • 18
    • 63149119676 scopus 로고    scopus 로고
    • Testing the assumptions behind importance sampling
    • Koopman, S.J., Shephard, N., Creal, D.: Testing the assumptions behind importance sampling. J. Econom. 149, 2–11 (2009)
    • (2009) J. Econom. , vol.149 , pp. 2-11
    • Koopman, S.J.1    Shephard, N.2    Creal, D.3
  • 19
    • 0031500277 scopus 로고    scopus 로고
    • On the variability of case-deletion importance sampling weights in the Bayesian linear model
    • Peruggia, M.: On the variability of case-deletion importance sampling weights in the Bayesian linear model. J. Am. Stat. Assoc. 92, 199– 207 (1997)
    • (1997) J. Am. Stat. Assoc. , vol.92 , pp. 199-207
    • Peruggia, M.1
  • 20
    • 84964030922 scopus 로고    scopus 로고
    • Comparison of Bayesian predictive methods for model selection
    • In press
    • 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
    • (2016) Stat. Comput.
    • Piironen, J.1    Vehtari, A.2
  • 21
    • 45849088346 scopus 로고    scopus 로고
    • Penalized loss functions for Bayesian model comparison
    • Plummer, M.: Penalized loss functions for Bayesian model comparison. Biostatistics 9, 523–539 (2008)
    • (2008) Biostatistics , vol.9 , pp. 523-539
    • Plummer, M.1
  • 22
    • 32444450670 scopus 로고    scopus 로고
    • Vienna, Austria
    • R Core Team: R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria (2016). https://www.R-project.org/
    • (2016) R Foundation for Statistical Computing
  • 23
    • 0000656694 scopus 로고
    • Estimation in parallel randomized experiments
    • Rubin, D.B.: Estimation in parallel randomized experiments. J. Educ. Stat. 6, 377–401 (1981)
    • (1981) J. Educ. Stat. , vol.6 , pp. 377-401
    • Rubin, D.B.1
  • 26
    • 85058382931 scopus 로고    scopus 로고
    • Stan Development Team: The Stan C++ Library, version 2.10.0 (2016a)
    • Stan Development Team: The Stan C++ Library, version 2.10.0 (2016a). http://mc-stan.org/
  • 27
    • 85058408882 scopus 로고    scopus 로고
    • RStan: the R interface to Stan, version 2.10.1
    • Stan Development Team: RStan: the R interface to Stan, version 2.10.1 (2016b). http://mc-stan.org/interfaces/rstan.html
    • (2016)
  • 28
    • 0000859675 scopus 로고
    • An asymptotic equivalence of choice of model cross-validation and Akaike’s criterion
    • Stone, M.: An asymptotic equivalence of choice of model cross-validation and Akaike’s criterion. J. R. Stat. Soc. B 36, 44–47 (1977)
    • (1977) J. R. Stat. Soc. B , vol.36 , pp. 44-47
    • Stone, M.1
  • 29
    • 15544368884 scopus 로고    scopus 로고
    • DIC in variable selection
    • van der Linde, A.: DIC in variable selection. Stat. Neerl. 1, 45–56 (2005)
    • (2005) Stat. Neerl. , vol.1 , pp. 45-56
    • van der Linde, A.1
  • 32
    • 84988932233 scopus 로고    scopus 로고
    • Bayesian leave-one-out cross-validation approximations for Gaussian latent variable models
    • 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, 1–38 (2016b)
    • (2016) J. Mach. Learn. Res , vol.17 , pp. 1-38
    • Vehtari, A.1    Mononen, T.2    Tolvanen, V.3    Sivula, T.4    Winther, O.5
  • 33
    • 0036781790 scopus 로고    scopus 로고
    • Bayesian model assessment and comparison using cross-validation predictive densities
    • Vehtari, A., Lampinen, J.: Bayesian model assessment and comparison using cross-validation predictive densities. Neural Comput. 14, 2439–2468 (2002)
    • (2002) Neural Comput , vol.14 , pp. 2439-2468
    • Vehtari, A.1    Lampinen, J.2
  • 34
    • 84874387472 scopus 로고    scopus 로고
    • A survey of Bayesian predictive methods for model assessment, selection and comparison
    • Vehtari, A., Ojanen, J.: A survey of Bayesian predictive methods for model assessment, selection and comparison. Stat. Surv. 6, 142– 228 (2012)
    • (2012) Stat. Surv. , vol.6 , pp. 142-228
    • Vehtari, A.1    Ojanen, J.2
  • 35
    • 84901481264 scopus 로고    scopus 로고
    • Laplace approximation for logistic Gaussian process density estimation and regression
    • Vehtari, A., Riihimäki, J.: Laplace approximation for logistic Gaussian process density estimation and regression. Bayesian Anal. 9, 425– 448 (2014)
    • (2014) Bayesian Anal , vol.9 , pp. 425-448
    • Vehtari, A.1    Riihimäki, J.2
  • 36
    • 79551500649 scopus 로고    scopus 로고
    • Asymptotic equivalence of Bayes cross validation and widely applicable information criterion in singular learning theory
    • Watanabe, S.: Asymptotic equivalence of Bayes cross validation and widely applicable information criterion in singular learning theory. J. Mach. Learn. Res. 11, 3571–3594 (2010)
    • (2010) J. Mach. Learn. Res. , vol.11 , pp. 3571-3594
    • Watanabe, S.1
  • 37
    • 69249150497 scopus 로고    scopus 로고
    • A new and efficient estimation method for the generalized Pareto distribution
    • Zhang, J., Stephens, M.A.: A new and efficient estimation method for the generalized Pareto distribution. Technometrics 51, 316–325 (2009)
    • (2009) Technometrics , vol.51 , pp. 316-325
    • Zhang, J.1    Stephens, M.A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.