Understanding predictive information criteria for Bayesian models

Statistics and Computing

Volumn 24, Issue 6, 2014, Pages 997-1016

  Gelman, Andrew ^a   Hwang, Jessica ^b   Vehtari, Aki ^c  

^a Och Spine at New York Presbyterian Hospitals   (United States)

^b HARVARD UNIVERSITY   (United States)

^c AALTO UNIVERSITY   (Finland)

Author keywords

AIC; Bayes; Cross validation; DIC; Prediction; WAIC

Indexed keywords

EID: 84916213666     PISSN: 09603174     EISSN: 15731375     Source Type: Journal    
DOI: 10.1007/s11222-013-9416-2     Document Type: Article

References (40)

1. Aitkin, M.: Statistical Inference: an Integrated Bayesian/Likelihood Approach. Chapman & Hall, London (2010)
2. 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). Reprinted in: Kotz, S. (ed.) Breakthroughs in Statistics, pp. 610–624. Springer, New York (1992)
3. Ando, T., Tsay, R.: Predictive likelihood for Bayesian model selection and averaging. Int. J. Forecast. 26, 744–763 (2010)
4. Bernardo, J.M.: Expected information as expected utility. Ann. Stat. 7, 686–690 (1979)
5. Bernardo, J.M., Smith, A.F.M.: Bayesian Theory. Wiley, New York (1994)
6. Burman, P.: A comparative study of ordinary cross-validation, v-fold cross-validation and the repeated learning-testing methods. Biometrika 76, 503–514 (1989)
7. Burman, P., Chow, E., Nolan, D.: A cross-validatory method for dependent data. Biometrika 81, 351–358 (1994)
8. Burnham, K.P., Anderson, D.R.: Model Selection and Multimodel Inference: a Practical Information Theoretic Approach. Springer, New York (2002)
9. Celeux, G., Forbes, F., Robert, C., Titterington, D.: Deviance information criteria for missing data models. Bayesian Anal. 1, 651–706 (2006)
10. DeGroot, M.H.: Optimal Statistical Decisions. McGraw-Hill, New York (1970)
11. Dempster, A.P.: The direct use of likelihood for significance testing. In: Proceedings of Conference on Foundational Questions in Statistical Inference, Department of Theoretical Statistics: University of Aarhus, pp. 335–352 (1974)
12. Draper, D.: Model uncertainty yes, discrete model averaging maybe. Stat. Sci. 14, 405–409 (1999)
13. Efron, B., Tibshirani, R.: An Introduction to the Bootstrap. Chapman & Hall, New York (1993)
14. Geisser, S., Eddy, W.: A predictive approach to model selection. J. Am. Stat. Assoc. 74, 153–160 (1979)
15. Gelfand, A., Dey, D.: Bayesian model choice: asymptotics and exact calculations. J. R. Stat. Soc. B 56, 501–514 (1994)
16. Gelman, A., Carlin, J.B., Stern, H.S., Rubin, D.B.: Bayesian Data Analysis, 2nd edn. CRC Press, London (2003)
17. Gelman, A., Meng, X.L., Stern, H.S.: Posterior predictive assessment of model fitness via realized discrepancies (with discussion). Stat. Sin. 6, 733–807 (1996)
18. Gelman, A., Shalizi, C.: Philosophy and the practice of Bayesian statistics (with discussion). Br. J. Math. Stat. Psychol. 66, 8–80 (2013)
19. Gneiting, T.: Making and evaluating point forecasts. J. Am. Stat. Assoc. 106, 746–762 (2011)
20. Gneiting, T., Raftery, A.E.: Strictly proper scoring rules, prediction, and estimation. J. Am. Stat. Assoc. 102, 359–378 (2007)
21. Hibbs, D.: Implications of the ‘bread and peace’ model for the 2008 U.S. presidential election. Public Choice 137, 1–10 (2008)
22. Hoeting, J., Madigan, D., Raftery, A.E., Volinsky, C.: Bayesian model averaging (with discussion). Stat. Sci. 14, 382–417 (1999)
23. Jones, H.E., Spiegelhalter, D.J.: Improved probabilistic prediction of healthcare performance indicators using bidirectional smoothing models. J. R. Stat. Soc. A 175, 729–747 (2012)
24. McCulloch, R.E.: Local model influence. J. Am. Stat. Assoc. 84, 473–478 (1989)
25. Plummer, M.: Penalized loss functions for Bayesian model comparison. Biostatistics 9, 523–539 (2008)
26. Ripley, B.D.: Statistical Pattern Recognition and Neural Networks. Cambridge University Press, Cambridge (1996)
27. Robert, C.P.: Intrinsic losses. Theory Decis. 40, 191–214 (1996)
28. Rubin, D.B.: Estimation in parallel randomized experiments. J. Educ. Stat. 6, 377–401 (1981)
29. Rubin, D.B.: Bayesianly justifiable and relevant frequency calculations for the applied statistician. Ann. Stat. 12, 1151–1172 (1984)
30. Schwarz, G.E.: Estimating the dimension of a model. Ann. Stat. 6, 461–464 (1978)
31. Shibata, R.: Statistical aspects of model selection. In: Willems, J.C. (ed.) From Data to Model, pp. 215–240. Springer, Berlin (1989)
32. Spiegelhalter, D.J., Best, N.G., Carlin, B.P., van der Linde, A.: Bayesian measures of model complexity and fit (with discussion). J. R. Stat. Soc. B (2002)
33. 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/
34. Stone, M.: An asymptotic equivalence of choice of model cross-validation and Akaike’s criterion. J. R. Stat. Soc. B 36, 44–47 (1977)
35. van der Linde, A.: DIC in variable selection. Stat. Neerl. 1, 45–56 (2005)
36. Vehtari, A., Lampinen, J.: Bayesian model assessment and comparison using cross-validation predictive densities. Neural Comput. 14, 2439–2468 (2002)
37. Vehtari, A., Ojanen, J.: A survey of Bayesian predictive methods for model assessment, selection and comparison. Stat. Surv. 6, 142–228 (2012)
38. Watanabe, S.: Algebraic Geometry and Statistical Learning Theory. Cambridge University Press, Cambridge (2009)
39. 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)
40. Watanabe, S.: A widely applicable Bayesian information criterion. J. Mach. Learn. Res. 14, 867–897 (2013)