NML, Bayes and true distributions: A comment on Karabatsos and Walker (2006)

Akaike, 1973, Information theory and an extension of the maximum likelihood principle, 267 Balasubramanian, 2005, MDL, Bayesian inference and the geometry of the space of probability distributions Berger, 1985 Bernardo, 1994 Browne, 2000, Cross-validation methods, Journal of Mathematical Psychology, 44, 108, 10.1006/jmps.1999.1279 Dawid, 1984, Present position and potential developments: Some personal views, statistical theory, the prequential approach, Journal of the Royal Statistical Society, Series A, 147, 278, 10.2307/2981683 Escobar, 1995, Bayesian density estimation and inference using mixtures, Journal of the American Statistical Association, 90, 577, 10.2307/2291069 Ferguson, 1973, A Bayesian analysis of some nonparametric problems, Annals of Statistics, 1, 209, 10.1214/aos/1176342360 Ghosh, 2003 Grünwald, 2007 Grünwald, 2007, Suboptimal behavior of Bayes and MDL in classification under misspecification, Machine Learning, 66, 119, 10.1007/s10994-007-0716-7 Karabatsos, 2006, On the normalized maximum likelihood and Bayesian decision theory, Journal of Mathematical Psychology, 50, 517, 10.1016/j.jmp.2006.07.005 Kadane, 1980, Bayesian decision theory and the simplification of models Mackay, 2003 Meehl, 1990, Why summaries of research on psychological theories are often uninterpretable, Psychological Reports, 66, 195, 10.2466/pr0.1990.66.1.195 Myung, 2006, Model selection by normalized maximum likelihood, Journal of Mathematical Psychology, 50, 167, 10.1016/j.jmp.2005.06.008 Petrone, 1997, A note on the Dirichlet process prior in Bayesian nonparametric inference with partial exchangeability, Statistics & Probability Letters, 36, 69, 10.1016/S0167-7152(97)00050-3 Rissanen, 2001, Strong optimality of the normalized ML models as universal codes and information in data, IEEE Transactions on Information Theory, 47, 1712, 10.1109/18.930912 Schwarz, 1978, Estimating the dimension of a model, The Annals of Statistics, 6, 461, 10.1214/aos/1176344136 Sethuraman, 1994, A constructive definition of Dirichlet priors, Statistica Sinica, 4, 639 Shtarkov, 1987, Universal sequential coding of single messages, Problems of Information Transmission, 23, 3 Van Erven, 2008, Catching up faster in Bayesian model selection and model averaging, Advances in Neural Information Processing Systems, 20 Vapnik, 1998 Yang, 1999, Model selection for nonparametric regression, Statistica Sinica, 9, 475