The Intrinsic Bayes Factor for Model Selection and Prediction
Journal article by James O. Berger, Luis R. Pericchi; Journal of the American Statistical Association, Vol. 91, 1996
Journal Article Excerpt
| The Intrinsic Bayes Factor for Model Selection and Prediction. by James O. Berger , Luis R. Pericchi I. INTRODUCTION 1.1 Is Another Model Selection Criterion Needed? We obviously think so, but why? First, we feel that model selection should have a Bayesian basis. This is based not so much on generic Bayesian arguments as on a belief that Bayesian methods of model selection and hypothesis testing are particularly needed for the following reasons: a. Measures based on frequentist computations, such as P values (in, say, chi-squared testing of fit), are at best difficult to interpret and at worst highly misleading (Berger and Delampady 1987; Berger and Sellke 1987; Delampady and Berger 1990; Edwards, Lindman, and Savage 1963). b. Analysis of nonnested and/or multiple models or hypotheses is very difficult in a frequentist framework. c. Non-Bayesian methods have difficulty incorporating "Occam's razor," the notion that if two models explain data equally well, then the simpler model is to be preferred; Bayes factors do this automatically (Jefferys and Berger 1992, Spiegelhalter and Smith 1982 and the references therein), whereas other methods require introduction of ad hoc penalties for model complexity. d. Prediction is often the real goal and, in accounting for model uncertainty in prediction, Bayesian methods are natural in that they can keep all models under consideration, weighted by their Posterior probabilities (see Draper 1995 for a review and earlier references, and also Sec. 5 herein). Among the many fine discussions of these issues are those provided by Edwards et al. (1963), Jeffreys (1961), and Kass and Raftery (1995). A second basic premise of our motivation is that one needs automatic methods of model sel... |
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