Consistent fractional Bayes factor for nested normal linear models |
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| Institution: | 1. Quantitative Psychology and Individual Differences Research Group, KU Leuven – University of Leuven, Tiensestraat 102, Box 3713, 3000 Leuven, Belgium;2. Division of Clinical Psychology, Psychotherapy and Health Psychology, Department of Psychology, University of Salzburg, Salzburg, Austria;1. Department of Neuropsychiatry, Teikyo University School of Medicine, 2-11-1 Kaga, Itabashi, Tokyo 173-0003, Japan;2. Faculty of Human Sciences, Department of Psychology, University of Tsukuba, 1-1-1 Ten-nodai, Ibaraki, Tsukuba 305-8572, Japan;3. Department of Physical and Health Education, Graduate School of Education, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan;4. The University of Tokyo Secondary School attached to the Faculty of Education, 1-15-1 Minamidai, Nakano, Tokyo 164-0014, Japan;5. Department of Psychiatry and Behavioral Science, Tokyo Metropolitan Institute of Medical Science, 2-1-6 Kamikitazawa, Setagaya, Tokyo 156-8506, Japan;1. Neuroscience Center, University of Helsinki, Finland;2. Claudio Munari Epilepsy Surgery Centre, Niguarda Hospital, Italy |
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| Abstract: | In the Bayesian approach to parametric model comparison, the use of improper priors is problematic due to the indeterminacy of the resulting Bayes factor (BF). The need for developing automatic and robust methods for model comparison has led to the introduction of alternative BFs. Intrinsic Bayes factors (Berger and Pericchi, 1996a) and fractional Bayes factors (FBF) (O'Hagan, 1995) are two alternative strategies for default model selection. We show in this paper that the FBF can be inconsistent. To overcome this problem, we propose a generalization of the FBF approach that leads to the usual FBF or to some variants of it in some special cases. As an important problem, we consider and discuss this generalization for model selection in nested linear models. |
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