On Properties of Predictive Priors in Linear Models |
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Authors: | Joseph G Ibrahim |
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Institution: | 1. Department of Biostatistics , Harvard School of Public Health , USA;2. Department of Biostatistics , Dana Farber Cancer Institute , Boston , MA , 02115 , USA |
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Abstract: | Utilizing the notion of matching predictives as in Berger and Pericchi, we show that for the conjugate family of prior distributions in the normal linear model, the symmetric Kullback-Leibler divergence between two particular predictive densities is minimized when the prior hyperparameters are taken to be those corresponding to the predictive priors proposed in Ibrahim and Laud and Laud and Ibrahim. The main application for this result is for Bayesian variable selection. |
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Keywords: | Kullback-Leibler divergence Matching predictives Predictive distribution Prior distribution Variable selection |
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