Bayesian predictive distribution for a Poisson model with a parametric restriction |
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Authors: | Yasuyuki Hamura Tatsuya Kubokawa |
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Institution: | Graduate School of Economics, Faculty of Economics, University of Tokyo, Bunkyo-ku, Tokyo, Japan |
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Abstract: | AbstractPredictive probability estimation for a Poisson distribution is addressed when the parameter space is restricted. The Bayesian predictive probability against the prior on the restricted space is compared with the non-restricted Bayes predictive probability. It is shown that the former predictive probability dominates the latter under some conditions when the predictive probabilities are evaluated by the risk function relative to the Kullback-Leibler divergence. This result is proved by first showing the corresponding dominance result for estimating the restricted parameter and then translating it into the framework of predictive probability estimation. |
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Keywords: | Bayes dominance estimation Kullback-Leibler divergence prediction restricted parameter space |
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