Bayesian bootstrap prediction |
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Authors: | Tadayoshi Fushiki |
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Institution: | aThe Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, Minato-ku, Tokyo 106-8569, Japan |
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Abstract: | In this paper, bootstrap prediction is adapted to resolve some problems in small sample datasets. The bootstrap predictive distribution is obtained by applying Breiman's bagging to the plug-in distribution with the maximum likelihood estimator. The effectiveness of bootstrap prediction has previously been shown, but some problems may arise when bootstrap prediction is constructed in small sample datasets. In this paper, Bayesian bootstrap is used to resolve the problems. The effectiveness of Bayesian bootstrap prediction is confirmed by some examples. These days, analysis of small sample data is quite important in various fields. In this paper, some datasets are analyzed in such a situation. For real datasets, it is shown that plug-in prediction and bootstrap prediction provide very poor prediction when the sample size is close to the dimension of parameter while Bayesian bootstrap prediction provides stable prediction. |
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Keywords: | Bagging Bayesian bootstrap Bootstrap Kullback– Leibler divergence Probabilistic prediction |
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