Bayesian prediction of a density function in terms of e -mixture

The optimum Bayesian predictor under the e -divergence loss is proposed and discussed. Notable dualistic structure is observed between the proposed predictor and the optimum predictor under the m -divergence loss, the latter of which is dominantly discussed in the existing literature. An advantage o...

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Bibliographic Details
Published in:Journal of statistical planning and inference 2009-09, Vol.139 (9), p.3064-3075
Main Authors: Yanagimoto, Takemi, Ohnishi, Toshio
Format: Article
Language:English
Subjects:
Conjugate prior
DIC
Dual structure
Exact sciences and technology
General topics
Inference from stochastic processes
time series analysis
Jeffreys’ prior
Linear inference, regression
Mathematics
Plug-in predictor
Probability and statistics
Probability theory and stochastic processes
Pythagorean relationship
Sciences and techniques of general use
Statistics
Stochastic processes
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Summary:The optimum Bayesian predictor under the e -divergence loss is proposed and discussed. Notable dualistic structure is observed between the proposed predictor and the optimum predictor under the m -divergence loss, the latter of which is dominantly discussed in the existing literature. An advantage of the proposed optimum predictor is that it is estimative, when the sampling density is in the exponential family. Potential advantages of the proposed predictor over its dual one are discussed, which include the shrinkage estimator and the Bayesian model selection criterion DIC (deviance information criterion). Further, we emphasize potential usefulness of the use of Jeffreys’ prior.
ISSN:0378-3758
1873-1171
DOI:10.1016/j.jspi.2009.02.005