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Extensions of the conjugate prior through the Kullback-Leibler separators

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  • Yanagimoto, Takemi
  • Ohnishi, Toshio

Abstract

The conjugate prior for the exponential family, referred to also as the natural conjugate prior, is represented in terms of the Kullback-Leibler separator. This representation permits us to extend the conjugate prior to that for a general family of sampling distributions. Further, by replacing the Kullback-Leibler separator with its dual form, we define another form of a prior, which will be called the mean conjugate prior. Various results on duality between the two conjugate priors are shown. Implications of this approach include richer families of prior distributions induced by a sampling distribution and the empirical Bayes estimation of a high-dimensional mean parameter.

Suggested Citation

  • Yanagimoto, Takemi & Ohnishi, Toshio, 2005. "Extensions of the conjugate prior through the Kullback-Leibler separators," Journal of Multivariate Analysis, Elsevier, vol. 92(1), pages 116-133, January.
    • Handle: RePEc:eee:jmvana:v:92:y:2005:i:1:p:116-133
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    References listed on IDEAS

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    5. Betrò, B. & Rotondi, R., 1991. "On Bayesian inference for the Inverse Gaussian distribution," Statistics & Probability Letters, Elsevier, vol. 11(3), pages 219-224, March.
    6. Takemi Yanagimoto, 1994. "The Kullback-Leibler risk of the Stein estimator and the conditional MLE," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(1), pages 29-41, March.
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