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On the Greatest Class of Conjugate Priors and Sensitivity of Multivariate Normal Posterior Distributions

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  • Bischoff, W.

Abstract

When samples are taken from a (multivariate) normal distribution then under suitable conditions we characterize the greatest class of priors such that the posterior distribution is also (multivariate) normal. In this case exact formulas are given showing how the mean and covariance matrix of the posterior normal distribution depend on the sample and on the a priori distribution; these formulas may be viewed as sensitivity of the posterior distribution to the prior and sample distribution.

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  • Bischoff, W., 1993. "On the Greatest Class of Conjugate Priors and Sensitivity of Multivariate Normal Posterior Distributions," Journal of Multivariate Analysis, Elsevier, vol. 44(1), pages 69-81, January.
    • Handle: RePEc:eee:jmvana:v:44:y:1993:i:1:p:69-81
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    Cited by:

    1. 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.
    2. Bischoff, Wolfgang, 1996. "Characterizing multivariate normal distributions by some of its conditionals," Statistics & Probability Letters, Elsevier, vol. 26(2), pages 105-111, February.

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