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Conjugate Priors for Exponential Families

Persi Diaconis and Donald Ylvisaker
The Annals of Statistics
Vol. 7, No. 2 (Mar., 1979), pp. 269-281
Stable URL: http://www.jstor.org/stable/2958808
Page Count: 13
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Conjugate Priors for Exponential Families
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Abstract

Let X be a random vector distributed according to an exponential family with natural parameter θ ∈ Θ. We characterize conjugate prior measures on Θ through the property of linear posterior expectation of the mean parameter of X : E{E(X|θ)|X = x} = ax + b. We also delineate which hyperparameters permit such conjugate priors to be proper.

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