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March, 1979 Conjugate Priors for Exponential Families
Persi Diaconis, Donald Ylvisaker
Ann. Statist. 7(2): 269-281 (March, 1979). DOI: 10.1214/aos/1176344611

Abstract

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

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Persi Diaconis. Donald Ylvisaker. "Conjugate Priors for Exponential Families." Ann. Statist. 7 (2) 269 - 281, March, 1979. https://doi.org/10.1214/aos/1176344611

Information

Published: March, 1979
First available in Project Euclid: 12 April 2007

zbMATH: 0405.62011
MathSciNet: MR520238
Digital Object Identifier: 10.1214/aos/1176344611

Subjects:
Primary: 62E10
Secondary: 62A15

Keywords: Admissibility , Bayesian analysis , characterization theorems , conjugate priors , credibility theory , exponential families , linearity of regression

Rights: Copyright © 1979 Institute of Mathematical Statistics

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Vol.7 • No. 2 • March, 1979
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