The Annals of Statistics

Conjugate Priors for Exponential Families

Persi Diaconis and Donald Ylvisaker

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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.

Article information

Source
Ann. Statist., Volume 7, Number 2 (1979), 269-281.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176344611

Digital Object Identifier
doi:10.1214/aos/1176344611

Mathematical Reviews number (MathSciNet)
MR520238

Zentralblatt MATH identifier
0405.62011

JSTOR
links.jstor.org

Subjects
Primary: 62E10: Characterization and structure theory
Secondary: 62A15

Keywords
Conjugate priors linearity of regression Bayesian analysis characterization theorems exponential families credibility theory admissibility

Citation

Diaconis, Persi; Ylvisaker, Donald. Conjugate Priors for Exponential Families. Ann. Statist. 7 (1979), no. 2, 269--281. doi:10.1214/aos/1176344611. https://projecteuclid.org/euclid.aos/1176344611


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