## The Annals of Statistics

### Conjugate Priors for Exponential Families

#### 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