Conjugate Priors for Exponential Families
Diaconis, Persi ; Ylvisaker, Donald
Ann. Statist., Tome 7 (1979) no. 1, p. 269-281 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
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.
Publié le : 1979-03-14
Classification:  Conjugate priors,  linearity of regression,  Bayesian analysis,  characterization theorems,  exponential families,  credibility theory,  admissibility,  62E10,  62A15 
@article{1176344611,
     author = {Diaconis, Persi and Ylvisaker, Donald},
     title = {Conjugate Priors for Exponential Families},
     journal = {Ann. Statist.},
     volume = {7},
     number = {1},
     year = {1979},
     pages = { 269-281},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176344611}
}

Diaconis, Persi; Ylvisaker, Donald. Conjugate Priors for Exponential Families. Ann. Statist., Tome 7 (1979) no. 1, pp.  269-281. http://gdmltest.u-ga.fr/item/1176344611/