Let X be a random vector distributed according to an exponential family with natural parameter 0 E O.We characterize conjugate prior measures on O through the property of linear posterior expectation of the mean parameter of X : E(E(XI0)IX = x) = ax + b. We also delineate which hyperparameters permit such conjugate priors to be proper.
CITATION STYLE
Diaconis, P., & Ylvisaker, D. (2007). Conjugate Priors for Exponential Families. The Annals of Statistics, 7(2). https://doi.org/10.1214/aos/1176344611
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