Conjugate Priors for Exponential Families

  • Diaconis P
  • Ylvisaker D
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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.

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  • Persi Diaconis

  • Donald Ylvisaker

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