Conjugate Parameterizations for Natural Exponential Families
- 1 December 1995
- journal article
- theory and-method
- Published by Taylor & Francis in Journal of the American Statistical Association
- Vol. 90 (432) , 1347-1356
- https://doi.org/10.1080/01621459.1995.10476639
Abstract
Recently, Consonni and Veronese have shown that the form of the standard conjugate distribution for the mean parameter μ of a univariate natural exponential family F coincides with that of the distribution induced on μ by the standard conjugate distribution for the canonical parameter if and only if F has a quadratic variance function. In this article we present significant extensions of this result, identifying conditions under which transformations of the canonical or mean parameter preserve the form of the standard conjugate family. Generalizations to the multivariate case are also considered, and results relating Jeffreys's prior to the standard conjugate family are presented. The variance function is seen to play an important role throughout.Keywords
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