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How regular are conjugate exponential families?

Author

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  • Müller-Funk, Ulrich
  • Pukelsheim, Friedrich

Abstract

Given an exponential family of sampling distributions of order k, one may construct in a natural way an exponential family of conjugate (that is, prior) distributions depending on a k-dimensional parameter c and an additional weight w> 0. We compute the bias term by which the expectation of the sampling mean-value parameter under the conjugate distribution deviates from the conjugate parameter c. This bias term vanishes for regular exponential families, providing an appealing interpretation of the conjugate parameter c as a 'prior location' of the sampling mean-value parameter. By way of example we explore the extension of this approach to moments of higher order, in order to interprete the conjugate weight w as a 'prior sample size'.

Suggested Citation

  • Müller-Funk, Ulrich & Pukelsheim, Friedrich, 1989. "How regular are conjugate exponential families?," Statistics & Probability Letters, Elsevier, vol. 7(4), pages 327-333, February.
    • Handle: RePEc:eee:stapro:v:7:y:1989:i:4:p:327-333
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