A Representation Theorem and Applications to Measure Selection and Noninformative Priors

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Abstract

We introduce a set of transformations on the set of all probability distributions over a finite state space, and show that these transformations are the only ones that preserve certain elementary probabilistic relationships. This result provides a new perspective on a variety of probabilistic inference problems in which invariance considerations play a role. Two particular applications we consider in this paper are the development of an equivariance-based approach to the problem of measure selection, and a new justification for Haldane's prior as the distribution that encodes prior ignorance about the parameter of a multinomial distribution.
Original languageEnglish
JournalInternational Journal of Approximate Reasoning
Volume38
Issue number3
Pages (from-to)217-243
ISSN0888-613X
Publication statusPublished - 2005

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