A representation theorem and applications to measure selection and 
noninformative priors

Jaeger, Manfred

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A representation theorem and applications to measure selection and noninformative priors

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Jaeger, Manfred
Programming Logics, MPI for Informatics, Max Planck Society;

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2003-2-002
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Jaeger, M.(2003). A representation theorem and applications to measure selection and noninformative priors (MPI-I-2003-2-002). Saarbrücken: Max-Planck-Institut für Informatik.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0014-6AFE-E

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.