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A representation theorem and applications to measure selection and noninformative priors

MPS-Authors
http://pubman.mpdl.mpg.de/cone/persons/resource/persons44689

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

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2003-2-002
(Any fulltext), 10KB

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Citation

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: http://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.