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MPI-INF/SWS Research Reports 1991-2017

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MPI-I-2003-2-002

A representation theorem and applications to measure selection and noninformative priors

Jaeger, Manfred

April 2003, 35 pages.

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Status: available - back from printing

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.

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URL to this document: http://domino.mpi-inf.mpg.de/internet/reports.nsf/NumberView/2003-2-002

Hide details for BibTeXBibTeX
@TECHREPORT{Jaeger2003,
  AUTHOR = {Jaeger, Manfred},
  TITLE = {A representation theorem and applications to measure selection and noninformative priors},
  TYPE = {Research Report},
  INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
  ADDRESS = {Stuhlsatzenhausweg 85, 66123 Saarbr{\"u}cken, Germany},
  NUMBER = {MPI-I-2003-2-002},
  MONTH = {April},
  YEAR = {2003},
  ISSN = {0946-011X},
}