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 language | English |
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Journal | International Journal of Approximate Reasoning |
Volume | 38 |
Issue number | 3 |
Pages (from-to) | 217-243 |
ISSN | 0888-613X |
Publication status | Published - 2005 |