A note on the inevitability of maximum entropy
International Journal of Approximate Reasoning
Theoretical foundations for non-monotonic reasoning in expert systems
Logics and models of concurrent systems
The uncertain reasoner's companion: a mathematical perspective
The uncertain reasoner's companion: a mathematical perspective
Constraints as data: a new perspective on inferring probabilities
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
Minimum cross-entropy reasoning: a statistical justification
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 2
Axiomatic derivation of the principle of maximum entropy and the principle of minimum cross-entropy
IEEE Transactions on Information Theory
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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.