Distention for Sets of Probabilities

Dilation for Sets of Probabilities

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Updating Sets of Probabilities

There are several well-known justifications for conditioning as the appropriate method for updating a single probability measure, given an observation. However, there is a significant body of work arguing for sets of probability measures, rather than single mea­ sures, as a more realistic model of uncer­ tainty. Conditioning still makes sense in this context-we can simply condition each mea­ su...

Revision Rules for Convex Sets of Probabilities

Independence Concepts for Convex Sets of Probabilities

In this paper we study different concepts of independence for convex sets of probabilities. There will be two basic ideas for independ­ ence. The first is irrelevance. Two variables are independent when a change on the know­ ledge about one variable does not affect the other. The second one is factorization. Two variables are independent when the joint con­ vex set of probabilities can be decom...

Exponential Models: Approximations for Probabilities

Welch & Peers (1963) used a root-information prior to obtain posterior probabilities for a scalar parameter exponential model and showed that these Bayes probabilities had the confidence property to second order asymptotically. An important undercurrent of this indicates that the constant information reparameterization provides location model structure, for which the confidence property ...