Coherent Predictive Inference under Exchangeability with Imprecise Probabilities
(Extended Abstract)
Abstract
Coherent reasoning under uncertainty can be represented in a very general manner by coherent sets
of desirable gambles. This leads to a more general
foundation for coherent (imprecise-)probabilistic inference that allows for indecision. In this framework, and for a given finite category set, coherent
predictive inference under exchangeability can be
represented using Bernstein coherent cones of multivariate polynomials on the simplex generated by
this category set. We define an inference system as
a map that associates a Bernstein coherent cone of
polynomials with every finite category set. Inference
principles can then be represented mathematically
as restrictions on such maps, which allows us to develop a notion of conservative inference under such
inference principles. We discuss, as particular examples, representation insensitivity and specificity, and
show that there is an infinity of inference systems
that satisfy these two principles