Exchangeable Belief Structures
Michael Goldstein · Journal of the American Statistical Association · 1986
The static features of beliefs, namely those structures that relate to one's beliefs at a particular moment, are described. It is argued that expectation (or prevision) should be the fundamental quantification of individual statements of uncertainty and that inner product spaces (or belief structures) should be the fundamental organizing structure for collections of such statements. Objections are given to the usual Bayesian justification of relative frequency-based statistical models via exchangeability. I offer an alternative approach, via exchangeable and co-exchangeable belief structures, and derive the representation theorem, and thus the implied statistical models, for these structures.