Urn models for Markov exchangeability (Q795405)

A probability on finite strings of letters is said to be Markov exchangeable if it assigns the same probability to strings which have the same initial letter and the same transition counts. \textit{P. Diaconis} and \textit{D. Freedman} [De Finetti's generalizations of exchangeability. R. Jeffrey (ed.): Studies in Inductive Logic and Probability. Vol. II, 233- 249 (1980)] considered the problem of expressing the extreme points of the set of Markov exchangeable probability measures. They gave an urn model for a two letter alphabet and posed the general solution as an unsolved problem. A solution to the general alphabet was given by the author [An approximation theorem for finite Markov exchangeability. Ph. D. Thesis, Stanford University (1981)] in terms of urn models. Presently the author is giving a simpler proof by using a well known identification between strings of letters and paths on a graph. The original solution can then be seen as a restatement of the BEST theorem of graph theory.