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Colloquium - 14 Sept 2000

Department of Statistics
Texas A&M University

ABSTRACT: In view of the renowned de Finetti's representation theorem, exchangeability plays a crucial role in the reconstruction of the Bayes-Laplace approach to induction and statistics. Besides immediately providing a justification for the classical case of conditionally independent and identically distributed random variables, de Finetti suggested that exchangeability - and partial exchangeability - could also be used to characterize s tatistical models with a more complex conditional dependence structure. Following his hint, we study the possibility of characterizing mixtures of distributions of discrete Markov chains in terms of partial exchangeability of successor states.

We prove that discrete chains are recurrent and Markov exchangeable if and only if they generate partially exchangeable successor states. This permits to give a new proof of a well-known characterization result - due to Diaconis and Freedman - for mixtures of distributions of Markov chains.

Attention is also given to the problem of characterizing mixtures of distributions of Markov chains with arbitrary state space. This is done by introducing the concept of split successor state.

Refreshments will be served in the Blocker Building, Room 447, at 3:30 p.m.

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