Analyzing Partially Exchangeable Data
by
Xin Dang
University of Mississippi
Coauthors: Hanxiang Peng, Latonya Garner

In this talk, I will present a procedure to analyze partially exchangeable data which also can be viewed as realizations of mixtures of Markov chains. Rectangular complete monotonicity (RCM) will be introduced to characterize partial exchangeability. A distribution of partially exchangeable binary random variables is derived, which generalizes the binomial distribution of exchangeable binary random variables. A rich class of parsimonious parametric mixtures of Markov chains resulted from RCM functions will be provided. The class is shown to be closed under convex linear combination, product, and two types of composite. A forward model selection method is presented about how a possible best model can be obtained. The procedure is mathematically simple and computationally easy. Application on two real data sets from dairy science and a bladder cancer study demonstrates superior results.

Date received: January 23, 2008