University of Wisconsin - Madison - Department of Statistics & Biostatistics
We discuss modeling probability measures constrained to a convex set. We represent measures in such sets as mixtures of simple, known extreme measures, and so the problem of estimating a constrained measure becomes one of estimating an unconstrained mixing measure. Such convex constraints arise in many modeling situations, such as empirical likelihood and modeling under stochastic ordering constraints. We describe mixture representation techniques for these two situations, and present a data analysis of an experiment in cancer genetics, where we assume a partial stochastic ordering but the data are incomplete.