SCAIM Seminar: Jim Burke (Washingtion)

In the maximum likelihood mixture density estimation problem one is given a parametric family of densities and a data set. The question is then to find the regular Borel probability measure over the family's parameter space that yields the maximum likelihood mixture density for the given data set. Mixture density estimation problems arise in a number of statistical applications. We briefly describe two such applications: nonparametric maximum likelihood density estimation and model based clustering. The duality theory for these problems as well as techniques for reducing them to equivalent finite dimensional problems will be described. Finally, we use a Bender's decomposition along with interior point methodology to describe an algorithm for computing the maximum likelihood mixture density estimates. The results of some numerical experiments will be presented.