Statistics and Data Science Seminar
Elizabeth Gross
UIC
Maximum Likelihood Degree for the Random Effects Mode
Abstract: Maximum likelihood estimation is a common problem explored in Algebraic Statistics, a field that focuses on the applications of algebraic geometry to the study of statistical models. In maximum likelihood estimation if the likelihood equations are algebraic, the maximum likelihood degree (ML degree) is a measure of the algebraic complexity of the estimation problem. It is the degree of the variety characterized by the system of likelihood equations, or, equivalently, the number of complex solutions of the system for generic data. The ML degree is specific to the statistical model and there are only two other classes of models for which an explicit formula for the ML degree is known. In this talk, we will look at the analysis of variance model with random effects and give an explicit formula for the ML degree. We also explore the number of feasible (real, positive) solutions computationally. This is joint work with Mathias Drton and Sonja Petrovic.
Wednesday November 10, 2010 at 3:00 PM in SEO 636