graduate computational algebraic geometry seminar
Sonja Petrovic
UIC
Existence of maximum likelihood estimators for Bradley-Terry models of pairwise comparisons
Abstract: Given a data point and a statistical model, the maximum likelihood estimators (MLE) are the values of the model parameters that "best describe the data" -
that is, they make the given data most likely to have been observed. If parameter values where this is achieved lie on the boundary of the model polytope,
only certain linear combinations of the parameters are estimable, and we say that the MLE does not exist.?
In this talk I will describe polyhedral conditions for the existence of the MLEs for three classes of models: a directed random graph model, the
Bradley-Terry model for paired comparisons, and graphs with fixed degree sequence. I will explain how these three models are related, and show how the
polytope of the corresponding toric varieties is used to determine the existence of the MLEs.?
This is joint work with Alessandro Rinaldo (Carnegie-Mellon University), and, in part, with Stephen E. Fienberg (Carnegie-Mellon University).
Thursday April 7, 2011 at 10:00 AM in SEO 1227