Orlando Marigliano: Classifying one-dimensional discrete statistical models with maximum likelihood degree one

Abstract

A discrete statistical model with maximum likelihood degree one is a kind of subvariety of the n-simplex of discrete probability distributions which is of special interest in algebraic statistics. This talk is about the problem of classifying these models in finite terms in the one-dimensional case. I describe an approach that gives such a finite description for n = 2,3,4 and makes progress toward solving the problem for greater n. I also introduce the combinatorial game of 'splitting chips on a grid' which crucially facilitates this strategy. This talk is based on joint work with Arthur Bik.