Nonlinear Algebra and Statistics (NLASTATS) Seminar by Felix Almendra Hernandez - Algebraic Methods in Statistics: an Exploration of Markov bases
Speaker: Felix Almendra Hernandez, University of California Davis
Title: Algebraic Methods in Statistics: an Exploration of Markov Bases
Abstract: The concept of Markov basis was first introduced by Diaconis and Sturmfels as a means of using algebraic methods to perform exact tests on discrete exponential families. While certain statistical models possess compact Markov bases, such as decomposable models as illustrated by Dobra, non-decomposable models present significant challenges, as exemplified by De Loera and Onn. This talk presents our contributions to the understanding of the good and bad behavior of Markov basis, with a focus on two specific models. In the first part, we provide a simple Markov basis for the beta Stochastic Block Model. In the second part, we explore the limitations of non-negative relaxation on table entries in the no-three-way interaction model. These findings are the result of collaborative work with Prof. Jesus De Loera and Prof. Sonja Petrović.
Nonlinear Algebra and Statistics seminar