Date/Time
Date(s) - 17/09/2024
3:30 pm - 4:30 pm

Location: MDCL 3020

Speaker: JE Paguyo (Britton Postdoctoral Fellow, McMaster University)

Title: Homozygosity of the hierarchical Dirichlet process

Abstract: The Dirichlet process is a discrete random measure specified by a concentration parameter and a base distribution, and is used as a prior distribution in Bayesian nonparametrics. The hierarchical Dirichlet process generalizes the Dirichlet process by randomizing the base distribution through a draw from another Dirichlet process. It is motivated by the study of groups of clustered data, where the group specific Dirichlet processes are linked through an intergroup Dirichlet process. In this talk, we give a brief introduction to the hierarchical Dirichlet process and survey some previous results. We then discuss our recent work on the asymptotic behavior of the power sum symmetric polynomials for the vector of weights of the hierarchical Dirichlet process, as the corresponding concentration parameters tend to infinity. These objects are related to the homozygosity in population genetics, the Simpson diversity index in ecology, and the Herfindahl-Hirschman index in economics.

Based on joint work with Shui Feng.