You are cordially invited to the seminars organized by the Department of Mathematics.
Speaker: J. E. Paguyo (McMaster University)
“Asymptotic behavior of the hierarchical Pitman-Yor process”
Abstract: The Pitman-Yor process is a discrete random measure used as a fundamental prior distribution in Bayesian nonparametrics. The hierarchical Pitman-Yor process (HPYP) is a generalization obtained by randomizing the base distribution through a draw from another Pitman-Yor process. It is motivated by the study of groups of clustered data, where the group specific Pitman-Yor processes are linked through an intergroup Pitman-Yor process. A special case of the HPYP is the celebrated hierarchical Dirichlet process (HDP), first introduced by Teh et al.
In this talk, we will introduce the HPYP, survey its connection to the Bayesian nonparametric approach to species sampling problems, and discuss our recent work on the asymptotic behavior of the HPYP. First, we consider a random sample of size $N$ from a population whose species distribution is given by the vector of weights of the HPYP and discuss the large $N$ asymptotic behavior of the number of species in the sample. Second, we discuss limit theorems associated with the power sum symmetric polynomials for the vector of weights of the HDP, objects which are related to the homozygosity in population genetics, the Simpson diversity index in ecology, and the Herfindahl-Hirschman index in economics. This talk is based on joint work with Stefano Favaro and Shui Feng.
Date: January 8, Thursday
Time: 18:00 PM (Ankara)
Place: Zoom
To request the event link, please send a message to gokhan.yildirim@bilkent.edu.tr