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UID:20260427T033145EDT-5177zSjkOT@132.216.98.100
DTSTAMP:20260427T073145Z
DESCRIPTION:Title: Asymptotic behavior of the hierarchical Pitman-Yor proce
 ss.\n\nAbstract: The Pitman-Yor process is a discrete random measure speci
 fied by a concentration parameter\, discount parameter\, and base distribu
 tion\, and is used as a fundamental prior in Bayesian nonparametrics. The 
 hierarchical Pitman-Yor process (HPYP) is a generalization obtained by ran
 domizing the base measure 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. Setting both discount parameters to zero gives the hierarchical 
 Dirichlet process (HDP)\, first introduced by Teh et al. in the machine le
 arning literature.\n	\n	In this talk\, we discuss our recent work on the asy
 mptotic behavior of the HPYP and HDP. In the first part\, we establish lim
 it theorems associated with the power sum symmetric polynomials for the ve
 ctor of weights of the HDP as the concentration parameters tend to infinit
 y. These objects are related to the homozygosity in population genetics\, 
 the Simpson diversity index in ecology\, and the Herfindahl-Hirschman inde
 x in economics. In the second part\, we consider a random sample of size $
 N$ from a population whose type distribution is given by the vector of wei
 ghts of the HPYP and study the large $N$ asymptotic behavior of the number
  of clusters in the sample. This talk is based on joint work with Stefano 
 Favaro and Shui Feng.\n
DTSTART:20260319T153000Z
DTEND:20260319T163000Z
LOCATION:Room 920\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue 
 Sherbrooke Ouest
SUMMARY:J E Paguyo (McMaster University)
URL:/mathstat/channels/event/j-e-paguyo-mcmaster-unive
 rsity-371987
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