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Last edited on
Oct 18, 2021 by JJ
.
Thesis:
Master in Mathematics

Author:
Florian Schimmel

Title:
Nonparametric Priors in Bayesian Statistics and their clustering

Supervisors:
Moritz von Rohrscheidt and Jan JOHANNES

Abstract:
In this thesis we present in detail fundamental properties of nonparametric Bayesian priors, namely, the widely used Dirichlet process and its extension, the Pitman-Yor process. Besides others, the Dirichlet process possesses desirable clustering properties of the data which causes its application in many areas, for example, language modeling and species sampling. A generalization, enhancing even more the clustering properties, leads naturally to the Pitman-Yor process which characterization is more sophisticated. We analyze theoretically and practically the clustering behavior for both priors con- cluding in a significant advantage of the Pitman-Yor process in comparison to the Dirichlet process. More precisely, we show an theoretical improvement in adjustability of cluster number growth which we illustrate by a practical application.

Talk (.pdf):
Masterseminar Statistics of inverse problems, Ruprecht-Karls-Universität Heidelberg, 05.04.2017