- 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
| Statistics Group | Institute for Mathematics | Faculty of Mathematics and Computer Science | University Heidelberg |