Probability Seminar Essen
Winterterm 2024-25
| Jan 14 |
Roman Gambelin (University of Duisburg-Essen) Abstract: Pitman-Yor processes are a class of random probability measures on an arbitrary Polish space, which are notably used as prior distributions in nonparametric Bayesian statistics. Their laws are indexed by three parameters: a discount parameter in [0,1), a positive strength parameter, and a (deterministic) probability measure on the Polish space, which serves as the mean measure of the process. As the strength increases, the distribution of the standardized version of the integral of a square integrable function by the process was shown to be asymptotically normal. In this talk, we will give a presumably optimal bound on the convergence rate toward a Gaussian distribution in the Wasserstein 1-distance. The proof relies on a simple application of Stein's method, combined with a Mecke-type formula for Pitman-Yor processes. |