Univ. Heidelberg
Statistics Group   Institute for Mathematics   Faculty of Mathematics and Computer Science   University Heidelberg
Ruprecht-Karls-Universität Heidelberg Institute for Mathematics Statistics of inverse problems Research Group
german english french


Publications
Cooperations
Research projects
Events
Teaching
Completed theses
People
Contact

Last edited on
Oct 17, 2024 by JJ.
Jan JOHANNES Oct 25,2019 Theses
Thesis:
Bachelor in Mathematics

Author:
Bérénice Robert

Title:
Posterior concentration rates for Aalen processes

Supervisors:
Sergio Brenner Miguel and Jan JOHANNES

Abstract:
In this thesis, we derive posterior contraction rates in the context of Aalen multiplicative intensity models. We will impose on a finite time interval sufficient conditions, which are similar to those proposed in the density estimation problem. We will look at two examples; in the first one, we will notice that a counting process in right-censoring models fulfills the Aalen multiplicative intensity model and in the second one, we will consider the Dirichlet process as a prior on the set of monotone nonincreasing densities using their representation as mixtures of uniform densities.

References:
S. Donnet, V. Rivoirard, J. Rousseau, and C. Scricciolo. Posterior concentration rates for empirical Bayes procedures with applications to Dirichlet process mixtures. Bernoulli, 24(1):231–256, 2018.
S. Donnet, V. Rivoirard, J. Rousseau, and C. Scricciolo. Posterior concentration rates for counting processes with Aalen multiplicative intensities. Bayesian Analysis, 12(1):53–87, 2017.