Posterior concentration rates for counting processes with Aalen multiplicative intensities

TL;DR

This paper establishes general conditions for posterior concentration rates in Aalen counting processes, adapting density estimation techniques to this setting and applying them to specific prior models like Dirichlet process mixtures and log-splines.

Contribution

It introduces a framework for deriving posterior concentration rates for Aalen counting processes, bridging methods from density estimation.

Findings

Conditions resemble those in density estimation literature

Applicable to Dirichlet process mixtures of uniform densities

Effective for estimating monotone non-increasing intensities

Abstract

We provide general conditions to derive posterior concentration rates for Aalen counting processes. The conditions are designed to resemble those proposed in the literature for the problem of density estimation, for instance in Ghosal et al. (2000), so that existing results on density estimation can be adapted to the present setting. We apply the general theorem to some prior models including Dirichlet process mixtures of uniform densities to estimate monotone non-increasing intensities and log-splines.