Martingale posterior distributions for cumulative hazard functions

Abstract

This paper is about the modeling of cumulative hazard functions using martingale posterior distributions. The focus is on uncertainty quantification from a nonparametric perspective. The foundational Bayesian model in this case is the beta process and the classic estimator is the Nelson–Aalen. We use a sequence of estimators which form a martingale in order to obtain a random cumulative hazard function from the martingale posterior. The connection with the beta process is established and a number of illustrations is presented.