Martingale posterior distributions for cumulative hazard functions
SCANDINAVIAN JOURNAL OF STATISTICS(2024)
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.
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Key words
beta process,bootstrap,uncertainty quantification
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