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Martingale posterior distributions for cumulative hazard functions

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  • Stephen G. Walker

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.

Suggested Citation

  • Stephen G. Walker, 2024. "Martingale posterior distributions for cumulative hazard functions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 51(3), pages 936-955, September.
    • Handle: RePEc:bla:scjsta:v:51:y:2024:i:3:p:936-955
    DOI: 10.1111/sjos.12712
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