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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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    References listed on IDEAS

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    1. Lancelot F. James & Antonio Lijoi & Igor Prünster, 2009. "Posterior Analysis for Normalized Random Measures with Independent Increments," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(1), pages 76-97, March.
    2. Stephen G. Walker & Paul Damien & PuruShottam W. Laud & Adrian F. M. Smith, 1999. "Bayesian Nonparametric Inference for Random Distributions and Related Functions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 485-527.
    3. Ghosal,Subhashis & van der Vaart,Aad, 2017. "Fundamentals of Nonparametric Bayesian Inference," Cambridge Books, Cambridge University Press, number 9780521878265, November.
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