MULTISCALE BAYESIAN SURVIVAL ANALYSIS

Ismaël Castillo, Stéphanie van der Pas

Research output: Contribution to journalArticleAcademicpeer-review

2 Citations (Scopus)

Abstract

We consider Bayesian nonparametric inference in the right-censoring survival model, where modeling is made at the level of the hazard rate. We derive posterior limiting distributions for linear functionals of the hazard, and then for ‘many’ functionals simultaneously in appropriate multiscale spaces. As an application, we derive Bernstein–von Mises theorems for the cumulative hazard and survival functions, which lead to asymptotically efficient confidence bands for these quantities. Further, we show optimal posterior contraction rates for the hazard in terms of the supremum norm. In medical studies, a popular approach is to model hazards a priori as random histograms with possibly dependent heights. This and more general classes of arbitrarily smooth prior distributions are considered as applications of our theory. A sampler is provided for possibly dependent histogram posteriors. Its finite sample properties are investigated on both simulated and real data experiments.
Original languageEnglish
Pages (from-to)3559-3582
Number of pages24
JournalANNALS OF STATISTICS
Volume49
Issue number6
DOIs
Publication statusPublished - 1 Dec 2021

Keywords

  • Frequentist analysis of Bayesian procedures
  • Nonparametric Bernstein–von Mises theorem
  • Supremum norm contraction rate
  • Survival analysis

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