Hjort, Nils Lid Nonparametric Bayes estimators based on beta processes in models for life history data. (English) Zbl 0711.62033 Ann. Stat. 18, No. 3, 1259-1294 (1990). The problem of finding Bayes estimators for cumulative hazard rates and related quantities, w.r.t. prior distributions that correspond to cumulative hazard rate processes with positive, independent increments, is studied. A class of prior processes, termed beta processes, is introduced and shown to constitute a conjugate class. As an introduction, a nonparametric time-discrete model for survival data, which is of some independent interest, is studied. An advantage of modelling cumulative hazard rates instead of cumulative distribution functions is that extensions are possible, for instance to time-inhomogeneous Markov chains. Reviewer: G.Broström Cited in 5 ReviewsCited in 117 Documents MSC: 62G07 Density estimation 62C10 Bayesian problems; characterization of Bayes procedures 60G57 Random measures 62G05 Nonparametric estimation Keywords:life history data; time-inhomogeneous Markov chains; posterior distributions; semiparametric Bayesian analysis of the Cox regression model; vague prior; Nelson-Aalen estimator; Kaplan-Meier estimator; censoring; Lévy process; nonparametric Bayes; Bayes estimators; cumulative hazard rates; prior distributions; cumulative hazard rate processes; positive, independent increments; beta processes; conjugate class; time-discrete model for survival data PDF BibTeX XML Cite \textit{N. L. Hjort}, Ann. Stat. 18, No. 3, 1259--1294 (1990; Zbl 0711.62033) Full Text: DOI OpenURL