Nonparametric Bayes estimators based on beta processes in models for life history data. (English) Zbl 0711.62033

Hjort, Nils Lid

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

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