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

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
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