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September, 1990 Nonparametric Bayes Estimators Based on Beta Processes in Models for Life History Data
Nils Lid Hjort
Ann. Statist. 18(3): 1259-1294 (September, 1990). DOI: 10.1214/aos/1176347749


Several authors have constructed nonparametric Bayes estimators for a cumulative distribution function based on (possibly right-censored) data. The prior distributions have, for example, been Dirichlet processes or, more generally, processes neutral to the right. The present article studies the related 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 nonnegative independent increments. A particular class of prior processes, termed beta processes, is introduced and is shown to constitute a conjugate class. To arrive at these, a nonparametric time-discrete framework for survival data, which has some independent interest, is studied first. An important bonus of the approach based on cumulative hazards is that more complicated models for life history data than the simple life table situation can be treated, for example, time-inhomogeneous Markov chains. We find posterior distributions and derive Bayes estimators in such models and also present a semiparametric Bayesian analysis of the Cox regression model. The Bayes estimators are easy to interpret and easy to compute. In the limiting case of a vague prior the Bayes solution for a cumulative hazard is the Nelson-Aalen estimator and the Bayes solution for a survival probability is the Kaplan-Meier estimator.


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Nils Lid Hjort. "Nonparametric Bayes Estimators Based on Beta Processes in Models for Life History Data." Ann. Statist. 18 (3) 1259 - 1294, September, 1990.


Published: September, 1990
First available in Project Euclid: 12 April 2007

zbMATH: 0711.62033
MathSciNet: MR1062708
Digital Object Identifier: 10.1214/aos/1176347749

Primary: 62C10
Secondary: 60G57

Keywords: Beta processes , Censoring , Cox regression , cumulative hazard , Levy process , nonparametric Bayes , time-discrete , time-inhomogeneous

Rights: Copyright © 1990 Institute of Mathematical Statistics


Vol.18 • No. 3 • September, 1990
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