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. A particular class of prior processes, termed beta processes, is introduced and is shown to constitute a conjugate class.
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Nils Lid Hjort and Stephen G. With quantile pyramids we instead fix probabilities and use random partitions. For nonparametric Bayesian inference we use a prior which supports piecewise linear quantile functions, based on the need to work with a finite set of partitions, yet we show that the limiting version of the prior exists.
We also discuss and investigate an alternative model based on the so-called substitute likelihood. Both approaches factorize in a convenient way leading to relatively straightforward analysis via MCMC, since analytic summaries of posterior distributions are too complicated. We give conditions securing the existence of an absolute continuous quantile process, and discuss consistency and approximate normality for the sequence of posterior distributions.
Illustrations are included. Source Ann. Zentralblatt MATH identifier Quantile pyramids for Bayesian nonparametrics.
More by Stephen G. Article information Source Ann. Export citation. Export Cancel. References Barron, A. The consistency of posterior distributions in nonparametric problems.
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