Nonparametric Priors for Vectors of Survival Functions

Ilenia Epifani and Antonio Lijoi ()
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Ilenia Epifani: Politecnico di Milano
Antonio Lijoi: Department of Economics and Quantitative Methods, University of Pavia, and Collegio Carlo Alberto

No 98, Quaderni di Dipartimento from University of Pavia, Department of Economics and Quantitative Methods

Abstract: The paper proposes a new nonparametric prior for two–dimensional vectors of survival functions (S1, S2). The definition we introduce is based on the notion of L´evy copula and it will be used to model, in a nonparametric Bayesian framework, two–sample survival data. Such an application will yield a natural extension of the more familiar neutral to the right process of Doksum (1974) adopted for drawing inferences on single survival functions. We, then, obtain a description of the posterior distribution of (S1, S2), conditionally on possibly right–censored data. As a by–product of our analysis, we find out that the marginal distribution of a pair of observations from the two samples coincides with the Marshall–Olkin or the Weibull distribution according to specific choices of the marginal L´evy measures.

Keywords: Bayesian nonparametrics; Completely random measures; Dependent stable processes; L´evy copulas; Posterior distribution; Right–censored data; Survival function (search for similar items in EconPapers)
Pages: 31 pages
Date: 2009-05
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