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Statistica Sinica 20 (2010), 1455-1484



Ilenia Epifani$^1$ and Antonio Lijoi$^{2,3}$

$^1$Politecnico di Milano, $^2$Università di Pavia and $^3$Collegio Carlo Alberto, Italy

Abstract: The paper proposes a new nonparametric prior for two-dimensional vectors of survival functions $(S_1,S_2)$. The definition is based on the Lévy copula and it is used to model, in a nonparametric Bayesian framework, two-sample survival data. Such an application yields 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 $(S_1,S_2)$, conditionally on possibly right-censored data. As a by-product, we find 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 Lévy measures.

Key words and phrases: Bayesian nonparametrics, completely random measures, dependent stable processes, Lévy copulas, posterior distribution, right-censored data, survival function.

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