Nonparametric Priors for Vectors of Survival Functions - Ilenia Epifani; Antonio Lijoi (Università degli Studi di Pavia, Dipartimento di Economia Politica e Metodi Quantitativi (EPMQ), 2009)
The paper proposes a new nonparametric prior for twodimensional vectors of survival functions (S1, S2). The definition we introduce is based on the notion of Levy copula and it will be used to model, in a nonparametric Bayesian framework, twosample 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 rightcensored data. As a byproduct of our analysis, we find out that the marginal distribution of a pair of observations from the two samples coincides with the MarshallOlkin or the Weibull distribution according to specific choices of the marginal Levy measures.
Keywords: 330; Bayesian nonparametrics; Completely random measures; Dependent stable processes; Levy copulas; Posterior distribution; Rightcensored data; Survival function