Statistica Sinica 17(2007), 427-444

BAYESIAN NONPARAMETRIC ESTIMATION OF

A BIVARIATE SURVIVAL FUNCTION

Paolo Bulla$^1$, Pietro Muliere$^1$ and Stephen Walker$^2$

$^1$Università Bocconi and $^2$University of Kent

Abstract: We use a bivariate reinforced process derived from a Generalized Pólya Urn scheme to provide an estimator for a bivariate survival function. The estimator may be considered as a Bayesian nonparametric predictive estimator and it can be obtained easily via an implementation of a Gibbs sampler. Consistency of the estimator is studied.

Key words and phrases: Bayesian nonparametric, beta-Stacy process, bivariate survival function, Pólya urn scheme.