Bayesian bivariate survival estimation
Abstract
There is no easy extension of Kaplan-Meier and Nelson-Aalen estimators to the bivariate case, and estimating bivariate survival distributions nonparametrically is associated with various non-trivial problems. The Dabrowska estimator will for example associate negative mass to some subsets. Bayesian methods hold some promise as they will avoid the negative mass problem, butare also prone to difficulties. We simplify and extend an example by Pruitt to show that the posterior distribution from a Dirichlet process prior is inconsistent. We construct a different nonparametric prior via Beta processes and provide an updating scheme that utilizes only the most relevant parts of the likelihood, and show that this leads to a consistent estimator.
Cite
@article{arxiv.2604.11819,
title = {Bayesian bivariate survival estimation},
author = {J. K. Ghosh and Nils Lid Hjort and C. Messan and R. V. Ramamoorthi},
journal= {arXiv preprint arXiv:2604.11819},
year = {2026}
}
Comments
15 pages, 0 figures. This is a 2005 technical report, with some more material than in the published version (Journal of Statistical Planning and Inference, vol. 136, 2006, pages 2297-2308). NLH honours JK Ghosh (1937-2017) and RV Ramamoorthi (1950-2023) by this arXiv version, for better visibility and easier access