Electronic Journal of Statistics

Exchangeable Markov survival processes and weak continuity of predictive distributions

Walter Dempsey and Peter McCullagh

Full-text: Open access

Abstract

We study exchangeable, Markov survival processes – stochastic processes giving rise to infinitely exchangeable non-negative sequences $(T_{1},T_{2},\ldots)$. We show how these are determined by their characteristic index $\{\zeta_{n}\}_{n=1}^{\infty}$. We identify the harmonic process as the family of exchangeable, Markov survival processes that compose the natural set of statistical models for time-to-event data. In particular, this two-dimensional family comprises the set of exchangeable, Markov survival processes with weakly continuous predictive distributions. The harmonic process is easy to generate sequentially, and a simple expression exists for both the joint probability distribution and multivariate survivor function. We show a close connection with the Kaplan-Meier estimator of the survival distribution. Embedded within the process is an infinitely exchangeable ordered partition. Aspects of the process, such as the distribution of the number of blocks, are investigated.

Article information

Source
Electron. J. Statist., Volume 11, Number 2 (2017), 5406-5451.

Dates
Received: April 2017
First available in Project Euclid: 28 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1514430423

Digital Object Identifier
doi:10.1214/17-EJS1381

Mathematical Reviews number (MathSciNet)
MR3743735

Zentralblatt MATH identifier
06825051

Keywords
infinite exchangeability survival analysis characteristic index Bayesian nonparametrics Gibbs-type splitting rules

Rights
Creative Commons Attribution 4.0 International License.

Citation

Dempsey, Walter; McCullagh, Peter. Exchangeable Markov survival processes and weak continuity of predictive distributions. Electron. J. Statist. 11 (2017), no. 2, 5406--5451. doi:10.1214/17-EJS1381. https://projecteuclid.org/euclid.ejs/1514430423


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