Open Access
2020 Approximation of Bayesian models for time-to-event data
Marta Catalano, Antonio Lijoi, Igor Prünster
Electron. J. Statist. 14(2): 3366-3395 (2020). DOI: 10.1214/20-EJS1746


Random measures are the key ingredient for effective nonparametric Bayesian modeling of time-to-event data. This paper focuses on priors for the hazard rate function, a popular choice being the kernel mixture with respect to a gamma random measure. Sampling schemes are usually based on approximations of the underlying random measure, both a priori and conditionally on the data. Our main goal is the quantification of approximation errors through the Wasserstein distance. Though easy to simulate, the Wasserstein distance is generally difficult to evaluate, making tractable and informative bounds essential. Here we accomplish this task on the wider class of completely random measures, yielding a measure of discrepancy between many noteworthy random measures, including the gamma, generalized gamma and beta families. By specializing these results to gamma kernel mixtures, we achieve upper and lower bounds for the Wasserstein distance between hazard rates, cumulative hazard rates and survival functions.


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Marta Catalano. Antonio Lijoi. Igor Prünster. "Approximation of Bayesian models for time-to-event data." Electron. J. Statist. 14 (2) 3366 - 3395, 2020.


Received: 1 February 2020; Published: 2020
First available in Project Euclid: 11 September 2020

zbMATH: 1448.62043
MathSciNet: MR4148234
Digital Object Identifier: 10.1214/20-EJS1746

Keywords: Bayesian nonparametrics , completely random measures , gamma random measure , kernel mixtures , posterior sampling , Survival analysis , Wasserstein distance

Vol.14 • No. 2 • 2020
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