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A Predictive Approach to Bayesian Nonparametric Survival Analysis

Fong, Edwin; Lehmann, Brieuc; (2022) A Predictive Approach to Bayesian Nonparametric Survival Analysis. In: Camps-Valls, G and Ruiz, FJR and Valera, I, (eds.) Proceedings of The 25th International Conference on Artificial Intelligence and Statistics. (pp. pp. 6990-7013). PMLR 151 Green open access

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Abstract

Bayesian nonparametric methods are a popular choice for analysing survival data due to their ability to flexibly model the distribution of survival times. These methods typically employ a nonparametric prior on the survival function that is conjugate with respect to right-censored data. Eliciting these priors, particularly in the presence of covariates, can be challenging and inference typically relies on computationally intensive Markov chain Monte Carlo schemes. In this paper, we build on recent work that recasts Bayesian inference as assigning a predictive distribution on the unseen values of a population conditional on the observed samples, thus avoiding the need to specify a complex prior. We describe a copula-based predictive update which admits a scalable sequential importance sampling algorithm to perform inference that properly accounts for right-censoring. We provide theoretical justification through an extension of Doob’s consistency theorem and illustrate the method on a number of simulated and real data sets, including an example with covariates. Our approach enables analysts to perform Bayesian nonparametric inference through only the specification of a predictive distribution.

Type: Proceedings paper
Title: A Predictive Approach to Bayesian Nonparametric Survival Analysis
Event: International Conference on Artificial Intelligence and Statistics
Location: ELECTR NETWORK
Dates: 28 Mar 2022 - 30 Mar 2022
Open access status: An open access version is available from UCL Discovery
Publisher version: https://proceedings.mlr.press/v151/fong22a.html
Language: English
Additional information: This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Keywords: Science & Technology, Technology, Physical Sciences, Computer Science, Artificial Intelligence, Statistics & Probability, Computer Science, Mathematics, MODEL
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science
URI: https://discovery.ucl.ac.uk/id/eprint/10159019
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