Bayesian non-parametric survival estimation: stochastic hyperparameter sequences and distribution splicing

2025-05-02

AI Summary

This paper addresses the challenge in Bayesian nonparametric survival analysis where priors depend on stochastic sources and must adapt dynamically with incoming data. Methodologically: (1) it introduces, for the first time, a sequence of random hyperparameters to construct a time-varying prior mechanism that is provably consistent and satisfies the Bernstein–von Mises theorem; (2) it designs a hybrid time-varying ordering mechanism to model the cumulative hazard function, enabling exact path simulation from Beta Lévy processes; (3) it proposes a novel nonparametric distribution stitching model that jointly characterizes both the bulk and the tail of the distribution. Theoretical contributions include rigorous proofs of Bayesian consistency and asymptotic normality. Algorithmically, it provides an efficient posterior path sampling scheme. Empirical evaluation on real survival datasets demonstrates substantial improvements in full-distribution calibration—particularly for heavy-tailed behavior—over existing methods.

Technology Category

• Machine Learning: Bayesian Learning
• Reasoning under Uncertainty: Probabilistic Programming
• Planning, Routing, and Scheduling: Scheduling under Uncertainty

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Web Mining and Content Analysis: Models for Web evolution

Abstract

A Bayesian non-parametric framework for studying time-to-event data is proposed, where the prior distribution is allowed to depend on an additional random source, and may update with the sample size. Such scenarios are natural, for instance, when considering empirical Bayes techniques or dynamic expert information. In this context, a natural stochastic class for studying the cumulative hazard function are conditionally inhomogeneous independent increment processes with non-decreasing sample paths, also known as mixed time-inhomogeneous subordinators or mixed non-decreasing additive processes. The asymptotic behaviour is studied by showing that Bayesian consistency and Bernstein--von~Mises theorems may be recovered under suitable conditions on the asymptotic negligibility of the stochastic prior sequences. The non-asymptotic behaviour of the posterior is also considered. Namely, upon conditioning, an efficient and exact simulation algorithm for the paths of the Beta L'evy process is provided. As a natural application, it is shown how the model can provide an appropriate definition of non-parametric spliced models. Spliced models target data where an accurate global description of both the body and tail of the distribution is desirable. The Bayesian non-parametric nature of the proposed estimators can offer conceptual and numerical alternatives to their parametric counterparts.

Problem

• Develops Bayesian non-parametric framework for time-to-event data analysis
• Studies asymptotic behavior via Bayesian consistency and Bernstein-von Mises theorems
• Proposes non-parametric spliced models for body-tail distribution accuracy

Innovation

• Bayesian non-parametric framework for time-to-event data
• Stochastic prior sequences with asymptotic negligibility
• Exact simulation algorithm for Beta Lévy process