Modeling Complex Life Systems: Bayesian Inference for Weibull Failure Times Using Adaptive MCMC

TL;DR

This paper introduces an adaptive Bayesian MCMC method using NUTS in STAN for Weibull failure time analysis, effectively handling complex life system data and providing practical lifetime predictions.

Contribution

It develops a novel hierarchical Bayesian framework with an adaptive semi-parametric MCMC algorithm for Weibull failure times, addressing prior selection challenges and improving modeling flexibility.

Findings

The method accurately models increasing and decreasing hazard rates.

Simulation studies identify optimal priors for regularization.

Application to prostate cancer data demonstrates practical utility.

Abstract

This research develops a Bayesian framework for analyzing failure times using the Weibull distribution, addressing challenges in prior selection due to the lack of conjugate priors and multi-dimensional sufficient statistics. We propose an adaptive semi-parametric MCMC algorithm for lifetime data analysis, employing a hierarchical Bayesian model and the No-U-Turn Sampler (NUTS) in STAN. Twenty-four combinations of prior distributions are evaluated, with a noninformative LogNormal hyper-prior ensuring flexibility. A simulation study of seventy-two datasets with varying structures compares MCMC and classical methods, identifying optimal priors for Bayesian regularization. The approach effectively handles the Increasing Hazard Rate (IHR) and Decreasing Hazard Rate (DHR) scenarios. Finally, we demonstrate the algorithm's utility by predicting the remaining lifetime of prostate cancer patients, showcasing its practical application. This work advances Bayesian methodologies for modeling complex life systems and testing processes.