Loading...
No-U-Turn Sampler Bayesian inference for Weibull failure time modeling under small-sample conditions
Dial, Alexander Yildirim, Ayse Angkyiire, David
Dial, Alexander
Yildirim, Ayse
Angkyiire, David
Citations
Altmetric:
Files
Other Names
Location
Time Period
Advisors
Original Date
Digitization Date
Issue Date
2026-04-24
Type
Abstract
Genre
Keywords
Subjects (LCSH)
Citation
Dial, Alexander; Yildirim, Ayse; Angkyiire, David; Dao, Mai. 2026. No-U-Turn Sampler Bayesian inference for Weibull failure time modeling under small-sample conditions. -- In Proceedings: 25th Annual Undergraduate Research and Creative Activity Forum. Wichita, KS: Wichita State University.
Abstract
The Weibull distribution is one of the most widely used models in reliability engineering analysis because of its flexibility in handling increasing, decreasing, and constant hazard behaviors. However, the estimation of the scale (α) and shape (β) parameters of the Weilbull distribution can be difficult in applications with small samples, thus making the classical method of maximum likelihood estimation (MLE) process unstable or inefficient. Likewise, the Bayesian inference procedure for such parameters also presents challenges in non-conjugate prior settings. In this study, we will use the No-U-Turn Sampler (NUTS), an adaptive Bayesian inference framework, for Weibull failure-time modeling to improve the stability and accuracy of the predictive performance in such settings. We will examine three prior families for α (Gamma, LogNormal, and Exponential) and three prior families for β (Gamma, HalfNormal, and LogNormal) to assess the effects of both light- and heavy-tailed regularization strategies. Our Bayesian posterior estimates are compared with classical MLEs using weighted relative efficiency (WRE) using both simulated data and a real-data application in prostate cancer. The numerical results show that the adaptive prior selection and sampling method greatly improve stability of parameter estimation, reduce estimation variability, and yield more efficient estimation, providing a proof-of-concept for Bayesian alternatives in reliability and survival analysis.
Table of Contents
Description
Presented to the 25th Undergraduate Research and Creative Activity Forum (URCAF) held in Woolsey Hall, Wichita State University, April 24, 2026.
Publisher
Wichita State University
Journal
Book Title
Series
URCAF;v.25