Bayes Analysis of Weibull Regression Model with Variable Selection: A Study Using Shrinkage Prior

Abstract

This article considers the Bayes analysis of the Weibull regression model when a number of covariates are involved in the model. Considering appropriate prior distributions for the model parameters and independent Laplace priors for the regression coefficients, the Bayes analysis is performed using the Gibbs sampler algorithm. Both empirical Bayes and hierarchical Bayes approaches are used to deal with the shrinkage parameter involved in the Laplace prior. Since the final objective is variable selection, the article uses Bayesian least absolute selection and shrinkage operator for the same. A comparison of the full model with the reduced model is done using a few important Bayesian tools. Finally, the numerical illustration is provided using both simulated and a real data set of comprehensive Micro-Ribonucleic acid profiling of nasopharyngeal carcinoma specimens. It may be noted that such an analysis might be useful in a variety of fields, including medical research, reliability analysis and several other experiments involving time to event data. © 2025 Taylor & Francis Group, LLC.