Bayesian model inference: Exploring parsimonious models with MCMC and optimization approximations
Devashish Devashish, Shazia Farhin, Mohammad Parvej, Athar Ali khan · Communication in Statistics- Theory and Methods · 2025
The rapid advancement in processing power and software accessibility has led to the widespread adoption of Bayesian modeling for comparing various distribution types. Parsimonious models, characterized by fewer parameters, are favored to mitigate the risk of overfitting. In this study, we apply Bayesian inference techniques to fit three parsimonious lifetime models to censored survival data. Leveraging the probabilistic programming language Stan, we employ Hamiltonian Monte Carlo sampling and its extensions based on the Markov chain Monte Carlo (MCMC) algorithm to sample from analytically complex posterior distributions. The study includes both numerical and graphical illustrations. Additionally, the full Bayesian information criteria are utilized to compare these models. Subsequently, Bayesian optimization is conducted for the best-performing model. Furthermore, a visual comparison of the density plot derived from optimization, utilizing the sampling importance resampling technique and MCMC sampling, is performed.