Bayesian Estimation for α-Mixture Survival Models

Heterogeneity in survival data poses substantial challenges for identifying appropriate mixture structures. The α-mixture family provides a flexible class of survival models that generalizes standard mixture formulations through a continuous weighting parameter, allowing it to balance failure rates and distributional shapes. Despite its theoretical appeal, the Bayesian inference for α-mixture survival models has received limited attention. In this paper, we develop a Bayesian framework for inference for α-mixture survival models, with a particular emphasis on estimation and structural identification. The posterior inference is conducted using Markov chain Monte Carlo methods, and simulation studies demonstrate accurate recovery of model parameters across a range of heterogeneous survival settings. The posterior distribution of the mixing parameter α offers a principled mechanism for model selection by identifying the mixture structure most consistent with the observed data. Applications to real-world datasets illustrate the interpretability and practical utility of the proposed approach in survival analysis.