Robust Bayesian inference for the censored mixture of experts model using heavy-tailed distributions

Statistical analysis of censored data has received considerable interest across various fields, including biomedical, clinical and econometrical studies. The cause of censored measurement is usually induced by the limitation of measuring instruments and/or experimental design. In practice, regression modeling for censored data might encounter departure from normality of errors due primarily to the latent sources of heterogeneity, and/or the presence of atypical observations and outliers. A Bayesian analysis for the mixture of linear experts model is studied wherein the errors follow the scale mixture of normal distribution, and the responses suffer from either a left or right censoring schemes. We propose a weakly informative prior structure for the parameters and show that the corresponding posterior distributions are proper. Leveraging the Ultimate Pólya-Gamma data-augmentation method, we efficiently sample gating parameters and consequentially allocate cluster memberships. Compared to the traditional maximum likelihood method, our Bayesian approach is shown to mitigate the impact of censoring on deteriorating estimation and classification abilities. The effectiveness of our proposal is illustrated by undertaking some synthetic studies and a real data example. R scripts for the implementation of our Bayesian methods are available at the GitHub repository.