Bayesian analysis of linear regression models with autoregressive symmetrical errors and incomplete data

Abstract

Observations collected over time are often auto correlated rather than independent, and sometimes include incomplete information, e.g. censored values reported as less or more than a level of detection and/or missing values. Another complication arises when the data departs significantly from normality, such as asymmetry and fat tails. In this paper, we propose Bayesian analysis of linear regression models with autoregressive symmetrical errors. The model considers the symmetric class of scale mixture of normal distributions, which include the normal, slash, contaminated normal and Student-t distributions as special cases. A Markov-chain Monte Carlo (MCMC) algorithm is tailored to obtain Bayesian posterior distributions of the unknown quantities of interest. The likelihood function is utilized to compute some Bayesian model selection measures. We evaluate the proposed model under different settings of censored and/or missing levels using simulated data. Finally, we illustrate the usage of our proposal through the analysis of a real dataset.