Objective Bayesian Analysis for Heteroscedastic Regression
Helio S. Migon & Esther Salazar (UFRJ)
The normality assumption is very common in many statistical problems, but in some cases unatenable for natural phenomena due to the distribution of the data shows a leptokurtic or a platykurtic shape and is not robust to outliers. In order to accommodate this characteristic we propose the use of t-Student, which reduces the influence of outliers. Another choice is the exponential power (EP) distribution that can provide both heavier (leptokurtic) and lighter tails (platykurtic) than normal density.
Objective Bayesian analysis for linear heteroscedastic regression models is developed. We derive explicit expressions for Jeffreys priors for the model parameters and show that some of these priors lead to proper posterior distributions. Moreover, we show that our proposed Bayesian analysis compares favorably to frequentist analysis previously proposed in the literature. Finally, we illustrate our methodology with applications of the Student-t and exponential power regression models to different datasets.