Objective Bayesian analysis for exponential power regression models

Abstract

We develop objective Bayesian analysis for the linear regression model with random errors distributed according to the exponential power distribution. More specifically, we derive explicit expressions for three different Jeffreys priors for the model parameters. We show that only one of these Jeffreys priors leads to a proper posterior distribution. In addition, we develop fast posterior analysis based on Laplace approximations. Moreover, we show that our proposed Bayesian analysis compares favorably to a posterior analysis based on a competing noninformative prior. Finally, we illustrate our methodology with applications of the exponential power regression model to two different datasets.