Bayesian calibration under a student-t model

Abstract

In this paper we consider linear calibration problems in regressions models with independent errors distributed according to the Student-t distribution. The approach followed is Bayesian, thus, involving the need for the specification of prior distributions for the model parameters. It is shown that the problem is equivalent to considering an heteroscedastic regression model with an appropriate prior distributions on the model variances. By considering this alternative construction for the Student-t calibration model it is possible to use the Gibbs sampler to estimate the marginal posterior distributions. Simulation studies are reported which illustrate the performance of the approach proposed. An application to a data set analyzed by Smith and Corbett (1987) on measuring marathon courses is considered by using the approach developed in the paper.