Semiparametric Bayesian measurement error modeling

This work introduces a Bayesian semi-parametric approach for dealing with regression models where the covariate is measured with error. The main advantage of this extended Bayesian approach is the possibility of considering generalizations of the elliptical family of models by using Dirichlet process priors in the dependent and independent situations. Conditional posterior distributions are implemented which allow using Markov Chain Monte Carlo (MCMC) for generating from the prior distributions. An interesting result shown is that the Dirichlet process prior is not updated in the case of the dependent elliptical model. Further, an analysis of a real data set is reported illustrating the usefulness of the approach.