Some comments on misspecification of priors in Bayesian modelling of measurement error problems

In this paper we discuss some aspects of misspecification of prior distributions in the context of Bayesian modelling of measurement error problems. A Bayesian approach to the treatment of common measurement error situations encountered in epidemiology has been recently proposed. Its implementation involves, first, the structural specification, through conditional independence relationships, of three submodels-a measurement model, an exposure model and a disease model- and secondly, the choice of functional forms for the distributions involved in the submodels. We present some results indicating how the estimation of the regression parameters of interest, which is carried out using Gibbs sampling, can be influenced by a misspecification of the parametric shape of the prior distribution of exposure.