Bayesian smoothing for measurement error problems

In the presence of covariate measurement error, estimating a regression function nonparametrically is extremely difficult, the problem being related to deconvolution. In this paper we describe Bayesian approaches to modeling a flexible regression function when the predictor variable is measured with error. The regression function is modeled with smoothing splines.. We provide simulations with several nonlinear regression functions. Our simulations indicate that the frequentist mean squared error properties of the fully Bayesian method axe better than those of previously proposed frequentist methods, at least in the examples we have studied.