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Bayesian consistency for regression models under a supremum distance

by Fei Xiang and Stephen G. Walker

This paper studies the consistency of Bayesian nonparametric regression models. We concentrate on the use of the sup metric and dealing with non-stochastic, i.e. designed, covariate values. We illustrate our results on a normal mean regression function and demonstrate the usefulness of a model based on piecewise constant functions.

Keywords: Bayesian nonparametric; Consistency; Regression model; Hellinger neighborhood; Piecewise constant function.

Full text of the paper (pdf), which has recently appeared in the Journal of Statistical Planning and Inference. See http://dx.doi.org/10.1016/j.jspi.2012.09.002