Robust Bayesian Nonparametric Regression

Abstract

We discuss a Bayesian approach to nonparametric regression which is robust against outliers and discontinuities in the underlying function. Our approach uses Markov chain Monte Carlo methods to perform a Bayesian analysis of conditionally Gaussian state space models. In these models, the observation and state transition errors are assumed to be mixtures of normals, so the model is Gaussian conditionally on the mixture indicator variables. We present several examples of conditionally Gaussian state space models, and, for each example, we discuss several possible Markov chain Monte Carlo sampling schemes. We show empirically that our approach (i) provides a good estimate of the smooth part of the regression curve; (ii) discriminates between real and spurious jumps; and (iii) allows for outliers in the observation errors. We also show empirically that our sampling schemes converge rapidly to the posterior distribution.