Bayesian nonparametric regression with varying residual density.

Published

Journal Article

We consider the problem of robust Bayesian inference on the mean regression function allowing the residual density to change flexibly with predictors. The proposed class of models is based on a Gaussian process prior for the mean regression function and mixtures of Gaussians for the collection of residual densities indexed by predictors. Initially considering the homoscedastic case, we propose priors for the residual density based on probit stick-breaking (PSB) scale mixtures and symmetrized PSB (sPSB) location-scale mixtures. Both priors restrict the residual density to be symmetric about zero, with the sPSB prior more flexible in allowing multimodal densities. We provide sufficient conditions to ensure strong posterior consistency in estimating the regression function under the sPSB prior, generalizing existing theory focused on parametric residual distributions. The PSB and sPSB priors are generalized to allow residual densities to change nonparametrically with predictors through incorporating Gaussian processes in the stick-breaking components. This leads to a robust Bayesian regression procedure that automatically down-weights outliers and influential observations in a locally-adaptive manner. Posterior computation relies on an efficient data augmentation exact block Gibbs sampler. The methods are illustrated using simulated and real data applications.

Full Text

Duke Authors

Cited Authors

  • Pati, D; Dunson, DB

Published Date

  • February 2014

Published In

Volume / Issue

  • 66 / 1

Start / End Page

  • 1 - 31

PubMed ID

  • 24465053

Pubmed Central ID

  • 24465053

Electronic International Standard Serial Number (EISSN)

  • 1572-9052

International Standard Serial Number (ISSN)

  • 0020-3157

Digital Object Identifier (DOI)

  • 10.1007/s10463-013-0415-z

Language

  • eng