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Bayesian nonparametric regression with varying residual density.

Publication ,  Journal Article
Pati, D; Dunson, DB
Published in: Annals of the Institute of Statistical Mathematics
February 2014

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.

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Published In

Annals of the Institute of Statistical Mathematics

DOI

EISSN

1572-9052

ISSN

0020-3157

Publication Date

February 2014

Volume

66

Issue

1

Start / End Page

1 / 31

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 0104 Statistics
 

Citation

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Pati, D., & Dunson, D. B. (2014). Bayesian nonparametric regression with varying residual density. Annals of the Institute of Statistical Mathematics, 66(1), 1–31. https://doi.org/10.1007/s10463-013-0415-z
Pati, Debdeep, and David B. Dunson. “Bayesian nonparametric regression with varying residual density.Annals of the Institute of Statistical Mathematics 66, no. 1 (February 2014): 1–31. https://doi.org/10.1007/s10463-013-0415-z.
Pati D, Dunson DB. Bayesian nonparametric regression with varying residual density. Annals of the Institute of Statistical Mathematics. 2014 Feb;66(1):1–31.
Pati, Debdeep, and David B. Dunson. “Bayesian nonparametric regression with varying residual density.Annals of the Institute of Statistical Mathematics, vol. 66, no. 1, Feb. 2014, pp. 1–31. Epmc, doi:10.1007/s10463-013-0415-z.
Pati D, Dunson DB. Bayesian nonparametric regression with varying residual density. Annals of the Institute of Statistical Mathematics. 2014 Feb;66(1):1–31.
Journal cover image

Published In

Annals of the Institute of Statistical Mathematics

DOI

EISSN

1572-9052

ISSN

0020-3157

Publication Date

February 2014

Volume

66

Issue

1

Start / End Page

1 / 31

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 0104 Statistics