Bayesian nonparametric regression with varying residual density
Debdeep Pati (debdeep@stat.fsu.edu) and
David Dunson (dunson@stat.duke.edu)
Annals of the Institute of Statistical Mathematics, 2014, vol. 66, issue 1, 31 pages
Abstract:
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 (GP) 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 mixtures. We provide sufficient conditions to ensure strong posterior consistency in estimating the regression function, generalizing existing theory focused on parametric residual distributions. The homoscedastic priors are generalized to allow residual densities to change nonparametrically with predictors through incorporating GP 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. The methods are illustrated using simulated and real data applications. Copyright The Institute of Statistical Mathematics, Tokyo 2014
Keywords: Data augmentation; Exact block Gibbs sampler; Gaussian process; Nonparametric regression; Outliers; Symmetrized probit stick-breaking process (search for similar items in EconPapers)
Date: 2014
References: Add references at CitEc
Citations: View citations in EconPapers (1)
Downloads: (external link)
http://hdl.handle.net/10.1007/s10463-013-0415-z (text/html)
Access to full text is restricted to subscribers.
Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text
Persistent link: https://EconPapers.repec.org/RePEc:spr:aistmt:v:66:y:2014:i:1:p:1-31
Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10463/PS2
DOI: 10.1007/s10463-013-0415-z
Access Statistics for this article
Annals of the Institute of Statistical Mathematics is currently edited by Tomoyuki Higuchi
More articles in Annals of the Institute of Statistical Mathematics from Springer, The Institute of Statistical Mathematics
Bibliographic data for series maintained by Sonal Shukla (sonal.shukla@springer.com) and Springer Nature Abstracting and Indexing (indexing@springernature.com).