Bayesian nonparametric regression with varying residual density
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
Volume (Year): 66 (2014)
Issue (Month): 1 (February)
|Contact details of provider:|| Web page: http://www.springer.com|
Web page: http://www.ism.ac.jp/index_e.html
|Order Information:||Web: http://www.springer.com/statistics/journal/10463/PS2|
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Omiros Papaspiliopoulos & Gareth O. Roberts, 2008. "Retrospective Markov chain Monte Carlo methods for Dirichlet process hierarchical models," Biometrika, Biometrika Trust, vol. 95(1), pages 169-186.
- Ongaro, Andrea & Cattaneo, Carla, 2004. "Discrete random probability measures: a general framework for nonparametric Bayesian inference," Statistics & Probability Letters, Elsevier, vol. 67(1), pages 33-45, March.
- Deborah Burr & Hani Doss, 2005. "A Bayesian Semiparametric Model for Random-Effects Meta-Analysis," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 242-251, March.
- David Nott, 2006. "Semiparametric estimation of mean and variance functions for non-Gaussian data," Computational Statistics, Springer, vol. 21(3), pages 603-620, December.
- Pelenis, Justinas, 2012. "Bayesian Semiparametric Regression," Economics Series 285, Institute for Advanced Studies.
- David B. Dunson & Natesh Pillai & Ju-Hyun Park, 2007. "Bayesian density regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(2), pages 163-183.
- Norets, Andriy & Pelenis, Justinas, 2014.
"Posterior Consistency In Conditional Density Estimation By Covariate Dependent Mixtures,"
Cambridge University Press, vol. 30(03), pages 606-646, June.
- Norets, Andriy & Pelenis, Justinas, 2011. "Posterior Consistency in Conditional Density Estimation by Covariate Dependent Mixtures," Economics Series 282, Institute for Advanced Studies.
- Taeryon Choi, 2009. "Asymptotic properties of posterior distributions in nonparametric regression with non-Gaussian errors," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(4), pages 835-859, December.
- Choi, Taeryon & Schervish, Mark J., 2007. "On posterior consistency in nonparametric regression problems," Journal of Multivariate Analysis, Elsevier, vol. 98(10), pages 1969-1987, November.
- Kottas A. & Gelfand A.E., 2001. "Bayesian Semiparametric Median Regression Modeling," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1458-1468, December.
- Chung, Yeonseung & Dunson, David B., 2009. "Nonparametric Bayes Conditional Distribution Modeling With Variable Selection," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1646-1660.
- Chib, Siddhartha & Greenberg, Edward, 2010. "Additive cubic spline regression with Dirichlet process mixture errors," Journal of Econometrics, Elsevier, vol. 156(2), pages 322-336, June.
- Gramacy, Robert B & Lee, Herbert K. H, 2008. "Bayesian Treed Gaussian Process Models With an Application to Computer Modeling," Journal of the American Statistical Association, American Statistical Association, vol. 103(483), pages 1119-1130.
- Pati, Debdeep & Dunson, David B. & Tokdar, Surya T., 2013. "Posterior consistency in conditional distribution estimation," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 456-472.
- Griffin, J.E. & Steel, M.F.J., 2006. "Order-Based Dependent Dirichlet Processes," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 179-194, March.
- Thaís C. O. Fonseca & Marco A. R. Ferreira & Helio S. Migon, 2008. "Objective Bayesian analysis for the Student-t regression model," Biometrika, Biometrika Trust, vol. 95(2), pages 325-333.
- David B. Dunson & Ju-Hyun Park, 2008. "Kernel stick-breaking processes," Biometrika, Biometrika Trust, vol. 95(2), pages 307-323. Full references (including those not matched with items on IDEAS)
When requesting a correction, please mention this item's handle: RePEc:spr:aistmt:v:66:y:2014:i:1:p:1-31. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Sonal Shukla)or (Rebekah McClure)
If references are entirely missing, you can add them using this form.