Advanced Search
MyIDEAS: Login to save this article or follow this journal

Bayesian nonparametric regression with varying residual density

Contents:

Author Info

  • Debdeep Pati

    ()

  • David Dunson

    ()

Registered author(s):

    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

    Download Info

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
    File URL: http://hdl.handle.net/10.1007/s10463-013-0415-z
    Download Restriction: Access to full text is restricted to subscribers.

    As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

    Bibliographic Info

    Article provided by Springer in its journal Annals of the Institute of Statistical Mathematics.

    Volume (Year): 66 (2014)
    Issue (Month): 1 (February)
    Pages: 1-31

    as in new window
    Handle: RePEc:spr:aistmt:v:66:y:2014:i:1:p:1-31

    Contact details of provider:
    Web page: http://www.springerlink.com/link.asp?id=102845

    Order Information:
    Web: http://link.springer.de/orders.htm

    Related research

    Keywords: Data augmentation; Exact block Gibbs sampler; Gaussian process; Nonparametric regression; Outliers; Symmetrized probit stick-breaking process;

    References

    References listed on IDEAS
    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.:
    as in new window
    1. 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.
    2. Norets, Andriy & Pelenis, Justinas, 2014. "Posterior Consistency In Conditional Density Estimation By Covariate Dependent Mixtures," Econometric Theory, Cambridge University Press, vol. 30(03), pages 606-646, June.
    3. 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.
    4. David B. Dunson & Ju-Hyun Park, 2008. "Kernel stick-breaking processes," Biometrika, Biometrika Trust, vol. 95(2), pages 307-323.
    5. 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.
    6. ThaĆ­s 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.
    7. 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.
    8. 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.
    9. 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.
    10. Taeryon Choi, 2009. "Asymptotic properties of posterior distributions in nonparametric regression with non-Gaussian errors," Annals of the Institute of Statistical Mathematics, Springer, vol. 61(4), pages 835-859, December.
    11. 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.
    12. David Nott, 2006. "Semiparametric estimation of mean and variance functions for non-Gaussian data," Computational Statistics, Springer, vol. 21(3), pages 603-620, December.
    13. 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.
    14. Pelenis, Justinas, 2012. "Bayesian Semiparametric Regression," Economics Series 285, Institute for Advanced Studies.
    15. 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.
    16. 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.
    17. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Lists

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    Statistics

    Access and download statistics

    Corrections

    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: (Guenther Eichhorn) or (Christopher F Baum).

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.