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Locally Adaptive Bayes Nonparametric Regression via Nested Gaussian Processes.

Publication ,  Journal Article
Zhu, B; Dunson, DB
Published in: Journal of the American Statistical Association
January 2013

We propose a nested Gaussian process (nGP) as a locally adaptive prior for Bayesian nonparametric regression. Specified through a set of stochastic differential equations (SDEs), the nGP imposes a Gaussian process prior for the function's mth-order derivative. The nesting comes in through including a local instantaneous mean function, which is drawn from another Gaussian process inducing adaptivity to locally-varying smoothness. We discuss the support of the nGP prior in terms of the closure of a reproducing kernel Hilbert space, and consider theoretical properties of the posterior. The posterior mean under the nGP prior is shown to be equivalent to the minimizer of a nested penalized sum-of-squares involving penalties for both the global and local roughness of the function. Using highly-efficient Markov chain Monte Carlo for posterior inference, the proposed method performs well in simulation studies compared to several alternatives, and is scalable to massive data, illustrated through a proteomics application.

Duke Scholars

Published In

Journal of the American Statistical Association

DOI

EISSN

1537-274X

ISSN

0162-1459

Publication Date

January 2013

Volume

108

Issue

504

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 3802 Econometrics
  • 1603 Demography
  • 1403 Econometrics
  • 0104 Statistics
 

Citation

APA
Chicago
ICMJE
MLA
NLM
Zhu, B., & Dunson, D. B. (2013). Locally Adaptive Bayes Nonparametric Regression via Nested Gaussian Processes. Journal of the American Statistical Association, 108(504). https://doi.org/10.1080/01621459.2013.838568
Zhu, Bin, and David B. Dunson. “Locally Adaptive Bayes Nonparametric Regression via Nested Gaussian Processes.Journal of the American Statistical Association 108, no. 504 (January 2013). https://doi.org/10.1080/01621459.2013.838568.
Zhu B, Dunson DB. Locally Adaptive Bayes Nonparametric Regression via Nested Gaussian Processes. Journal of the American Statistical Association. 2013 Jan;108(504).
Zhu, Bin, and David B. Dunson. “Locally Adaptive Bayes Nonparametric Regression via Nested Gaussian Processes.Journal of the American Statistical Association, vol. 108, no. 504, Jan. 2013. Epmc, doi:10.1080/01621459.2013.838568.
Zhu B, Dunson DB. Locally Adaptive Bayes Nonparametric Regression via Nested Gaussian Processes. Journal of the American Statistical Association. 2013 Jan;108(504).

Published In

Journal of the American Statistical Association

DOI

EISSN

1537-274X

ISSN

0162-1459

Publication Date

January 2013

Volume

108

Issue

504

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 3802 Econometrics
  • 1603 Demography
  • 1403 Econometrics
  • 0104 Statistics