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Journal of Mathematical Sciences

, Volume 203, Issue 6, pp 789–798 | Cite as

Properties of the Bayesian Parameter Estimation of a Regression Based on Gaussian Processes

  • A. A. Zaytsev
  • E. V. Burnaev
  • V. G. Spokoiny
Article

Abstract

We consider the regression approach based on Gaussian processes and outline our theoretical results about the properties of the posterior distribution of the corresponding covariance function’s parameter vector. We perform statistical experiments confirming that the obtained theoretical propositions are valid for a wide class of covariance functions commonly used in applied problems.

Keywords

Posterior Distribution Covariance Function Gaussian Process Kernel Density Estimate Hellinger Distance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • A. A. Zaytsev
    • 1
    • 2
  • E. V. Burnaev
    • 3
  • V. G. Spokoiny
    • 3
    • 4
    • 5
  1. 1.DatadvanceMoscowRussia
  2. 2.Institute for Information Transmission ProblemsRussian Academy of SciencesMoscowRussia
  3. 3.Premolab, Moscow Institute of Physics and TechnologyMoscowRussia
  4. 4.Weierstrass Institute (WIAS)BerlinGermany
  5. 5.Humboldt University of BerlinBerlinGermany

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