The reproducing kernel Hilbert space structure of the sample paths of a Gaussian process

  title={The reproducing kernel Hilbert space structure of the sample paths of a Gaussian process},
  author={Michael F. Driscoll},
  journal={Zeitschrift f{\"u}r Wahrscheinlichkeitstheorie und Verwandte Gebiete},
  • M. Driscoll
  • Published 1 December 1973
  • Mathematics
  • Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete

Small Sample Spaces for Gaussian Processes

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The signal-noise problem — a solution for the case that signal and noise are Gaussian and independent

  • M. Driscoll
  • Mathematics
    Journal of Applied Probability
  • 1975
A solution is obtained for the signal-noise problem X = M + Z in which M and Z are independent Gaussian processes. Conditions on the processes are given which insure that the best estimate under

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A bridge between Bayesian learning based on Gaussian process and frequentist kernel methods with reproducing kernel Hilbert space is established and it is found that when the sampling scheme is quasi-uniform, the optimal convergence rate can be attained even if the smoothness of the imposed correlation function exceeds that of the true correlation function.



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