Skip to main content

Equivalence of Gaussian Measures and Prediction

  • Chapter
  • 2680 Accesses

Part of the Springer Series in Statistics book series (SSS)

Abstract

The basic message of the results of 3.8 is that for interpolating a mean 0 weakly stationary random field based on observations on an infinite square lattice, the smaller the distance between neighboring observations in the lattice, the less the low frequency behavior of the spectrum matters. This suggests that if our goal is to interpolate our observations and we need to estimate the spectral density from these same observations, we should focus on getting the high frequency behavior of the spectral density as accurately as possible while not worrying so much about the low frequency behavior. Supposing that our observations and predictions will all take place in some bounded region R, a useful first question to ask is what can be done if we observe the process everywhere in R. Answering this question will put an upper bound on what one can hope to learn from some finite number of observations in R.

Keywords

  • Spectral Density
  • Random Field
  • Gaussian Process
  • Linear Prediction
  • Gaussian Measure

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.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-1-4612-1494-6_4
  • Chapter length: 35 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   119.00
Price excludes VAT (USA)
  • ISBN: 978-1-4612-1494-6
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   159.99
Price excludes VAT (USA)
Hardcover Book
USD   159.99
Price excludes VAT (USA)

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and Permissions

Copyright information

© 1999 Springer Science+Business Media New York

About this chapter

Cite this chapter

Stein, M.L. (1999). Equivalence of Gaussian Measures and Prediction. In: Interpolation of Spatial Data. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1494-6_4

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-1494-6_4

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7166-6

  • Online ISBN: 978-1-4612-1494-6

  • eBook Packages: Springer Book Archive