20. Spatial Prediction or Kriging

  1. Steven K. Thompson

Published Online: 10 FEB 2012

DOI: 10.1002/9781118162934.ch20

Sampling, Third Edition

Sampling, Third Edition

How to Cite

Thompson, S. K. (2012) Spatial Prediction or Kriging, in Sampling, Third Edition, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9781118162934.ch20

Author Information

  1. Simon Fraser University, Canada

Publication History

  1. Published Online: 10 FEB 2012
  2. Published Print: 23 FEB 2012

Book Series:

  1. Wiley Series in Probability and Statistics

Book Series Editors:

  1. Walter A. Shewhart and
  2. Samuel S. Wilks

ISBN Information

Print ISBN: 9780470402313

Online ISBN: 9781118162934

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Keywords:

  • kriging;
  • prediction equations;
  • spatial covariance function;
  • spatial prediction;
  • variogram

Summary

The spatial prediction problem and its solution—termed kriging in geostatistics—are essentially the same as the model-based prediction approach to survey sampling with auxiliary information. The prediction equations can be written equivalently either with covariances or with variances of differences. In this chapter the covariance form is used first to emphasize the connection to the regression methods of survey sampling. The approaches are exactly equivalent provided that the covariance function-or the variogram-is known. In ecological and geological surveys, the values of the variable of interest at different sites are typically not independent of each other. Rather, the values at sites in close proximity tend to be related to each other. In the geological sciences, spatial variation has traditionally been summarized using the variogram in place of the covariance function. The linear prediction equations are derived using Lagrange’s method for finding the minimum of a function subject to a set of constraints.

Controlled Vocabulary Terms

covariance