Mathematical Geology

, Volume 25, Issue 2, pp 219–240 | Cite as

Multivariable spatial prediction

  • Jay M. Ver Hoef
  • Noel Cressie
Articles

Abstract

For spatial prediction, it has been usual to predict one variable at a time, with the predictor using data from the same type of variable (kriging) or using additional data from auxiliary variables (cokriging). Optimal predictors can be expressed in terms of covariance functions or variograms. In earth science applications, it is often desirable to predict the joint spatial abundance of variables. A review of cokriging shows that a new cross-variogram allows optimal prediction without any symmetry condition on the covariance function. A bivariate model shows that cokriging with previously used cross-variograms can result in inferior prediction. The simultaneous spatial prediction of several variables, based on the new cross-variogram, is then developed. Multivariable spatial prediction yields the mean-squared prediction error matrix, and so allows the construction of multivariate prediction regions. Relationships between cross-variograms, between single-variable and multivariable spatial prediction, and between generalized least squares estimation and spatial prediction are also given.

Key words

geostatistics kriging cokriging cross-variogram best linear unbiased prediction generalized least squares 

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Copyright information

© International Association for Mathematical Geology 1993

Authors and Affiliations

  • Jay M. Ver Hoef
    • 1
  • Noel Cressie
    • 1
  1. 1.Iowa State UniversityAmes

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