Comparison of Linear Interpolators

• Kernel: simple, fast, stable; does not take sampling pattern into consideration; ad hoc. Can be made multivariate.
• Cokriging: Minimizes estimation variance: if used well, can out-perform kriging. It gives a trend surface, called the ``drift''. It may lead to large, ill-conditioned systems; hard to model variograms well; may be hard to choose additional variables. ``Zoo'' of models.
• Kriging: Minimizes estimation variance; more stable than cokriging, as it requires no cross-variogram modelling and uses smaller systems. It too gives a drift surface, and may lead to large, ill-conditioned systems; and it may be hard to find the ``best'' model.
• Radial Basis Functions: univariate, ad hoc versions of kriging. The only known generalization to multivariate case is cokriging.
• Black Box Routines: may give pretty pictures, but it is not clear that users understand that they may lose in optimality what they gain in ease-of-use.

Illustrations: cokriging, radial, kriging maps

• contours of cokriged nitrate and magnesium, 1977
• contours of cokriged nitrate and calcium, 1985
• kriged nitrate, 1985
• multiquadric nitrate, 1985
• contours of cokriged nitrate and magnesium, 1988