Kriging universal

To use what is termed universal kriging, it is assumed that Z(2 ) is an intrinsic random function of order k. But the problem of identifying the drift and the semi-variogram when they are both unknown is still present. However, Matheron (11) defined a family of functions called the generalized covariance, K(h). and the variance of the generalized increment of order k can be defined in terms of K(h ). That is. 

Simple kriging is actually a subset of universal kriging since the assumption that Z(2 ) is an intrinsic random function of order 0 is the same as the assumption that ZCjc) is intrinsic. Additionally, when l x) is intrinsic, the generalized covariance and the semi-variogram are related as follows ... 

Krige, D.G. M.Sc. Thesis, University of Witwatersrand, 1951a cited from [AKIN and SIEMES, 1988] Rrige, D.G. J. Chem. Metall. Min. Soc. S. Africa 52 (1951b) 119 cited from [AKIN and SIEMES,... 

S.N. Eophaven, H.B. Nielsen, J. Sondergaard, DACE - A MATLAB Kriging Toolbox. Teehnieal University of Denmark, Teehnieal Report IMM-TR2002-12, 2002. 

Sasena, M. J. 2002. Flexibility and Effieieney Enhaneements for Constrained Global Design Optimization with Kriging Approximations. Ph. D Thesis, University of Miehigan... 

Universal Kriging In universal kriging the mean is unknown but a function of X in the form of a linear superposition of a small number of basis functions, which are here assumed to be orthonormal. Thus f ip (x) ip (x)d x = Ski, and h(x) = J2k where the coefficients bk are to be determined... 

In general the mean will be unknown, and following the lead of universal kriging, it is assumed that the mean is given by h x) = where... 

The radial basis function system (19) is the adjoint of the universal kriging system (11) and (12). 

To prove the equivalence of radial basis functions and the universal kriging method, the universal kriging system will be now transformed into the radial basis function equations. Multiply (11) by A and sum over i to give... 

G. Matheron (1981) Splines and kriging their formal equivalence. Down-to-Earth Statistics Solutions Looking for Geological Problems, D.F. Merriam (ed.), Syracuse University Geology Contributions, 77-95. 

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