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0.4 Problems with krigingThe covariance functioncov(Y (x 1 ),Y (x 2 )|β) = C(x 1 ,x 2 ) is assumed to beknown exactly. But generally the covariance functionis just an estimate and therefore always is uncertain.Stein (1999): kriging predictor=empirical BLUP.Pilz et. al. (1997): kriging predictor=plug-in predictor.Consequence: Kriging plug-in predictor is non linear.Christensen (1991): Kriging TMSEP underestimatesthe true unknown TMSEP of the plug-in krigingpredictor.Spatial covariance-robust minimax prediction based on experimental design ideas – p.5
0.5 SolutionsMake use of the Bayesian paradigm and specify priordistributions over a space of covariance functions.How should one get prior knowledge about thecovariance function?What are noninformative priors for covariancefunctions?Make use of the minimax principle, specify a class ofplausible covariance functions and calculate apredictor in such a way that the maximum possibleTMSEP becomes a minimum (Spöck, 1997, 2005).Spatial covariance-robust minimax prediction based on experimental design ideas – p.6
Page 1 and 2: Spatial covariance-robust minimaxpr
Page 3 and 4: Bayesian linear kriging0.1 The mode
Page 5: 0.3 The quality of predictionThe To
Page 9 and 10: Covariance-robust minimax kriging2
Page 11 and 12: In the squared marginal bias{µ T (
Page 13 and 14: where Ξ is the set of all probabil
Page 15 and 16: The minimax theorem of Sion (1958)
Page 17 and 18: 4 The Equivalence of the MinimaxPro
Page 19 and 20: Multiplication of the matrix M b (
Page 21 and 22: Lemma 11.6 and 11.7 in Pilz (1991)
Page 23 and 24: 6 ExampleData set considered: 591 C
Page 25 and 26: This has been done by restricting a
Page 27 and 28: 15032.51002501.5100.50−50−0.5
Page 29 and 30: 1503100250100−50−1−100−2−
Page 31 and 32: Figure 6: The semivariograms of the
Page 33 and 34: It is visible from Fig. 6 that one

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