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Indicator Kriging without Order Relation Violations

Tolosana-Delgado, Raimon
Pawlowsky-Glahn, Vera
Egozcue, Juan-Jose
Journal: Mathematical Geosciences, Mathematical Geosciences, 2008
40, 3: 327 - 347
DOI: https://doi.org/10.1007/s11004-008-9146-8
Persistent URL: http://resolver.sub.uni-goettingen.de/purl?gldocs-11858/7102
Tolosana-Delgado, Raimon; Pawlowsky-Glahn, Vera; Egozcue, Juan-Jose, 2008: Indicator Kriging without Order Relation Violations. In: Tolosana-Delgado, Raimon; Pawlowsky-Glahn, Vera; Egozcue, Juan-Jose (2008): Indicator Kriging without Order Relation Violations - Mathematical Geosciences; Vol. 40, Nr. 3, p. 327-347. Springer-Verlag, DOI: 10.1007/s11004-008-9146-8.
 
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  • Abstract
Indicator kriging (IK) is a spatial interpolation technique aimed at estimating the conditional cumulative distribution function (ccdf) of a variable at an unsampled location. Obtained results form a discrete approximation to this ccdf, and its corresponding discrete probability density function (cpdf) should be a vector, where each component gives the probability of an occurrence of a class. Therefore, this vector must have positive components summing up to one, like in a composition in the simplex. This suggests a simplicial approach to IK, based on the algebraic-geometric structure of this sample space: simplicial IK actually works with log-odds. Interpolated log-odds can afterwards be easily re-expressed as the desired cpdf or ccdf. An alternative but equivalent approach may also be based on log-likelihoods. Both versions of the method avoid by construction all conventional IK standard drawbacks: estimates are always within the (0,1) interval and present no order-relation problems (either with kriging or co-kriging). Even the modeling of indicator structural functions is clarified.
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