%0 Journal article
%A Tolosana-Delgado, Raimon
%A Pawlowsky-Glahn, Vera
%A Egozcue, Juan-Jose
%T Indicator Kriging without Order Relation Violations
%R 10.1007/s11004-008-9146-8
%R 10.23689/fidgeo-2789
%J Mathematical Geosciences
%J Mathematical Geosciences
%V 40
%N 3
%I Springer-Verlag
%X 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.
%U http://resolver.sub.uni-goettingen.de/purl?gldocs-11858/7102
%~ FID GEO-LEO e-docs