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Mathematical Geosciences

, Volume 40, Issue 3, pp 327–347 | Cite as

Indicator Kriging without Order Relation Violations

  • Raimon Tolosana-Delgado
  • Vera Pawlowsky-Glahn
  • Juan-Jose Egozcue
Open Access
Article

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.

Keywords

Aitchison geometry Ilr coordinates Indicator variogram Logistic regression 

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Copyright information

© The Author(s) 2008

Authors and Affiliations

  • Raimon Tolosana-Delgado
    • 1
  • Vera Pawlowsky-Glahn
    • 2
  • Juan-Jose Egozcue
    • 3
  1. 1.Department of Sedimentology and Environmental GeologyUniversity of GöttingenGöttingenGermany
  2. 2.Department of Informatics and Applied MathematicsUniversity of GironaGironaSpain
  3. 3.Department of Applied Mathematics IIITechnical University of CataloniaBarcelonaSpain

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