Indicator Kriging without Order Relation Violations |
| |
Authors: | Raimon Tolosana-Delgado Vera Pawlowsky-Glahn Juan-Jose Egozcue |
| |
Affiliation: | 1.Department of Sedimentology and Environmental Geology,University of G?ttingen,G?ttingen,Germany;2.Department of Informatics and Applied Mathematics,University of Girona,Girona,Spain;3.Department of Applied Mathematics III,Technical University of Catalonia,Barcelona,Spain |
| |
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 |
本文献已被 SpringerLink 等数据库收录! |
|