Multivariate Estimation Using Log Ratios: A Worked Alternative

Abstract

Common implementations of geostatistical methods, kriging and simulation, ignore the fact that geochemical data are usually reported in weight percent and are thus compositional data. Compositional geostatistics is an approach developed to ensure that the constant sum constraint is respected in estimation and simulation. The compositional geostatistical framework was implemented to test its applicability to an iron ore mine in Western Australia. Cross-validation was used to compare the results from ordinary cokriging of the additive log ratio variables with those from conventional ordinary cokriging. Two methods were used to back-transform the additive logratio estimates, the additive generalized logistic back transformation and Gauss-Hermite Quadrature approximation. Both the Aitchison distance and the Euclidean distance were used to quantify the error between the estimates and original sample values. The results follow the required constraints and produce better estimates when considering the Aitchison distance. When the Euclidean errors are considered the conventional ordinary cokriging estimates are less biased but the distribution of errors for the additive logratio estimates appear to be superior to the conventional ordinary cokriging estimates.