Shortcomings of multiple indicator kriging for assessing local distributions

Abstract

This paper examines several drawbacks and limitations of indicator kriging applied to continuous variables, in the scope of the lognormal random function model. In particular, it focuses on precision problems, inconsistencies of the results when one sample is added or removed, and biases generated by the post-processing steps (tail extrapolation and change of support) and by the use of a non-bias condition in the kriging system. The selectivity of the local distributions is shown to be systematically overestimated when performing a change of support based on the global variance reduction factor, and underestimated when using an ordinary kriging instead of a simple kriging. This situation may lead to strong biases in the evaluation of the resources and reserves in ore deposits. To solve the change-of-support problem, a local variance reduction factor is given for the lognormal case; the proposed approach may be generalised to other models so as to improve the estimates.