Multiple-Indicator Kriging of Gaussian and Non-Gaussian Data

Abstract

Multiple-indicator kriging (MIK) manages outlier values through the indicator transform, it generates the distribution of uncertainty non-parametrically through direct estimation of the indicator-probability thresholds, and it readily incorporates secondary, categorical data into the estimate. These features make it attractive for use in the mining industry, especially for mineral deposits containing highly positively skewed data distributions. Order-relations corrections leading to an inconsistent probability distribution present a notable drawback. Furthermore, the use of constant, indicator-class means impacts estimate quality in the upper tail of the distribution, which often comprises significant economic value. The first contribution of this thesis documents the deviations and spatial variability of the estimated probability distribution against a fully consistent, and known probability distribution. Next, the indicator-class-mean component of the MIK estimator is isolated and compared to the known distribution of correct values. This research demonstrates that the indicator-class means vary as a function of the conditioning values. The greatest variability is observed in the lower and upper tails. The second contribution of this thesis is a comparison of MIK and multivariate-Gaussian kriging (MGK) estimates using non-Gaussian data. Motivating the comparison is the assertion that when using Gaussian data, MGK will always generate estimates with lower mean-squared error than MIK. Multiple scenarios ranging from highly non-Gaussian to Gaussian, are generated with the expectation that MIK will outperform MGK once the data were sufficiently non-Gaussian. In the scenarios tested, MGK consistently generates more accurate and precise estimates, demonstrating that MGK can produce robust estimates, even in the presence of highly non-Gaussian data. The place of MIK remains unclear; however, the procedures and standards to assess the relative performance of MIK and other techniques are documented more clearly.