The treatment of missing ‘not at random’ geological data for ore grade modelling

Abstract

Geostatistics aims to spatially model multiple correlated attributes with some under-sampled variables. Missing samples can distort the data set statistics, and for the model to be consistent, it is necessary to understand the mechanisms that cause the missing data (MD). There are three mechanisms that can govern MD: Missing Completely at Random (MCAR), Missing at Random (MAR) and Missing Not At Random (MNAR). More specifically, when there is a systematic difference between measured and the missing samples, the data is subject to the MNAR mechanism, which leads to biases in the final model if not dealt with adequately. A case is presented where an under-sampled attribute, U (ppm), is modelled to infer its values over the study area through co-simulation approach and an univariate simulation performed on an artificially complete set, considering the MNAR mechanism, which shows a reduction in the relative estimation errors compared to the co-simulated model.