Blog


Note Regarding Modeling Geospatial Uncertainty with Bayesian Models

The Resource Modeling Solutions Team,

The paper “Modeling Geospatial Uncertainty of Geometallurgical Variables with Bayesian Models and Hilbert–Kriging” by Hoffimann and others draws attention to the important topic of multivariate geostatistical modeling of geological and metallurgical variables. As with all methodologies, there are pros and cons to their proposal. Our biggest concern with the paper is their unfounded criticism of standard geostatistical methodologies.

The authors criticize the use of variograms with few data, yet the Hilbert-Kriging proposal also requires variograms. They state that non-additive variables cannot be used, yet it is perfectly acceptable to simulate non-additive variables. Kriging non-additive variables would lead to biased estimates. The authors further criticize the use of the normal score transform, but that transformation is well understood and reversible, and employed in the proposed method. They criticize the lack of consideration of compositional constraints, but it is common to consider ratios or other compositional data transformation prior to normal scores (also applied in the proposed method). This ensures that the compositional constraints of non-negativity and closure are exactly satisfied at every location. They criticize the need for ad-hoc corrections, but nothing about conventional workflows are ad-hoc. The chained transformations all achieve a specific purpose, are theoretically valid, and are reversible to unbiased and spatially consistent models. Further, they claim that the conventional geostatistical workflows are non-robust to minor variations in the data. This is not true. Our experience with these methods with dozens (if not hundreds) of practical applications is that they are remarkably robust.

We appreciate that the authors are trying to motivate their method, but highlighting non-existent concerns with proven techniques is unreasonable.