Reply to note by "Resource Modeling Solutions"

The collateral effects of innovation

I love to see our #research and #development work shaking businesses around the world. Today I was informed of a note by the company "Resource Modeling Solutions" criticizing our recent journal publication on geostatistical modeling of geometallurgical variables, which you can find at this link.

Unfortunately, the author of the note did not understand our mathematical model. In this post I would like to correct their misunderstandings, one by one, to demystify our newly proposed alternative to Gaussian simulation in the #mining #industry.

Correcting misunderstandings

Our biggest concern with the paper is their unfounded criticism of standard geostatistical methodologies.

We wrote the paper to raise very serious issues related to geostatistical modeling of geometallurgical variables, and to start a wave of innovation that departs from the traditional solution with normal score transformation followed by Gaussian simulation. Our criticism is founded on (1) mathematical understanding and (2) empirical evidence from laboratory experiments.

The authors criticize the use of variograms with few data, yet the Hilbert-Kriging proposal also requires variograms.

In our proposed methodology, we do not estimate variograms of geometallurgical variables because there are too few comminution and flotation samples (~60). Instead, we predict the posterior probability (or PMFs) of the corresponding geometallurgical variables along all drill hole samples (~2000), and then estimate variograms of PMFs along the drill holes.

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.

As the author of the note already explained, trying to use traditional methodologies with non-additive variables leads to bias. That is enough motivation to try different solutions that depart from the old literature of Kriging and Gaussian simulation (or small variations around these methods). Bayesian modeling, machine learning, and more recent technologies should be leveraged to improve #uncertainty #quantification and #prediction #accuracy in #geometallurgy.

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.

We do not claim that the normal score transformation is poorly understood. What we claim is that the transformation is not suitable for some geometallurgical variables due to physical relationships that are not honored in the reverse transformation. We only employ the normal score transformation with chemical or mineralogical compositions used as predictors (or features) in our Bayesian models.

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).

We do not claim that ratios of compositional data are not considered in traditional methodologies. Likewise, we only apply this transformation with chemical or mineralogical compositions to standardize the features and remove spurious correlations before performing Bayesian inference.

They criticize the need for ad-hoc corrections, but nothing about conventional workflows are ad-hoc.

Any sequence of transformations that is performed as an attempt to convert a multivariate non-Gaussian distribution with well-known physical variables that are non-negative, bounded, etc., to a multivariate Gaussian distribution with non-physical variables that are unbounded with zero cross-correlations just to employ a given simulation method can be thought of as ad-hoc. There is no guarantee that reverting the sequence of transformations will honor physical relationships among the variables. We strongly believe that physical and geological understanding of variables should be exploited in geostatistical models, which is something that traditional methodologies based on Gaussian simulation often ignore.

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.

It suffices to construct a single example where reverting a transformation near the tails of the distribution leads to non-physical values of the original geometallurgical variable. There are various implementation details such as tail approximations and compositional constraints that can dramatically affect the results of traditional methodologies based on non-linear transformations (log-ratio, normal-score, projection pursuit, etc).

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

To many of us trying to improve the status quo, these "proven techniques" sold in the industry have flaws and should not be adopted blindly. We are sad to read such a statement about lack of reason coming from a team of experienced people.

Conclusions

None of the actual limitations of our proposed methodology has been mentioned by the author of the note. In spite of these limitations, our methodology provides a novel perspective on geometallurgical modeling that departs from the old-fashioned Gaussian simulation. We hope that this perspective will lead to more innovation in the mining industry and will educate professionals about the real challenges that the industry faces.

For those interested in more details, we have a live talk recorded about this work that you can watch at your own convenience:

#geostatistics #geostats #geometallurgy #innovation #technology #mining #industry #openscience #research