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## What is the purpose of sampling theory (3 replies)

Very brave and refreshing observations. I support your views because the geologist will never have anything other than here say without a sample that is sampled correctly. Theory of anything relies on the information fed into the equation. If that is wrong, the theory has no backbone and has no financial merit. What I would say is, don't be too down on the theory yet. The truth is, the theory hasn't yet had an opportunity to put its "data requirement" into practice. When the offered representivity of samples taken is an absolute, the theory of sampling (TOS) will grow wings. We are very close to absolute drill hole sampling representivity. Only when true information gathered is the norm will we be able to truly judge the "Theory of Sampling".

I try to avoid the terms representative and the like because there are many different definitions and interpretations of the word and because there is no useful measure of it for sampling. It is not a statistical term and what one individual might say is representative another would say it is not. In regard to exploration drill holes a variogram is most helpful if scaled properly and fitted to a proper model (not the too-often used spherical model, which is not a proper model). The intercept of a good variogram will give you an estimate of variance of preparation and analysis of the individual cores and you will then have the information needed to determine where the next exploration dollar need be spent, whether in improving your analyses of the cores or drilling more holes. Conditional simulation will provide you with estimates of the variability of the subject material and estimates of the variability of your exploration process. All of this is of course done within the extant theory.

With that prelude I basically wanted to ask if you mean by the term “representivity of samples” that the samples are taken in an economically optimal manner and that the resulting estimates of the quality and quantity of the resource are sufficiently precise for the intended purpose. I would share that objective.

I was curious as to whether there would be much comment on this.

Given that you went to the conference on Sampling Theory I presumed you would be in a position to answer your own question; however I note that on the actual site there is no definition of 'Sampling Theory'.

And yet we see that it is run by AUSIMM (Australian Institute of Mineral and Metallurgy) with the clear implication that Sampling Theory is a branch of Mining. (This is something I find quite extraordinary yet a quick scan of membership of this group indicates that indeed that predominantly members are are from mining backgrounds).

So I think in the context of this Group there are two issues surrounding Sampling Theory:

How to take a sample?

What is the optimum sampling strategy?

It is point 2 that interests me most. Sampling strategy means how to gain the most INFORMATION from your population via sampling at particular locations. (Hence the direct connection with Information theory)

And further this INFORMATION has to have some profitable objective. (To this extent there is a connection with a new branch of maths called Data Analytics)

Thus we could argue that the optimum sampling strategy is one which decreases any risk (or variance) of our planned or current mining operation.

Therefore the theory of sampling must also be contextualised or integrated with our mine design strategy.

Possibly one of the most visionary bosses I worked for was Guillermo Turner-Said (now Datamine) who had a vision for a holistic integrated sampling and mine planning strategy.

Yet a vision is not enough.

The mathematical and other technical details required to implement such a vision cannot be gained from simple textbooks. It requires a lot of work, discussion and thought.

I am among those with serious doubts about statements of absolute scientific truth. In reality we only process models of truth to enable us to rationally predict outcomes and connections to currently accepted science. This point of view categorically denies a “TOS” cast in stone, one worthy of eternal devoted worship. The sole purpose of any sampling theory is to support probability calculus, to enable useful predictions of the reliability of data obtained by sampling. If one with the aid of sampling theory can make these predictions with confidence, one can design systems that meet commercial requirements. Too, one can monitor the precision being achieved lot by lot and understand how to further optimize the measurement system.

Like others I have read numerous papers and texts discussing sampling theory. Many are mere intellectual exercises. Few describe rational and helpful procedures for studying a given mineral stream, predicting the outcomes from sampling and optimizing designs that will provide the levels of precision and bias commercially required. Coal and iron ore standards do include elementary procedures intended to address the problem of predicting sampling precision. However, these procedures are incomplete and frankly, sophomoric as they assume independence of the first stage sampling units. Often, stages of sampling downstream of the primary stage are often simply lumped into the category of “sample preparation” for which, supposedly, one has at hand or can easily obtain, measures of precision.

At the SAMPLING 2012 AUSIMM conference in Perth I presented a paper demonstrating theory and methods for both predicting sampling precision and subsequently monitoring the precision being achieved. In practice these methods are useful, even if incomplete. In continued study I find the fundamentals becoming deeper and continuously more fascinating. I strongly believe that no sampling theory for minerals is complete without use of the maximum entropy principle to address correlation.

We have wasted too much time focusing on minimum increment masses and numbers of particles.

Postings by others suggesting the purpose of sampling theory and where it should be headed would be of keen interest.