The Central Estimate Fallacy
Sometimes you can be so enmeshed in things that you don’t even know it. Like the proverbial forest-for-the-trees problem or the fish shrugging when asked ‘how’s the water boys’, there are some assumptions we simply don’t question. Worse, we don’t even recognise them as assumptions. They are so much a part of our mental models, our current reality, that we build complete edifices on their shaky foundations and then act surprised when our beautiful systems fail. Even they, post-failure, these mental prison bars are so strong that, instead of breaking their influence, we design ever more complex rules and regulations in a vain attempt to achieve an outcome that is impossible within their boundaries.
Or, to put it simply, some things are never discussed or considered. Some things are taken completely on faith and any attempt to examine their basis becomes an outside context problem. Until a complete paradigm shifts arrives.
I think that is the case with what I call the central estimate fallacy. It is one of a few conceptual archetypes that plague the art and science of Mineral Resource estimation. Here’s the framing question
“How do you know that your estimate (resource or reserve) is the central case within the realm of probabilities?”
Why does this matter? Well, if we accept that ‘all models are wrong’ (something that we also struggle to admit in practice) we also need to admit that ‘some models are useful’. That might sound trite but look at the corollary - ’some models are NOT useful’.
We can define some simple classes of ‘not useful’ models. They are the ones that are egregiously wrong. So poor as to invite failure. So poor that they should not see the light of day, much less be made public. Sadly we routinely see examples of these, even with the layers of protection we assure ourselves exist. We see estimates where the location of the mineralisation rotates 30 degrees in successive estimates. We see estimates where there are fundamental mismatches between the reported level of selectivity and the practically achievable mining practice. We see estimates where grades or tonnes are distorted by ill informed button-pushing estimators who don’t know what they don’t know.
It might be possible to identify and correct these ’not useful’ models. They are discoverable, albeit with a bit of effort.
There are however, other classes of ‘not useful’ models and estimates. And these are the ones we never discuss, never debate and never recognise. These are the central estimate fallacy models.
When we estimate a mineral resource, we all like to believe our estimate is ‘representative’ of the mineralisation. We believe we have diligently considered all the factors, made informed judgements and estimated a reasonable picture of the resource. And there’s one other thing… we invariably think that our estimate is in the centre of a distribution of possible estimates. And it is this central estimate belief that we then use to classify the resource and assess the risk.
But how do you know you have the central case? Have you even tried to assess if your estimate is optimistic or pessimistic? Have you considered the shape of the probability distribution of all possible models? Is it a Normal distribution? Is it skewed? Is it bimodal? Have you considered the implications?
This is not an easy problem and yet I feel it is an essential element if we are to improve the quality and efficacy of mineral resource and ore reserve estimates. We must abandon the central-case assumption and adopt a more nuanced approach. The challenge is the multi-dimensional nature of these estimates and models. For example a mineral resource estimate is an interconnected set of estimates of:
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- volume
- geometry
- grade (or quality)
- bulk density
- deleterious factors (ranging from simple single-variables to complex and fuzzy combinations human, economic and technological factors)
If you modify something in one dimension it impinges on other dimensions resulting in a blurry family of possibilities. No, it’s not easy to assess the centrality of your estimate!
I do not have an immediate answer to this problem. And yet, I think this is exactly the type of question our reporting Codes should be focusing on. Understanding centrality, understanding skewness of the families of possible estimates.
All models are wrong, some models are useful, some models are downright dangerous. Assuming you have captured the central case without evidence is naive.
Principal at Martlet Consultants
4 个月Perhaps you should be asking why the mining industry only wants a single solution that an individual believes is the central prophesy. Most boards just want the single solution with an NPV, as they use the simple rule that NPV>0 means invest and NPV<0 don't invest. For miners this is after allowing for capex. The directors, analysts and investing punters do not have the capacity to deal with uncertainty.
AMC Consultants
4 个月You could do all of the right things with a Mineral Resource model. Not saying that models are always right. But if any of the downstream uses of the model are imperfect--including...ahem...mining-- then one thing isn't going to look like the other. How can risk be conveyed correctly if someone opts to blow your ore all over the countryside after the model is cast? Or make an absurd GC model because maybe that's not really their forte yet? Gotta try harder to do better...across the board. Which may also have very little to do with reporting codes. Hard to soar with the eagles if you work with turkeys. Or vice versa. Or something to that effect. So you do the best that you can, lay out your vision (transparently) for how it was quite specifically meant to be used, and then stand back and take notes about what happens next.
Experienced Exploration and Evaluation Professional in Diamonds, Base metals and Iron ore with oversight in Health, Safety Environment & Community.
4 个月Insightful! How to check if the case chosen as central case, is even close to central or very far from it. May be an attempt to make multiple central cases based on each factor involved like volume, geometry, grade, bulk density, deleterious factors etc. should be made. There after an attempt to justify the selection of these cases in final composite central case, should be done giving adequate reasons for making a choice of central case of each factor. The review of historical practices of estimation of mineral deposits which are now exhausted or mined out may come in handy to check how close original estimates were in relation to the actual mined out resource. These are just my thoughts. Any discussion on this is welcome!
Principal Geologist at Resource Modeling Solutions, M.Sc., MAusIMM CP(Geo)
5 个月You certainly can have hundreds of different interpretations/realities for geometry, grades, volumes, densities; treating a combination of them is unfeasible now: for each geometry realization you have hundreds of grades realizations, for each grade realization, hundreds of densities, and so on - the number of realizations grows exponentially and very quickly you have millions/billions of simulated realizations. The current way to tackle this problem is to treat them in parallel (respecting all their relationships) and use the all realizations all the time. Geologic controls are paramount and need to drive these simulations; but if you are not considering probabilistic resource modelling, you are definitely narrowing the the possibilities "reality". https://link.springer.com/chapter/10.1007/978-3-319-78999-6_7
Mineral Resource Geologist
5 个月Another great post. In 30 odd years of estimating or reviewing estimates on two continents I have never met a shonky estimator. I believe that we are all (mostly) trying our level best to produce useful “central case” models but for whatever reason we on occasion may screw the cat and don’t. This is where external reviewers are invaluable. They should be qualified and competent and no estimate that matters should be released without it being comprehensively peer reviewed. I would like to see the Code adress this in some meaningfull way. Perhaps a register of Competent Peer Reviewers is the way to go. The same criteria that apply to CPs should apply to the CPRs. Keep thinking and keep posting, Scott. The industry needs more of what you have to offer.