Why probabilistic models are often true, but can be either useful or useless.

Abstract

“All models are wrong but some are useful” (most often credited to George Cox) is a commonly used aphorism, probably because it resonates with some truth to many. We argue though, that it would be more correct to say “All deterministic models are wrong but some are useful “. Here, a deterministic model refers to any single, and in some quantitative way ‘optimal’ model, typically the results of minimizing some objective function. A deterministic model may be useful to use as a base for making decisions, but, it may also lead to disastrous results. The real disturbing issue with deterministic models is that we do not know whether it is useful for a specific application, because of a lack of uncertainties.On the other hand, a probabilistic model, that is described by a probability density, or perhaps by many realizations of a probability density, can represent in principle arbitrarily complex uncertainty. In the simplest case where the probabilistic model is represented by a maximum entropy uncorrelated uniform distribution, one can say that “The simplest probabilistic model is true but not very useful.“.  It is true in the sense that the real Earth model is represented by the probabilistic model, i.e. it is a possible realization from the probabilistic model, but not very useful, as little to no information about the Earth can be inferred.In an ideal case, a probabilistic model can be set up from a variety of different sources, such that it is both informative (low entropy), and consistent with an actual subsurface model in which case we can say “An informative probabilistic model can be true and also very useful.“. Any uncertainty in the probabilistic model can then be propagated to any other related uncertainty assessment using simple Monte Carlo methods. In such a case clearly, uncertainty is useful.In practice though, when a probabilistic Earth model has been constructed from different sources (such as structural geology, well logs, and geophysical data) then one will often find that the uncertainty of each source of information will be underestimated, such that the combined model will describe too little uncertainty. This can lead to potentially worse decision-making than when using a deterministic model (that one knows is not correct), as one may take a decision related to a low probability of a risky scenario that may simply be related to the underestimation and/or bias of the uncertainty.We will show examples of constructing both deterministic and probabilistic Earth models, based on a variety of geo-based information. We hope to convince the audience, that a probabilistic model can be designed such that it is consistent with the actual subsurface, and at the same time provides an optimal base for decision-makers and risk analysis.In the end, we argue that: Uncertainty is not only useful but essential, to any decision-making, but also that it is of utmost importance that the underlying information is quantified in an unbiased way. If not, a probabilistic model may simply provide a complex base in which to take wrong decisions.