Chapter 10 of Uncertainty: The Soul of Modeling, Probability & Statistics FREE for New Subscribers!

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Bonus Chapter 10 Opening!

Here are the opening paragraphs of Chapter 10 (with math and references suitably adapted).

“A genuine expert can always foretell a thing that is 500 years away easier than he can a thing that’s only 500 seconds off. ——Mark Twain

An entire book could be written of various implementations of models in the predictive, observable form Pr(Y in y | X,D,M)$ (see the previous Chapter for the explanation of this form). Here I can do no more than cover those areas that seem most important to decisions common in science. I emphasize not so much particular models by specific persons, but how model results should be communicated and the errors usual in the classical methods. Universally, statistical results are presented as if they were not conditional on a model, which of course all are. Over-certainty abounds.

Regression is of paramount importance. The horrors to thought and clear reasoning committed in its name are legion, a fact which is well known, e.g. [various authors]. But it’s more than bad regression: misunderstandings of the nature of evidence are everywhere, but that this is so is increasingly gaining attention; see among many [these fellows], and in the hot field of neuroscience [like these guys]. It’s bad enough in academia, but if any reader has experienced consulting in non-academic settings, in, for instance, marketing, you will realize the problems detailed below are trivial. From my many experiences I have been able to discover that ordinary people think statistics is something akin to magic. The discussion on how statistical “control” is not control in the Section on regression should be read by everybody.

Reification is the deadly sin of modelling. The model is not the territory, though this fictional land is unfortunately where many choose to live. When the data do not match a theory, it is often the data that is blamed for marring a beautiful model. Models should never take the place of actual data, though they often do, particularly in regression and time series. Risk is nearly always exaggerated. The fallacious belief that we can quantify the unquantifiable, especially human emotions, is responsible for scientism. Hayek, in his Nobel prize speech, cautioned against assuming that the data we have, which is often times the only data we have, must therefore, because of its availability, be causal. This is a form of availability fallacy. Incidentally, Hayek also recommended (a version of) the predictive approach, especially with economic data. “Smoothed” data is often given pride of place over actual observations. Over-certainty is, as I have already claimed, at pandemic levels.

The general, overarching admonition is to escape the Cult of the Parameter. Speak of observables and not parameters. Models should be used in the predictive sense and checked against reality.

Because this Chapter describes the some of the many (infinite?) ways probabilistic thinking can go awry, it is more conversational in tone. Finally, at the end, I express some hope about the future.