All models are wrong, anyway

Today I gave a seminar on the ASA statement about p-values, the 5-sigma criterion, and other amenities. In the seminar I slipped by some comments on the stance of Bob Cousins on models, hypotheses, and laws of Nature, and ended up ranting about interventionist definitions of causality (following Pearl, mainly).

A few minutes ago I opened Twitter and found the somehow excessive prodromes of an internet flame sparked by a post by Sabine Hossenfelder titled “Predictions are Overrated”. I disagree with that post in a few key points, which are too long to describe on Twitter. Bear with me here.

 

The argument of the shady forecaster

The way in which scammer forecasters work is to generate huge amount of predictions, send them to random people, and finally follow up only with the people who received the predictions which a posteriori proved to be correct. The scammers then repeat this iteratively until for a small set of people they appear as if they always provided correct predictions. It’s a well-known strategy, which I think was described extensively in a book by Nate Silver. Or Nassim Taleb. Or Levitt and Dubner. I read too much.

Sabine uses this story to argue that since any successful prediction can be successful just by chance—because of the size of the pool of scientists producing models—therefore judging theories based on their predictive power is meaningless. However, the shady-forecaster example to me is quite disconnected from the topic at hand: the shady forecaster relies on selecting its targets based on a-posteriori considerations and conditional probabilities, whereas the point by Sabine is one of pure unconditional chance.

 

The power of doing

Sabine remarks that epidemic models are incomplete because they don’t include the  “actions society takes to prevent the spread”; that’s true, but Sabine hints that’s because “They require, basically, to predict the minds of political leaders”. The real point is instead that to some extent researchers cannot access the causal structure underlying the epidemic model because they are stuck with conditional probabilities and cannot trasform them into conditional interventions; in other words, they cannot fix some of the conditions to remove faux causal links and highlight the true causal structure—mainly because they would need the politicians to take certain actions which sometimes would be plainly unethical and sometimes would have too high a political cost.

 

A theory should describe nature

The exact quote from Sabine’s article is “If I have a scientific theory, it is either a good description of nature, or it is not“. Books have been written on the meaning of a good description of nature, but the full sentence is simply what Quine would call a logical truth, that is an expression which is true regardless of the effective content of the sentence—if I have a cup, it is either broken or not broken. I won’t into deeper considerations about factual truth vs logical truth.

Sabine in any case goes on defining an explanatory power which “measures how much data you can fit from which number of assumptions. The fewer assumption you make and the more data you fit, the higher the explanatory power, and the better the theory”. This is ultimately an expression of Occam’s Razor, which is embedded in our mentality of scientists—and in Bayesian model selection.

Sabine also points out that ultimately there is a trade-off between obtaining a better fit and introducing more (ad-hoc) assumptions, which again is something deeply embedded in Bayesian model selection and in formal procedures such as the Fisher test for choosing the minimal complexity of a model we want to fit to the data. So far so good.

We diverge towards the end, where Sabine claims that “By now I hope it is clear that you should not judge the scientific worth of a theory by looking at the predictions it has made. It is a crude and error-prone criterion.” and laments that “it has become widely mistaken as a measure for scientific quality, and this has serious consequences, way beyond physics”.

To me the explanatory power of a model, or even better its interpretability, should indeed be a fundamental characteristic of a model, but I subscribe to Box’s all models are wrong. I want to have a reasonable explanatory power or interpretability before considering a theory minimally acceptable as a physics model, but ultimately the sole judge for the success or a failure of a model are indeed the data. Rather than focussing on the possibility that a model predicts the data because of chance, I prefer to focus on requiring that a well-interpretable model predicts multiple data, in multiple scenarios, in multiple independent experiments. If its predictions are successful, I’ll take it as the current working assumption about how things work.

Particle physics, as pointed out by Bob Cousins in the paper linked above, is indeed a happy realm where we have tremendous predictive power and where we can often build models starting from first principles rather than just figuring out what type of line fits data the best (as is common in other sciences, I recently experienced). Bob is also right when he remarks that when we go from Newtonian motion to special/general relativity the former is the correct mathematical limits in a precise sense” rather than an approximation. However, all of this to me simply justifies the use of (quasi-)point null hypotheses: it does not imply any strong connection with a ground truth. More importantly, even our choice of those very reasonable assumptions (symmetries and whatnot) that generate the explanatory power or interpretability of the model might ultimately result in a very successful theory by chance alone. After all—I insist—all models are wrong anyway.

 

2 thoughts on “All models are wrong, anyway

  1. HI Pietro,

    this post was great, makes explicit some of the concerns that I thought of when I read Sabine’s post. The shady scammer (rather than forecaster) argument is indeed unrelated with the main argument and a bit strawman-ish because I do not believe she does not understand how it is clearly a different matter.

    Like

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