Probability-schmobability, just gimme a good model

In the past few days I have come across two short but thought-provoking papers that seem to voice some of the same concerns, yet arrive at very different conclusions.

One is by Jan Willems (among other things, the founder of the behavioral approach to systems and control):

JW, Probability in control? (to appear in European Journal of Control)

Probability is one of the success stories of applied mathematics. It is universally used, from statistical physics to quantum mechanics, from econometrics to financial math- ematics, from information theory to control, from psychology and social sciences to medicine. Unfortunately, in many applications of probability, very little attention is paid to the modeling aspect. That is, the interpretation of the probability used in the model is seldom discussed, and it is rarely explained how one comes to the numeri- cal values of the distributions of the random variables used in the model. The aim of this communication is to put forward some remarks related to the use of probability in Systems and Control.

The other is by Andrew Gelman and Christian Robert (two high priests of the Temple of Bayes):

AG and CR, “Not only defended but also applied”: A look back at Feller’s take on Bayesian inference

William Feller has a Note on Bayes’ rule in his classic probability book in which he expresses doubts about the Bayesian approach to statistics and decries it as a method of the past. We analyze in this note the motivations for Feller’s attitude, without aiming at a complete historical coverage of the reasons for this dismissal.

What are we to make of this?

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