| This essay is so weird to read. The author is extremely passionate, yet also claiming to be simply rational. He’s throwing terminology around (Dutch book, ZF) but seems unaware of the limits of the approach he advocates. There are so many cracks in the Bayesian edifice promoted in TFA! These problems are well-known in the Theories of Probability community [1] (which is only a subset of the larger set of theorists recognizing the limits of mechanical Bayesian reasoning in decision problems). Here are a couple. (1) Bayesian approaches force you to assign a sharp probability to every event. How do we map any event to a sharp probability? E.g., I need to give a number for the probability of rain tomorrow, a non-repeating event. How do I map that to a number? Not through relative frequencies- it’s non-repeating. If two people give different numbers, how do we decide who is right? This problem is what Peter Walley has called the “Bayesian dogma of precision.” [2] (2) As noted above in an aside, we have a hard time computing probabilities. This is a practical problem that we all are aware of, but often discount. In what we could call CMP (Conventional Mathematical Probability - Kolmogorov’s axioms) we typically can’t even correctly enumerate the sample space. We’re always forgetting something, so our models are too confident. (In the “Dutch book” analogy alluded to in TFA, we are following the axioms but are somehow always losing money, in a very real sense.) Related to this problem of computing probabilities, we don’t have a rigorous way to determine when two real-world events are independent. Yet we constantly invoke independence to construct models. Kolmororov’s 1933 manuscript was clear on this problem. [3] Not satisfied with this, we go on to hypothesize conditional independence relationships in order to feed our complex “rational” Bayesian machine. It’s thirsty for numbers, and we just make them up! * This all sounds somewhat hypothetical. It’s not. In my day job, I compute supposed Bayesian credible intervals for various physical variables. The people downstream who use those variables to assimilate into physical models typically multiply our credible intervals by 2. My friend across lab has it even worse, they multiply his Bayesian intervals by 3. This is not a well-functioning machine. [1] E.g., https://isipta23.sipta.org/, or https://plato.stanford.edu/entries/imprecise-probabilities/#... [2] https://issuu.com/impreciseprobabilities/docs/imprecise_prob..., first paragraph, although the whole short article is on-point [3] from memory, the quote is something like, “determining the conditions under which events may be judged independent is one of the major outstanding problems in theory of probability“ |