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Comment by throwawayjava | Hacker News Reader

The linked paper is a very nice overview. Of course there problems are known and there are people trying to fix all of the issues (mostly in the relative obscurity of non-overhyped corners of academia), but the concise example-guided description of these problems is great.

Somehow I think the most fundamentally damning critique, and causality shares this problem, is also the most vague. That applied scientists/experimentalists look at the "automation" that these approaches are supposed to enable and say "that's either doing the trivial part of the job or giving you BS answers".

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I've always felt bayesian statistics got more attention from researchers than was warranted (including today despite deterministic methods taking over the world) because it has a nice principled "theory of everything" starting point. But then of course you have to approximate the heck out of it to be able to solve it. Often far more than with other methods.

You have to approximate the heck out of the Schrödinger equation as well, otherwise we would be stuck describing the Hydrogen and maybe the Helium atoms and nothing more.

Yes, however as I said in the subsequent sentence, the approximation is "often far more than other methods". For the most obvious example, a point estimate like MAP doesn't need to compute the denominator in Bayes law. That's two (generally easier) terms to approximate rather than three. Those using Bayesian methods point out the value in providing a full distribution, but the necessary additional approximations to get it means the location of its maximum can now actually be less accurate than a simple MAP estimate. But what always bugged me is multivariate problems where the Bayesian paper presumes everything is independent and Gaussian. Great after getting all psyched by that intro talk about the value of getting a distribution, we get the simplest imaginable one, just a mean and variance for each variable.

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