Teaching Bayesianism

Nowhere does it follow from seeing the probability as a limit in the infinite number of trials (frequentism), that the mean of that distribution with unknown mean wouldn't be restricted to specific range.

In the particular case I gave, of course frequentists could produce an argument that the mean must be in the given range. But this could not be a statistical argument, it would have to be a deductive logical argument. And the only reason a deductive argument works here is that the posterior of the mean being in the given range is 1. If it were only slightly less than 1, 0.99 say, there would be no logical argument either. In that case, the frequentist could not account for the fact that we should be extremely confident the mean is in that range without implicitly employing Bayesian methods. Frequentist methods neglect an important part of our ordinary inductive practices.

Now look, I don't think frequentists are idiots. If they encountered the situation I describe in my toy example, they would of course conclude that the mean is in the interval [0.1, 1.0]. My point is that this is not a conclusion that follows from frequentist statistics. This doesn't mean frequentist methodology precludes this conclusion, it just does not deliver it. A frequentist who came to this conclusion would implicitly be employing Bayesian methods. In fact, I don't think there is any such creature as a pure frequentist (at least, not anymore). There are people who have a preference for frequentist methodology, but I doubt any of them would steadfastly refuse to assign probabilites to theoretical parameters in all contexts.

I expect most scientists and statisticians are pluralists, willing to apply whichever method is pragmatically suited to a particular problem. I'm in the same boat. I'm hardly a Bayesian zealot. I'm not arguing that actual applied statisticians divide into perfect frequentists and perfect Bayesians. What I'm arguing is against your initial claim that no significant methodological distinction follows from conceiving of probabilities as epistemic vs. conceiving of them as relative frequencies. There are significant methodological distinctions, and these distinctions are acknowledged by virtually all practicing statisticians. Applying the different methodologies can lead to different conclusions in certain situations.

If your objection to LW is that Bayesianism shouldn't be regarded as the one true logic of induction, to the exclusion of all others, then I'm with you brother. I don't agree with Eliezer's Bayesian exclusionism either. But this is not the objection you raised. You seemed to be claiming that the distinction between Bayesian and frequentist methods is somehow idiosyncratic to this community, and this is just wrong.

(Incidentally, I am sorry you find my example boring and stupid, but your quarrel is not with me. It is with Morris DeGroot, in whose textbook I first encountered the example. I mention this as a counter to the view you seem to be espousing, that all respectable statisticians agree with you and only "sloppy philosophers" disagree.)

Reasoning “over Turing machines” and thence getting the same results (or even using the same tools) as Bayesians.

The point here is that you want to go for physically justified stuff, and anything not physically justified that you are doing anywhere, is same in principle as wilfully putting cognitive bias into your calculations, and is just plain wrong, no philosophical stuff here, you'll end up losing games vs someone who solves it better.

Statisticians, by and large, don't lose sleep over this problem. Even in your not-quite-fair die problem, the calculations involved are really hard. It wasn't made explicit in my comment but I wasn't even assuming that opposite sides have equal probability, because some subtle error in the setup could break the symmetry. In the Bayesian case, I was considered mentioning a mixture model that would take advantage of the symmetry if the data supported it. In KDD Cup types of problems, nobody is worried that a domain expert will show up with a winning solution that doesn't even need to see the training data (why would it if it were maximally physically justified?).

putting cognitive bias into your calculations, and is just plain wrong, no philosophical stuff here, you'll end up losing games vs someone who solves it better. Maybe you guys need "Overcoming Bayes" blog.

Bayesians have made peace with bias. In fact, decision rules that are both Bayes and unbiased have zero risk, which is a nice way of saying that they don't exist in non-trivial situations. Noorbaloochi and Meeden (1983) have to go through definitional contortions to establish a positive connection between being Bayes and unbiased.

Bias is what lets you get good inferential performance in small-sample regimes. If I observe side counts (2, 0, 1, 3, 2, 2), I'd be okay with my estimator inferring equal side probabilities, because that will be closer to the truth than the unbiased estimator which guesses (0.2, 0.0, 0.1, 0.3, 0.2, 0.2); ten rolls is not enough data to tell me that I should never see a "2". On the other hand, with side counts (200, 0, 100, 300, 200, 200), something closer to the unbiased estimator seems like a good idea. As long as the estimator is asymptotically unbiased, you can even still have consistency.

Unlike cognitive bias, we have control over our statistical bias and we should not be squeamish about using it to learn about the parts of the world that are hard to model with complete accuracy to the extent that we wouldn't need statistics anyways.

Didn't work on me yet, coz i'm bored.

It's not even at the point of what ideas are endorsed, but how. E.g. I like MWI, okay? The arguments in favour of MWI here are utter crap, confused and irrelevant and go on for pages. Then the Bayes , irrelevant and confusing and for pages again every time, and with a poor style explanation to top it off, which is not even Bayesian but frequentist (and poor style in terms of useful stuff vs wankery ratio). The general pattern of 'endorsing' an idea on LW consists of very poor understanding of what idea is, how it differs from the rest, and some wankery slash signalling like "look at me i can choose correct idea in some way that you ought to understand if you are smart enough". If you read LW you would think that e.g. frequentists are people whom reject Bayes rule and can't solve the problem like in OP or something, the non-multiworlders are people who believe collapse literally happens when you look at stuff (which may well be the case among those 'non many worlders' whom don't know jack shit about quantum mechanics). Then the cryonics, for many times it's been told by experts that current methods lose a lot of important information irreversibly, you just go on with some crap about super-intelligence that will deduce missing info from life story, never mind algorithmic complexity or anything. Supposedly because you're a 'rationalist' you don't need to know anything or even think it over taking into account the subtleties, you'll be more correct without the subtleties than anyone would be with. (If it worked like that it'd be awesome).