= 27d567bc2d48d9f40e9ccc20ea370b15)
Pavitra comments on XKCD - Frequentist vs. Bayesians - Less Wrong Discussion
You are viewing a comment permalink. View the original post to see all comments and the full post content.
= 783df68a0f980790206b9ea87794c5b6)
Loading…= b715d02e85f7b3b4ae65ca3d3e450868)
Subscribe to RSS Feed
Powered by Reddit
= f037147d6e6c911a85753b9abdedda8d)
You are viewing a comment permalink. View the original post to see all comments and the full post content.
Comments (89)
My general impression is that Bayes is useful in diagnosis, where there's a relatively uncontroversially already-known base rate, and frequentism is useful in research, where the priors are highly subject to disagreement.
Why this isn't necessarily true:
If we look at Bayes' theorem (that picture above, with P(A|B) pronounced "probability of A if we learn B"), our probability of A after getting evidence B is equal to P(A) before you saw the evidence (the "prior probability"), times a factor P(B|A)/P(B).
This factor is called the "likelihood ratio," and it tells you how much impact the evidence should have on your probability - what it means is that the more unexpected the evidence would be if A wasn't true, the more the evidence supports A. Like how UFO abduction stories aren't very convincing, because we'd expect them to happen even if there weren't any aliens (so P(B|A)/P(B) is close to 1, so multiplying by that factor doesn't change our belief).
Anyhow, because Bayes' theorem can be split up into parts like this, research papers don't have to rely on priors! Each paper could just gather some evidence, and then report the likelihood ratio - P(evidence | hypothesis)/P(evidence). Then people with different priors would just multiply their prior, P(A), by the likelihood ratio, and that would be Bayes' theorem, so they would each get P(A|B). And if you want to gather evidence from multiple papers, you can just multiply them together.
Although, that's only in a fairy-tale world with e.g. no file-drawer effect. In reality, more care would be necessary - the point is just that differing priors don't halt science.
That's not true in general.
Fair enough. Can I take your point to be "when things get super complicated, sometimes you can make conceptual progress only by not worrying about keeping track of everything?" The only trouble is that once you stop keeping track of probability/significance, it becomes difficult to pick it up again in the future - you'd need to gather additional evidence in a better-understood way to check what's going on. Actually, that's a good analogy for hypothesis generation, with the "difficult to keep track of" stuff becoming the problem of uncertain priors.
My point is more like: If scientific interest only rests on some limited aspect of the problem, you can't avoid priors by, e.g., simpy reporting likelihood ratios. Likelihood ratios summarize information about the entire problem, including the auxiliary, scientifically uninteresting aspects. The Bayesian way of making statements free of the auxiliary aspects (marginalization) requires, at the very least, a prior over those aspects.
I'm not sure if I agree or disagree with the third sentence on down because I don't understand what you've written.
You can also do Bayesian analysis with 'non-informative' priors or weakly-informative priors. As an example of the latter: if you're trying to figure out the mean change earth's surface temperature you might say 'it's almost certainly more then -50C and less than 50C'.
Unfortunately, if there is disagreement merely about how much prior uncertainty is appropriate, then this is sufficient to render the outcome controversial.
I think your initial point is wrong.
There are 3 situations
You can get frequentism to work well by its own lights by throwing away information. The canonical example here would be the Mann-Whitney U test. Even if the prior info and data are both too sparse to indicate an adequate sampling distribution/data model, this test will still work (for frequentist values of "work").