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IlyaShpitser comments on The Statistician's Fallacy - Less Wrong
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Ilya, I'm curious what your thoughts on Beautiful Probability are.
Personally, I flinch whenever I get to the "accursèd frequentists" line. But beyond that I think it does a decent job of arguing that Bayesians win the philosophy of statistics battle, even if they don't generate the best tools for any particular application. And so it seems to me that in ML or stats, where the hunt is mostly for good tools instead of good laws, having the right philosophy is only a bit of a help, and can be a hindrance if you don't take the 'our actual tools are generally approximations' part seriously.
In this particular example, it seems to me that ChrisHallquist has a philosophical difference with his stats professor, and so her not being Bayesian is potentially meaningful. I think that LW should tell statisticians that they shouldn't believe cell phones cause cancer, even if they shouldn't tell them what sort of conditional independence tests to use when they're running PC on a continuous dataset.
Well, I am no Larry Wasserman.
But it seems to me that Bayesians like to make 'average case' statements based on their posterior, and frequentists like to make 'worst case' statements using their intervals. In complexity theory average and worst case analysis seem to get along just fine. Why can't they get along here in probability land?
I find the philosophical question 'what is probability?' very boring.
Unrelated comment : the issue does not arise with PC, because PC learns fully observable DAG models, for which we can write down the likelihood just fine even in the continuous case. So if you want to be Bayesian w/ DAGs, you can run your favorite search and score method. The problem arises when you get an independence model like this one:
{ p(a,b,c,d) | A marginally independent of B, C marginally independent of D (and no other independences hold) }
which does not correspond to any fully observable DAG, and you don't think your continuous-valued data is multivariate normal. I don't think anyone knows how to write down the likelihood for this model in general.
Agreed.
Correct; I am still new to throwing causality discovery algorithms at datasets and so have not developed strong mental separations between them yet. Hopefully I'll stop making rookie mistakes like that soon (and thanks for pointing it out!).