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> But even they do not admit Pearson (or any other type) of correlation, but rather the nebulous "statistical dependence". The notion of "Statistical dependenc
by xtacy 10y ago
> But even they do not admit Pearson (or any other type) of correlation, but rather the nebulous "statistical dependence".
The notion of "Statistical dependence" is not nebulous. X and Y are independent if the joint distribution factorises as
p(X, Y) = p(X) p(Y)
> even they do not admit Pearson (or any other type) of correlation,
Precisely. They operate purely in probabilistic dependence/independence terminology, from a theoretical point of view.
- mhermher 10y agoI understand, but from an inference point of view, it is nebulous because the distributions are unknown. Statistical dependence can be determined easily if you know the distributions, but not if you only have samples. The "c" in the proof, I assume means "observed correlation". Because we are in fact talking about "[Observed] correlation does not imply [Unobserved] causation", right?
- xtacy 10y agoI partly agree with you, but I wouldn't go to the extent of using "easily" in this phrase -- > Statistical dependence can be determined easily if you know the distributions, Even if you know the distribution, a statistical test will make Type-I/II errors that you would have to take care of. Actually, I find the text linked above hard to understand, without properly defining 'c.' What's the sample space? In general, my sentiments are with the xkcd comic strip, but nothing more. Pearl's theories lay a firm foundation for communicating a causal hypothesis and manipulating it algebraically, but the true tests of causal hypothesis are: - Experimental evidence - The predictions it makes, in cases where experiments are hard to perform (e.g., in physics, when we make certain causal conjectures about how the universe works).