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You always hear that correlation does not imply causation. But taking a Bayesian perspective, can one counterargue this statement? I was reading the paper linked below (Bayes-Ball argument), and it seems that it isn't true to say that correlation does not imply causation.

Am I wrong to tell students that correlation does not imply causation? This meaning that correlation actually can imply causation.

Link to paper

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  • $\begingroup$ Correlation doesn't imply causation, indeed. But let's point out that almost nothing implies causation! Singling out correlation strikes me as a little unfair, and (although this isn't often said, I think) its appeal as a succinct principle comes down partly to affection for alliteration and assonance, so that it is a slogan or mantra that comes to mind easily and can be passed on just as easily to the next generation. Otherwise put, it's a meme that allows easy mimicry. $\endgroup$ – Nick Cox Jan 30 '18 at 15:06
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In practice, where a large number of probabilities must be estimated from data, I have my doubts, unless the word 'cause' is used loosely. It may help to think through the situation where there are only two variables in the dataset. What would the Bayes-ball algorithm reduce to? To me a more fruitful way of thinking about this is to put a Bayesian prior probability on causation. An excellent example is the cigarette smoking and lung cancer one in Nate Silver's book The Signal and the Noise which I highly recommend.

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No. Correlation still does not imply causation.

The Bayes Ball algorithm is an algorithm to determine nodes that exhibit conditional independence in a belief network (also known as a Bayes network).

The only link with causality that I see is that belief networks can be used to represent causal relationships. But the presence or absence of conditional dependence relationships in such belief networks is not, in itself, enough to say that one variable causes another.

This is a whole interesting field of study but it looks challenging. This article gives an example on smoking showing that it's very possible to draw an inference such as smoking prevents cancer - I'll leave you to judge whether that's correct!

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