Timeline for Is the conditional distribution of Y given X the most we can know about how X "affects" Y?
Current License: CC BY-SA 4.0
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| when toggle format | what | by | license | comment | |
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| Feb 2, 2019 at 18:29 | vote | accept | ColorStatistics | ||
| Feb 2, 2019 at 18:10 | comment | added | ColorStatistics | Thank you for the follow up, nbro. I take my last question back. So, if I were to try to summarize your answers, you're saying if we're looking at dependence (i.e. how X "affects" Y) then the conditional distribution of Y given X contains exactly the same information as the joint distribution of X and Y. In this case, his statement is true. If we're looking at causality (i.e. how X "causes" Y) then the conditional distribution of Y given X is the wrong distribution to be looking at because P(Y=y|X=x) is different than P(Y=y|do(X=x)). In this case, his statement is false. A fair synthesis? | |
| Feb 2, 2019 at 17:22 | comment | added | ColorStatistics | Would your answer change if we were to put back our "Causal" hat? | |
| Feb 2, 2019 at 17:14 | comment | added | ColorStatistics | Good point. But isn't knowledge of how Y affects X potentially informative (however marginally) about how X affects Y? If so, from the joint distribution we can obtain both, whereas the conditional distribution of Y given X only gives us how X affects Y (albeit more directly). | |
| Feb 2, 2019 at 17:06 | comment | added | ColorStatistics | Thank you for the response. I agree with you. What about the part that says that this is most we can know about how X affects Y. Setting causality aside for a moment, isn't it the case that there is no more information about how X affects Y in the conditional distribution of Y given X than there is in the joint distribution of X and Y? In fact, knowing the joint distribution of X and Y, we can always build the conditional distribution of Y given X, but not vice versa. I would contend that the most we can know about how X affects Y is contained in the joint distribution of X and Y. | |
| Feb 2, 2019 at 16:57 | history | answered | user82135 | CC BY-SA 4.0 |