Timeline for Pearl's Causal Inference In Statistics, equation 3.11 - Calculation of group specific causal effects
Current License: CC BY-SA 4.0
7 events
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| Jan 26, 2023 at 14:36 | comment | added | Adrian Keister | Those are good questions. I'm not sure I can answer them fully - we probably need Carlos Cinelli for that (probably CrossValidated's best expert on causality). Off the top of my head, I'd say that some of those expressions are probably equivalent if the DAG has certain characteristics. For example, if $X$ and $Y$ are completely independent in the DAG, then you can say $P(Y|X)=P(Y).$ That sort of thing. But it requires detailed thinking to tease out all the possibilities. | |
| Jan 25, 2023 at 2:39 | comment | added | Anirban Chakraborty | Found the following reliable errata page from Pearl's own UCLA website. The errata here changes the figure to replace $W \leftarrow X$ to $W \leftarrow V \rightarrow X$ and also suggests $P(T=t|W=w)$. In fact an earlier version of this same errata page introduced $X=x$ in the first place. @AdrianKeister, do I need to edit the question accordingly? | |
| Jan 25, 2023 at 2:11 | comment | added | Anirban Chakraborty | Given the Rule 2 in this query, should it be $P(T=t|X=x,W=w)$ or $P(T=t|W=w)$ in equation 3.11? This is similar to the this query, where you supported the later expression. According to this source it should be $P(T=t)$. Any idea which should be the correct one, and some solid source for it? | |
| Jan 25, 2023 at 1:38 | vote | accept | Anirban Chakraborty | ||
| Jan 25, 2023 at 0:43 | comment | added | Adrian Keister | $W$ is post-intervention because the arrow goes from $X$ to $W.$ $W$ is measured, so it should be in the data. It's not possible to adjust for unmeasured variables, unless you do something like the front-door adjustment. | |
| Jan 24, 2023 at 22:16 | comment | added | Anirban Chakraborty | In $P(y|do(x),w)$ is $W=w$ measured post-intervention? And in the final expression of the second query - $P(Y=y|X=x,W=w)$ - is $w$ here a measure from observational/pre-intervention data? I think it should be because we are only theoretically simulating the intervention, and hence, do not have actual access to post-intervention data. | |
| Jan 23, 2023 at 13:56 | history | answered | Adrian Keister | CC BY-SA 4.0 |