Timeline for General version of $d$-separation
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Mar 9, 2022 at 8:42 | comment | added | Steve | Could you perhaps clarify whether you believe that what you write is still an answer to the question? How do you want to use the discrete result if $X_L$ is arbitrary? | |
| Jan 27, 2022 at 10:25 | comment | added | Steve | Thanks, I understand now that the characterization of conditional independence. However, I no longer understand why this immediately yields an answer to the question. It seems to me that if the variable $X_L$ that we condition on is continuous, the definition of the paper does not apply (or it leads to an empty statement for Theorem 2). | |
| Jan 26, 2022 at 17:49 | comment | added | Yuval Peres | You are right, I corrected my answer. | |
| Jan 26, 2022 at 17:49 | history | edited | Yuval Peres | CC BY-SA 4.0 |
added 30 characters in body
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| Jan 24, 2022 at 9:42 | comment | added | Steve | About the result you state, I slightly doubt that the "only if" direction holds (take $J=\{1\}, K = \{2\}, L=\{3\}$, $X_1 = X_2 = -X_3$, then it seems we can destroy the conditional independence quite easily by applying a suitable function $f$). However, the "only if" direction is also required to obtain the result? | |
| Jan 22, 2022 at 18:10 | comment | added | Steve | You are right, that seems to cover it. Is there a reference for the result you state? | |
| Jan 21, 2022 at 16:44 | history | answered | Yuval Peres | CC BY-SA 4.0 |