It’s possible to find “spurious” correlations in a limited data sample, if two things just “happen” to happen together often by chance. But I don’t think that really counts.
When absolute claims are made with exhaustive lists of possibilities then things can “not count” only when excluded explicitly. When dealing with things at the level of precision and rigour that Pearl works at the difference between ‘almost true’ and ‘true’ matters. Even with the (‘probably’ or ‘overwhelmingly likely’) caveat in place the statement remains valuable. It is still worth including such a parenthetical so as to avoid confusion.
Did you have any other scenarios in mind?
No, the set of all correlations that are not causally related in one of the listed ways seems to fit the criteria “limited” and to whatever extent they can be described as ‘spurious’ that description would apply to all of them. Admittedly, some of them are ‘limited’ only by such things as the size of the universe but the larger the sample the higher the improbability.
I would replace ‘spurious’ with ‘misleading’. A correlation just is. There isn’t anything ‘fake’ or ‘invalid’ about it. The only thing that could be wrong about it is using it to draw an incorrect conclusion.
I have a feeling including a parenthetical like that would invite more confusion than it avoids. “Oh cool, I guess my magical ESP powers are just one of the unlikely cases where I can be correlated with the hidden coin flips without any causal influence.”
Because “correlation” is normally taken to mean a systematic effect that can be expected to be predictive of future samples, or something. In this specific case, Pearl probably means something more precise by it (like correlations between nodes in a particular causal model).
I suppose you could accurately clarify the original quote by saying “systematic correlation”, which would pin down the idea referred to for people who haven’t read the book.
I have a feeling including a parenthetical like that would invite more confusion than it avoids. “Oh cool, I guess my magical ESP powers are just one of the unlikely cases where I can be correlated with the hidden coin flips without any causal influence.”
The unqualified version is more compatible with muddled thinking about ESP than the qualified version. Specifically, it outright excludes the possibility “No, you were just lucky” from consideration.
In this specific case, Pearl probably means something more precise by it (like correlations between nodes in a particular causal model).
When absolute claims are made with exhaustive lists of possibilities then things can “not count” only when excluded explicitly. When dealing with things at the level of precision and rigour that Pearl works at the difference between ‘almost true’ and ‘true’ matters. Even with the (‘probably’ or ‘overwhelmingly likely’) caveat in place the statement remains valuable. It is still worth including such a parenthetical so as to avoid confusion.
No, the set of all correlations that are not causally related in one of the listed ways seems to fit the criteria “limited” and to whatever extent they can be described as ‘spurious’ that description would apply to all of them. Admittedly, some of them are ‘limited’ only by such things as the size of the universe but the larger the sample the higher the improbability.
I would replace ‘spurious’ with ‘misleading’. A correlation just is. There isn’t anything ‘fake’ or ‘invalid’ about it. The only thing that could be wrong about it is using it to draw an incorrect conclusion.
I have a feeling including a parenthetical like that would invite more confusion than it avoids. “Oh cool, I guess my magical ESP powers are just one of the unlikely cases where I can be correlated with the hidden coin flips without any causal influence.”
Because “correlation” is normally taken to mean a systematic effect that can be expected to be predictive of future samples, or something. In this specific case, Pearl probably means something more precise by it (like correlations between nodes in a particular causal model).
I suppose you could accurately clarify the original quote by saying “systematic correlation”, which would pin down the idea referred to for people who haven’t read the book.
The unqualified version is more compatible with muddled thinking about ESP than the qualified version. Specifically, it outright excludes the possibility “No, you were just lucky” from consideration.
This exception applies in that case.