It’s a useless and misleading modeling choice to condition on irrelevant data, and even worse to condition on the assumption the unstated irrelevant data is actually relevant enough to change the outcome. That’s not what “irrelevant” means, and the argument that humans are bad at knowing what’s relevant does _NOT_ imply that all data is equally relevant, and even less does it imply that the unknown irrelevant data has precisely X relevance.
Wei is correct that UDT is a reasonable approach that sidesteps the necessity to identify a “centered” proposition (though I’d argue that it picks Sunday knowledge as the center). But I think it’s _also_ solvable by traditional means just be being clear what proposition about what prediction is being assigned/calculated a probability.
It’s a useless and misleading modeling choice to condition on irrelevant data
Strictly speaking, you should always condition on all data you have available. Calling some data D irrelevant is just a shorthand for saying that conditioning on it changes nothing, i.e., Pr(A∣D,X)=Pr(A∣X) . If you can show that conditioning on Ddoes change the probability of interest—as my calculation did in fact show—then this means that D is in fact relevant information, regardless of what your intuition suggests.
even worse to condition on the assumption the unstated irrelevant data is actually relevant enough to change the outcome.
There was no such assumption. I simply did the calculation, and thereby demonstrated that certain data believed to be irrelevant was actually relevant.
It’s a useless and misleading modeling choice to condition on irrelevant data, and even worse to condition on the assumption the unstated irrelevant data is actually relevant enough to change the outcome. That’s not what “irrelevant” means, and the argument that humans are bad at knowing what’s relevant does _NOT_ imply that all data is equally relevant, and even less does it imply that the unknown irrelevant data has precisely X relevance.
Wei is correct that UDT is a reasonable approach that sidesteps the necessity to identify a “centered” proposition (though I’d argue that it picks Sunday knowledge as the center). But I think it’s _also_ solvable by traditional means just be being clear what proposition about what prediction is being assigned/calculated a probability.
Strictly speaking, you should always condition on all data you have available. Calling some data D irrelevant is just a shorthand for saying that conditioning on it changes nothing, i.e., Pr(A∣D,X)=Pr(A∣X) . If you can show that conditioning on D does change the probability of interest—as my calculation did in fact show—then this means that D is in fact relevant information, regardless of what your intuition suggests.
There was no such assumption. I simply did the calculation, and thereby demonstrated that certain data believed to be irrelevant was actually relevant.