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supplement - question about language in quantiles section #80
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What does it mean for a random variable to be as low as possible? |
I'm not sure. What does it mean for a decision maker to select a random future loss? |
What about "The decision problem is then to select an action |
That's like buying a stock. It's a random payout. The buying is easy to define... saying why you want to buy it is the hard part. |
Sure. Will replace.
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Maybe this: The decision problem is then to select an action Admissibility with respect to the loss |
It feels like a lot of words that don't clarify the situation to me:
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I mean, this sentence and the 2 or 3 before and after it could get disappeared if the whole effort seems irreconcilable with immediate goals. That would put us in line with the standard forecast literature treatment. But for me, a lot is going on in this section conceptually and represents some amount of resolution of several years of confusion with this stuff. I'm pretty sure that admissibility is actually a core component of decision formalization via a loss function and not specific to minimax. And my attachment to the phrase "random future loss" is because the econ-theory and finance alternatives of "prospect" and "contingent claim/payoff" seem much worse, but the concept feels essential to But again, there is no reason for this stuff to be in this piece of writing if it seems inappropriate. I can cut and paste into something that isn't trying to deal with the decision theory stuff on the fly. |
Meant to add, the driving force in my brain for all of this is the insanely esoteric but (in my opinion) profound page 80 in Dawid. (Love how he calls this a "concrete framework.") |
Specifically, this line:
utility-eval-papers/alloscore_manuscript/supplement.rnw
Lines 227 to 228 in 4e0125a
My intuition sits more easily with the idea that the decision maker is going to select a decision$x$ in a way that aligns with the preference that the random future loss $l(x,Y)$ be as low as possible given any realization $Y=y$ .
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