Thank you for that detailed reply. I just have a few comments:
“data” could be any observable property of the world
in statistical decision theory, the details of the decision process that implements the mapping aren’t the focus because we’re going to try to go straight to the optimal mapping in a mathematical fashion
there’s no requirement that the decision function be smooth—it’s just useful to look at such functions first for pedagogical reasons. All of the math continues to work in the presence of discontinuities.
a weak point of statistical decision theory is that it treats the set of actions as a given; human strategic brilliance often finds expression through the realization that a particular action is possible
“data” could be any observable property of the world
Yes but using it to refer to a person’s ideas, without clarification, would be bizarre and many readers wouldn’t catch on.
in statistical decision theory, the details of the decision process that implements the mapping aren’t the focus because we’re going to try to go straight to the optimal mapping in a mathematical fashion
Straight to the final, perfect truth? lol… That’s extremely unPopperian. We don’t expect progress to just end like that. We don’t expect you get so far and then there’s nothing further. We don’t think the scope for reason is so bounded, nor do we think fallibility is so easily defeated.
In practice searches for optimal things of this kind always involve many premises with have substantial philosophical meaning. (Which is often, IMO, wrong.)
a weak point of statistical decision theory is that it treats the set of actions as a given; human strategic brilliance often finds expression through the realization that a particular action is possible
Does it use an infinite set of all possible actions? I would have thought it wouldn’t rely on knowing what each action actually is, but would just broadly specify the set of all actions and move on.
@smooth: what good is a mean or median with no smoothness? And for margins of error, with a non-smooth function, what do you do?
With a smooth region of a function, taking the midpoint of the margin of error region is reasonable enough. But when there is a discontinuity, there’s no way to average it and get a good result. Mixing different ideas is a hard process if you want anything useful to result. If you just do it in a simple way like averaging you end up with a result that none of the ideas think will work and shouldn’t be surprised when it doesn’t. It’s kind of like how if you have half an army do one general’s plan, and half do another, the result is worse than doing either one.
Thank you for that detailed reply. I just have a few comments:
“data” could be any observable property of the world
in statistical decision theory, the details of the decision process that implements the mapping aren’t the focus because we’re going to try to go straight to the optimal mapping in a mathematical fashion
there’s no requirement that the decision function be smooth—it’s just useful to look at such functions first for pedagogical reasons. All of the math continues to work in the presence of discontinuities.
a weak point of statistical decision theory is that it treats the set of actions as a given; human strategic brilliance often finds expression through the realization that a particular action is possible
Yes but using it to refer to a person’s ideas, without clarification, would be bizarre and many readers wouldn’t catch on.
Straight to the final, perfect truth? lol… That’s extremely unPopperian. We don’t expect progress to just end like that. We don’t expect you get so far and then there’s nothing further. We don’t think the scope for reason is so bounded, nor do we think fallibility is so easily defeated.
In practice searches for optimal things of this kind always involve many premises with have substantial philosophical meaning. (Which is often, IMO, wrong.)
Does it use an infinite set of all possible actions? I would have thought it wouldn’t rely on knowing what each action actually is, but would just broadly specify the set of all actions and move on.
@smooth: what good is a mean or median with no smoothness? And for margins of error, with a non-smooth function, what do you do?
With a smooth region of a function, taking the midpoint of the margin of error region is reasonable enough. But when there is a discontinuity, there’s no way to average it and get a good result. Mixing different ideas is a hard process if you want anything useful to result. If you just do it in a simple way like averaging you end up with a result that none of the ideas think will work and shouldn’t be surprised when it doesn’t. It’s kind of like how if you have half an army do one general’s plan, and half do another, the result is worse than doing either one.