The (in my opinion) valid criticism of the 90% number was that there
was a great deal of uncertainty in defining the urn. There was no
suggestion that the draw from the urn was illegitimate, only that the
urn was not a good model of reality.
The speaker went on to suggest that Bayesian methods overstate
confidence. I am not sure on what grounds he thought the asteroid
study was Bayesian, or whether he was simply pointing to a common
problem with statistical inference.
I challenged him afterward about decision-making under uncertainty.
It's my opinion that the hypothesis-testing view of statistics,
designed for climical experiments, is terribly misplaced in discussing
unavoidable decisions where the default is non-obvious.
If we can express only, say 3% confidence in X and say 0.08 %
confidence in not-X, we haven't used all the information available to
us. This hardly matters if the question X is purely theoretical. If we
are trying to decide whether to expend real resources on an asteroid
defense system, the 96.92 % probability, on this view, that
"statistics has nothing to say" is both ridiculous and unhelpful.
Surely we can conclude that X is more likely than not-X.
I understand that there is some philosophical problem with what
"likely" means, but it's hard for me to understand the idea that this
leads to a universal shrug and professed ignorance. At least you can
say these guys aren't cynically motivated in their attachment to the
idea that their work is very nearly useless.
mt
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