Eliezer Yudkowsky wrote
>> "It seems that thinkers in the field of probability and statistics are
>> divided into two armed camps, the Bayeseans and the Non- Bayeseans. The
>> fact that such a divsion has existed amongst educated people for over sixty
>> years suggests that neither side can clearly be shown to be wrong.
>
>Totally, unarguably CAUGHT over here.
It's quite admirable to be able to so easily admit that you've
been wrong (even if it was a minor aspect of the argument). Now
if you were as slippery as I am---they don't call me "eeL" for
nothing---then you'd learn to change sides at the first moment
that it started to appear that you were wrong, and thus convince
a lot of the spectators that you were on the winning side all
along.
>The impersistence of an argument is strong evidence that one side is
>right. The persistence of an argument is necessarily (from a Bayesian
>perspective) a blow, but not necessarily a *severe* blow; it can in fact
>be a very weak blow.
I agree. Did I ever say otherwise? :-)
>I would tend to see a Frequentist as a special case of a
>Bayesian making very odd assumptions about the priors.
Like maybe **no assumptions**.
>By contrast, I can think of no natural way to view a Bayesian
>as a Frequentist making odd assumptions,
Yes, a Frequentist can only allow that a Bayesian is making
intelligent assumptions. Only the scruples (or, more likely,
dogmatism) of the Frequentist causes him to shy away from
those most reasonable assumptions.
>which seems to me to place Frequentism at a severe disadvantage if a
>general theory is desired.
I'm not sure that a general theory is desired (contrary to the
existence of an actual "division into armed camps"). As Rodney
King said, "Can't we just all get along?" Amara Graps in her
last post on this topic refered to an email she'd posted in 1999
that was quite illuminating about Bayesian procedures in the
sciences. Evidently, for many scientific purposes, Bayesianism
works better. I wonder what the Frequentists would retort. Maybe
I should send them my problem of the guy who consults a mathematician
about the sex of his unborn child.
>It is not a question of "making up prior probabilities out
>of thin air", but rather the *necessity* of specifying *some*
>set of priors in order for a well-defined problem to exist at all.
Yes; a well-defined sensible real world problem, that's for sure.
>If the Frequentists don't like our priors they are perfectly willing to
>make up their own; the key point is that the priors should be explicitly
>stated and exposed to public challenge, and to do otherwise is indeed
>"concealing the problem instead of solving it".
Oh, I think that in most cases they do. On most problems, there
isn't any disagreement, just as you'd expect. They merely get
(childishly?) upset when Bayesians pronounce about a certain
problem, "The probability is X", when all they can do is point
to likelihood curves and what not.
>So, Lee, I suppose you would argue that the so-called
>"if statement" in programming should really be named
>the "if-and-only-if statement"?
Could you explain? I don't get it.
Lee Corbin
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