# Re: Fun With Bayes' Theorem

From: Eliezer S. Yudkowsky (sentience@pobox.com)
Date: Sat May 19 2001 - 15:40:04 MDT

Lee Corbin quoted:
>
> "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. When
> prior probabilities are given as data, the Non-Bayesean generally has no
> objection to the use of the Bayes formula, but when prior probabilities are
> lacking he deplores the Bayesean's tendency to make them up out of thin
> air. The Bayesean retorts that the Frequentist methods merely conceal the
> problem instead of solving it, and that he really is the more honest of the
> two."

Totally, unarguably CAUGHT over here. But I disagree with the summary of
the problem, which is trying to be fair to both sides. The persistence of
an argument does not, from a Bayesian perspective, demonstrate that both
sides are equally right; it can also demonstrate that both sides are
equally wrong or that the wrong side is exceptionally stubborn.

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 would tend to see a Frequentist as a special case of a Bayesian making
very odd assumptions about the priors. By contrast, I can think of no
natural way to view a Bayesian as a Frequentist making odd assumptions,
which seems to me to place Frequentism at a severe disadvantage if a
general theory is desired. 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.
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".

Hence my statement that I am "totally, unarguably CAUGHT".

Wow, there's like this whole cult of non-Bayesians that I never knew
existed. I thought they were hunted down and exterminated years ago, like
the Sith.

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"?

-- -- -- -- --
Eliezer S. Yudkowsky http://singinst.org/
Research Fellow, Singularity Institute for Artificial Intelligence

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