[ExI] Bayesian epistemology

Michael M. Butler mmbutler at gmail.com
Mon Aug 6 16:46:29 UTC 2007

> It appears you may be unclear about the distinction between
> probability and likelihood.

1) It's been a while since I've cracked open my E. T. Jaynes
(_Probability Theory As Extended Logic_) and I seem to have packed it
prior to my recent move. Can you point me (us) to someone on teh
Intarweb who does a good concise job of making this distinction clear
in a Bayesian (but not Bayesianismistic) context?

2) The other thing that is confusing me about the (0,1) range Russell
Wallace used is that a huge part of that book (even unto the title!)
was about propounding the view that probability theory starting with
Laplace generalizes Aristotelian logic. Which, it sems to me, means
that it reduces to deductive logic when hypotheses are T/F. And a true
"reduction", it seems to me, would be that the interval dealt with is
actually [0,1].

Now, is that a limit case that can only be approached, as the "open
interval" notation used by Russell W. indicates? Is it factually the
case that can only speak of the results of Bayesian/Jaynesian analyses
terms of zillions of dB rather than 0 or 1? And if so, is that an
indictment of any kind, or merely a description of fact--that
Aristotelian logic works fine at the limit, and Bayesian stuff works
all the way up to just outside that?

3) I agree with Russell W. that plucking numbers from the air seems
odd and prone to misestimation, but I also think that (empirically) if
someone claims to be 90% confident and reality shows them they "ought
to have been" only 30% confident, the problem is with their bias, not
with Bayes per se.

Robin Hanson has (as many on the list must know) been running the
Overcoming Bias website for some time now, and it's worth at least
peeking in from time to time.

In the case mentioned above, I think Jaynes would say that after you
got a negative outcome it would behoove you to include that in your
priors for your next estimate and revise your confidence rating.
Iteration and refinement are part of the deal. Am I right?

Sorry for the tyro questions.

         Michael M. Butler  :  m m b u t l e r  ( a t )  g m a i l . c o m
I've pulled birdshot out of ducks that didn't teleport at the right
time.  --J Thomas

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