From: Lee Corbin (lcorbin@tsoft.com)
Date: Wed Jul 09 2003 - 16:52:00 MDT
Eliezer writes
> Not the book, "Probability Theory, the Logic of Science".
That's the new one. It's unfinished and has all his great polemics
in it. Jaynes was quite the guy. I agreed very much with his
attitudes on many issues only marginally relevant to probability
and decision theory---but basically, he agreed with Kolmogorov
and disagreed with DeFinitti in the end.
I have to get that book. I could have sworn it was on-line too,
or at least a lot of the chapters. But maybe I was thinking of
> The lectures, "Probability Theory with Applications in Science
> and Engineering", which are online, and also more accessible.
>
> http://bayes.wustl.edu/etj/science.pdf.html
Amazon has the big book, I'll get it, but meanwhile thanks for the
link to this.
On Amazon, by the way, the reviews are quite interesting. Here is
an excerpt from one
Reviewer: Michael Hardy
To "pure" mathematicians, probability theory is measure
theory in spaces of measure 1. To the extent to which
you remain a "pure" mathematician, this book [Prob The
Logic of Science] will be incomprehensible to you.
To frequentist statisticians, probability theory is the
study of relative frequencies or of proportions of a
population; those are "probabilities".
To Bayesian statisticians, probability theory is the study
of degrees of belief. Bayesians may assign probability 1/2
to the proposition that there was life on Mars a billion
years ago; frequentists will not do that because they cannot
say that there was life on Mars a billion years ago in
precisely half of all cases -- there are no such "cases".
To _subjective_ Bayesians, probability theory is about
subjective degrees of belief. A subjective degree of belief
is merely how sure you happen to be.
"Noninformative" _objective_ Bayesians assign "noninformative"
probability distributions when they deal with uncertain
propositions or uncertain quantities, and replace them with
"informative" distributions only when they update them because
of "data". "Data", in this sense, consists of the outcomes of
random experiments.
"Informative" _objective_ Bayesians -- a rare species -- ask
what degree of belief in an uncertain proposition is logically
necessitated by whatever information one has, and they don't
necessarily require that information to consist of outcomes of
random experiments.
Jaynes is an "informative" objective Bayesian. This book is his
defense of that position and his account of how it is to be used.
Hooray! "Subjective" used to drive me crazy (even though now, after
further progress understanding Many Worlds, it's beginning to make
sense after all!). But I still hope that "objective" can be retained.
"Pure" mathematicians will not find that this book resembles that
branch of "pure" mathematics that they call probability theory.
...Unfortunately Jaynes's misunderstandings may cause some others
to misunderstand him when he is right. Statisticians are more
informed than "pure" mathematicians and will disagree with Jaynes
for better reasons. _Some_ statisticians will agree with him.
Jaynes has many flaws, made all the more annoying by the fact that
we need to overlook them in order to understand him. His message
is important.
Lee
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