Re: Journal ref for applied Bayesian Analysis

From: Osher Doctorow (mdoctorow_at_comcast.net)
Date: 11/15/04 

Date: Mon, 15 Nov 2004 21:10:01 +0000 (UTC)

On Mon, 15 Nov 2004 10:48:42 -0700, Bob Ehrlich wrote:
>Having lurked and learned in this forum for a number of years, I have

>begun to admit that the "old fashioned" frequentest statistical
>procedures that I engage in to this day are flawed in concept. Dr.
>Rubin's and others arguments are slowly sinking in. Now is the time
for
>me to read some journal articles written by Baysean practitioners
who
>are not professional statisticians. Such papers should not be
tutorials
>but should be an attempt to solve a problem in science or
engineering.
>Please recommend some gems.

I don't understand what causes something to "sink in" other than
Professor Rubin's high academic position - and if you regard that as
the "straw that broke the camel's back" (in a positive sense), then
I can "sell you the Brooklyn Bridge cheap".

Bayesians have very good methods compared with frequentists, but
you apparently haven't been reading my postings and threads comparing
Bayesian and Probable Influence methods. Where on the list do you
lurk - in the "conformist" part? A key point about having something
like Probable Influence (PI) to compare with Bayesian methods is that
it brings into the open various anomalies and difficulties with
Bayesian methods as well as good aspects of Bayesian methods. Bayes-
ian papers almost never give comparisons that put their whole theory
in a bad light regarding some topic, and this largely derives from
what in my opinion is a defective understanding of mathematical
probability, statistics, and other branches of mathematics as well
as hard sciences like physics.

You seem to want to leap into applications before questioning
foundations and issues and objections and pros and cons. Where has
Professor Rubin said anything about pros and cons in his email? In
fact, he refers us to other papers of his - apparently his time
cannot be wasted in summarizing issues concisely (or maybe he
doesn't consider that there are any - compare Professor Emeritus
Pearl's (a Bayesian Engineering Professor at UCLA) attacks upon
opponents of Bayesian methods in what comes close to a vendetta.
Pearl has hundreds of published papers and books - so do almost
all senior professors who have hardly contributed creative ideas
in their lives. See my last few threads for more on these types of
issues, but best of all see the next paragraph.

To show you how ridiculous the lack of consideration of issues has
become, Bayesians divide probabilities of form P(AB)/P(A) where
P(A) is the probability of A and is not 0 and P(AB) is the prob-
ability of "A and B" or technically the intersection of set/events
A, B. Probable Influence (PI), which is defined as P(A-->B) where
(A-->B) is the set/event (AB')' where AB' is the intersection of A
and the complement of B (the part of the universe outside B) and '
(prime) denotes complement. P(A-->B) reduces mathematically to
P(AB) - P(A) + 1 which is P(AB)/P(A) with division replaced by
subtraction (the 1 occurs from the mathematics and not from the
definition explicitly, although it has the interesting role of
keeping the result a probability). By comparing what happens to
P(AB)/P(A) versus P(AB) - P(A) + 1 in many difference scenarios, both
theoretical and practical, you get the various threads of my postings
on sci.stat.math. If some are harder, look a while and you'll find
ones that start from scratch. Then you'll learn the issues and
comparisons with Bayesian methods. They are far deeper than the
issues with "frequentist" methods. For example, P(A-->B) is defined
for P(A) = 0, but P(AB)/P(A) is not, and the latter also "blows up"
in a small neighborhood of 0. This is precisely where Rare Events
apply, and PI turns out to be the same as Rare Event Theory whose
asymptotic-approximation analog is Large Deviations Theory (with a
big literature but no history of connection with PI or Rare Event
Theory).

Osher Doctorow

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