Herman Rubin wrote:
>
> I consider the Fisherian one to be the only relevant one.
> In fact, I do not think it goes far enough; at best,
> probability is a property of the real world like length
> and mass.
On the contrary: length and mass are abstractions that approximately
describe certain aspects of the real world (quantum
mechanics demonstrates this.) They can also both be used, advan-
tageously, to describe other aspects of the real world other than
those that we normally associate with them (for instance, dimensional
analysis makes good use of the fact that the natural dimension of
capacitance is length...)
Probability works like that too. Mathematically probability
is very simple and paradox-free; it "exists" only in the sense
that 24-dimensional quaternionic space or the Monster Group "exist".
Various real-world things behave in roughly the same way: both
long-run frequencies (the frequentist application of probability
theory to the real world) and degrees of belief subject to certain
mental disciplines that individuals may or may not adhere to (the
Bayesian application).
(It is undoubtedly true that in the real world a person may well
"believe" incompatible things. The word "believe" is not the3 property
of the statistical community and we cannot say "oh no you don't" to such
a person. However, those whose degrees of belief in related events do
*not* fit the Bayesian yoga and who are prepared to bet when the odds
give them an edge according to their own beliefs can be reliably (in the
long run) relieved of their stakes. This gives some objective basis to
the idea of consistent belief systems.)
-Robert Dawson
=================================================================
Instructions for joining and leaving this list and remarks about
the problem of INAPPROPRIATE MESSAGES are available at
http://jse.stat.ncsu.edu/
=================================================================
