In article
<30309611.1209672492968.JavaMail.jakarta@[EMAIL PROTECTED]
>,
Luis A. Afonso <licas_@[EMAIL PROTECTED]
> wrote:
>( The axiomatic Theory of Probability (Kolmogorov)
>One starts with a sensible notion: The sample Space is the set of all
possible outcomes Omega = ( x1, x2,,xn) issued from a trial (random
experiment)... So far, so good.)
>Herman Rubin said relative to my above note:
>*** This is adequate only for the purpose of proving SOME theorems. The
above is a REPRESENTATION, and for any problem, there may be many usable
sample spaces. The representation, extended, is fine for probability, but
not adequate for statistics. For statistics, the measure on the sample
space depends on the model, which is unknown. There can be a choice of
experiments as well. The purpose of statistics is to come up with good
procedures for taking actions, given the user's loss-prior product. Now we
ass
>ume that the real world corresponds sufficiently to this model that we
can produce procedures for action. The loss-prior product gives the
im****tance of making "wrong" decisions for an action, and one is trying to
choose an action which minimizes this. I suggest that one try to make these
conceptions sufficiently internalized that good things result. Much harm is
done by the misuse of statistical methods without understanding. ***
>My comment
>Though I understood properly you agree (in general) with I said about
Probability and Statistics
>I should add something, I think essential, following your sentence, I
applaud
>*** The representation, extended, is fine for probability, but not
adequate for statistics.***
>THAT is (I didnt put down by lapse):
>A Statistician, reading the Kolmogorovs Axiomatic, dont fail to ask
himself: BUT WHAT A HELL WHAT PROBABILITY IS?
Just as length, mass, charge, energy exist, so does
probability.
Now the Kolmogorov Axioms are how we believe probability
behaves, just as the other objects named above have
axiomatic properties. We think we understand the other
properties of the real world well, because we can measure
them well, while the properties of probability are such
that it cannot be measured well.
We are stuck with that, and therefore often cannot be
that sure that our action is the correct one to take.
We cannot change that, so we must accept it.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@[EMAIL PROTECTED]
Phone: (765)494-6054 FAX: (765)494-0558
|
