In article
<13006311.1209555404726.JavaMail.jakarta@[EMAIL PROTECTED]
>,
Luis A. Afonso <licas_@[EMAIL PROTECTED]
> wrote:
>An example that Probability is not Mathematics
>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.
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 assume 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.
--
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
|
