Subject: [HM] on dependencies of events in probability theory
From: Vorob'ov O.Yu. (vorob@scn.ru)
Date: Wed Jun 21 2000 - 19:45:08 EDT
Dear HM list members,
thank everyone very much who responded to my request to vote on
classification of dependencies between events in probability theory.
Now the result is 23 "NO" and 2 "YES".
It is unexpectedly for me since the problem of classification of
dependencies of events is very important in my opinion. I think it is the
main problem of probability theory. The idea of independence differs the
probability theory from the general theory of measure. The probability
theory can be called the science that studies statistic dependencies and
statistic interactions. But the fact is that more often we tell about the
independence leaving for different kinds of dependencies the field where the
independence is absent. It's easy to understand, because the independent
situations are more obviously and simpler to analyze. But everybody will
agree that the ocean of dependencies is far richer with itself
representatives then a small isle of independence. Perhaps, only with
appearance and development of the theory of random finite abstract sets the
attention of researchers before trampled far and wide the isle of
independence and crowded on it's bored bank began to turn little by little
to unknown and inexhaustible ocean of statistic dependencies. The same
dependencies that are fastened to subsets of random set by probabilistic
measure, in side of the only worthy of note idea of the probability theory
distinguishes it from the general theory of measure.
Let's to turn upside down the pyramid and begin to study the diversity of
statistic dependencies on the poor independent background instead of study
the rare statistic independence on the boundless background of dependencies.
Statistic dependencies are founded on the dependencies between events,
elements of the algebra of probabilistic space, over what the probability, a
source and a creator of all kinds of statistic dependencies between events,
is given. The first humble wish which is appearing in a soul of researcher
has found himself on the bank of the foggy ocean of statistic dependencies
is to try to classify dependencies by the typical statistic signs in cause
of even mark the outlines of nearby banks and to plan the routes of the
first voyages.
Best wishes.
Oleg Yu. Vorob'ov
Institute of Computational Modeling
Russian Academy of Sciences
Krasnoyarsk State University
Akademgorodok 18-46
Krasnoyarsk, 660036, Russia
FAX: +7 3912 43-27-56
voice: +7 3912 49-47-95
email : vorob@scn.ru
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