Dear Kathy:
Thanks for the insightful comments. Here is what I have to say.
(a) Please note that my comment regarding imprecise
probabilities relates to standard axiomatics of standard probability
theory, PT, and not to what may be found in research monographs.
However, construction of an axiomatic system for probability theory with
imprecise probabilities is complicated by the fact that there are many
different ways in which probabilities may be imprecise. Can you point me
to a comprehensive theory which goes beyond what may be found in
Walley's treatise on imprecise probabilities? Is there a general
definition of conditional probability when the underlying probabilities
are imprecise?
(b) When we describe an imprecise probability by a second-order
probability distribution, we assume that the latter is known precisely.
Is this realistic? Furthermore, if at the end of analysis we compute
expectations, as we usually do, then the use of second-order
probabilities is equivalent to equating the imprecise probability to the
expected value of the second-order probability. For these and other
reasons, second-order probabilities are not in favor within the
probability community.
(c) When an imprecise probability is assumed to be
interval-valued, what is likely to happen is that after a few stages of
computation the bounding interval will be close to [0,l].
(d) With regard to your comment on perceptions, see my paper,"
A New Direction in AI--Toward a Computational Theory of Perceptions," in
the Spring issue of the AI Magazine. In my approach, the point of
departure is not a collection of raw perceptions,but their description
in a natural language,e.g.,"it is very unlikely that Jane is very rich
." Standard probability theory cannot deal with perception-based
information because there is no mechanism in the theory for
understanding natural language.
(e) Your points regarding novel modes of computation are well
taken. No disagreement.
With my warm regards.
Lotfi
-- Professor in the Graduate School, Computer Science Division Department of Electrical Engineering and Computer Sciences University of California Berkeley, CA 94720 -1776 Director, Berkeley Initiative in Soft Computing (BISC)Address: Computer Science Division University of California Berkeley, CA 94720-1776 Tel(office): (510) 642-4959 Fax(office): (510) 642-1712 Tel(home): (510) 526-2569 Fax(home): (510) 526-2433, (510) 526-5181 zadeh@cs.berkeley.edu http://www.cs.berkeley.edu/People/Faculty/Homepages/zadeh.html
This archive was generated by hypermail 2b29 : Sun Sep 30 2001 - 09:22:23 PDT