Subject: Re: BISC: A Challenge to Bayesians (augmented version)
From: MVCS (firstname.lastname@example.org)
Date: Mon Aug 07 2000 - 17:23:52 MET DST
"Michelle T. Lin" <email@example.com> wrote:
>....My examples are intended to challenge the unquestioned belief
>within the Bayesian community that probability theory can handle any
>kind of information, including information which is perception-based.
I question your assertion. Please provide documentation and cite
sources which prove and demonstrate your assertion.
Please also define what you mean by "handle" and show documentation
and cite sources that prove and demonstrate that your definition is
the same or different than that used "within the Bayesian community".
Alternately, please prove and demonstrate that "the Bayesian
community" is monolithic in "their" intrepretation, application, and
use of the term "handle".
>However, it is possible -- as sketched in the following -- to
>generalize standard probability theory,
Please provide a brief definition of what you call "standard
>PT, in a way that adds to PT a
>capability to operate on perception-based information.
>From the tone of your post, I assume that your statement here is
nothing less than global in breadth of application (as in "within the
Bayesian community", and "the unquestioned belief"). Do you not
purport that this "way" is unqualifiably capable of operating on
perception-based information, and that this capability is somehow
intrinsically and inherently different from any/all "ways" that "the
Bayesian community" is capable of handling such information? Or have I
misread your intent?
>...progression from crisp sets to fuzzy sets,
In your opinion this characteristic is unable to be shared or
represented in any way when using Bayesian methods?
>... In PT+, probabilities, functions,
>relations, measures and everything else are allowed to have fuzzy
>denotations, that is, be a matter of degree.
Again, this characteristic is unable to be shared or represented in
any way when using Bayesian methods?
> In particular,
>probabilities described as low, high, not very high, etc. are
>interpreted as labels of fuzzy subsets of the unit interval or,
>equivalently, as possibility distributions of their numerical values.
I've done the same with NNs. And then cast them as Bayesian
structures. Your assertion is inaccurate to the extent that it is
meant to circumscribe a sacred territory germain ONLY to fuzzy set
theory and its applications.
>... By fuzzy granulation of a variable, X,
>what is meant is a partition of the range of X into fuzzy granules,
>with a granule being a clump of values of X...
Again, I've done this in an NN implementation that has a direct
correlary in a Bayesian structure. Your assertion is again inaccurate
if meant to designate an exclusive processing method that can not be
reproduced by Bayesian means.
>...(c) nl-generalization involves an addition to PT++ of a
>capability to represent the meaning of propositions expressed in a
I do this with Bayesian nets all the time. Your assertion is
>...In summary, contrary to the central tenet of Bayesian belief,
Please define what you mean by "the" central tenet of Bayesian belief
as it supports your assertions, and provide citations that prove and
demonstrate that this is "the" "central tenet" of "the Bayesian
>... there is a widely held belief that probability theory,
>upgraded or not, is sufficient for dealing with any or all issues
>which relate to partial certainty or incompleteness of information.
Please specify. You seem to be jausting with windmills (IMO). You are
indeed becomming aware of the limitations of certain processing
methods and applications which have used certain technologies. But
these limitations are, IMO, to a large degree the fault of the
process, methodology, and implementation of technologies rather than
an inherent flaw of the basic technologies used to embody the
implementation of the concepts.
In other words, I think you are throwing the baby out with the bath
water. IMO, whatever technology works is the one to use. I've seen
perception-based Bayesian applications, and perception-based problems
for which it is obvious that Bayesian methods will not suffice. Same
for FL. Same for NNs. Same for LISP-based technologies. Same for
BTW, I am a pragmatist.... not a "Bayesian".
Mind & Vision Computer Systems
"Intelligent Processing Systems for the Energy Industry"
| Jeffrey L. Baldwin |
| Voice/Fax/Data: (972) 238-5503 |
| email: firstname.lastname@example.org email@example.com |
| http://idt.net/~mvcs |
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