[HM] Subjectivist vs. objectivist probability

Richard J. Griego (rjg@unm.edu)
Fri, 2 Apr 1999 10:33:59 -0700

Svein Olav Nyberg asks about the current state of the subjectivist
versus objectivist points of view regarding statistics. The discussion
is still going on among statisticians, although the vast majority of
statisticians utilize a toolkit that includes both non-Bayesian and
Bayesian methods. Some Bayesians are passionate about their point of
view (e.g. Dennis Lindley) and continue to press their perspective.
The book Operational Subjective Statistical Methods by Frank Lad of the
University of Canterbury (Wiley, 1996) presents a systematic treatment
of subjectivist methods along with a good discussion of the historical
and philosophical backgrounds of the major approaches to probability
and statistics (including what Lad calls Kolmogorov's formalist axiomatic
formulation). Lad's dismissal of Kolmogorov's approach to probability
as having "no meaning in itself" seems severe since the axioms are
based on intuitive ideas about reality and ultimately it is the
effectiveness of the results based on the axiom system that convince
us or not about the usefulness of the axioms.

Fuzzy logic approaches to probability (L.A. Zadeh and his followers)
present a difference between "possibility theory" and probability theory;
see, for example, Possibility Theory by D. Dubois and H. Prade, 1988 or
Fuzzy Set Theory by H. J. Zimmerman (Kluwer Academic Publishers, 1991).
This approach is used by engineers and operations researchers.

The successful applications of probability theory to other areas of
mathematics that I had previously mentioned are all based on Kolmogorov's
axioms and their extensions (such as conditional expectation given a sigma
algebra due to Joseph Doob). The working probabilists involved in these
activities accept and use the Kolmogorov/Doob formulations.

I am not an expert in these things, but the references can give one a good
orientation.

Richard J. Griego

-----Original Message-----
From: Svein Olav Nyberg <solan@pair.com>
To: historia-matematica@chasque.apc.org
Date: Wednesday, March 31, 1999 5:56 PM
Subject: Re: [HM] Is Statistics Part of Mathematics?

> To Richard J. Griego ...
>
>> (the probability of an event is the long run value of the relative
>> frequency of the event based on actual data).
>
> This is the frequentist view of probability. Since I am not in the
> field, I don't know where the arguments are going, but would be
> interested in knowing what the current state of development of the
> subjectivist/epistemological theory of probability.
>
>
> Svein Olav Nyberg <solan@pair.com>
> http://www.leikestova.org/solan/
>