Ivo Schneider
> 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