Bonjour,
Edwin T. Jaynes a publié, il y a plusieurs années déja, un article dans lequel le problème des distributions a priori est abordé de manière tout à fait différente en rapport avec une présentation basée sur la théorie de la mesure.
http://omega.albany.edu:8008/JaynesBook.html
Un travail qui semble avoir echappé et dont F.G Perye (Oak Ridge National Laboratory) avait ressorti des cartons.
Quand est-il aujourd'hui de cette approche dans l'enseignement des probabilités ?
Patrick
Bonsoir,
E. T. Jaynes : Juillet 1996
PatrickFortunately, the consistency theorems of R. T. Cox were enough to clinch matters; when one added P´olya’s qualitative conditions to them the result was a proof that, if degrees of plausibility are represented by real numbers, then there is a uniquely determined set of quantitative rules for conducting inference. That is, any other rules whose results conflict with them will necessarily violate an elementary –and nearly inescapable – desideratum of rationality or consistency.
But the final result was just the standard rules of probability theory, given already by Daniel Bernoulli and Laplace; so why all the fuss? The important new feature was that these rules were now seen as uniquely valid principles of logic in general, making no reference to ‘chance’ or ‘random variables’; so their range of application is vastly greater than had been supposed in the conventional probability theory that was developed in the early 20th century. As a result, the imaginary distinction between ‘probability theory’ and ‘statistical inference’ disappears, and the field achieves not only logical unity and simplicity, but far greater technical power and flexibility in applications.
Our system of probability could hardly be more different from that of Kolmogorov, in style, philosophy, and purpose. What we consider to be fully half of probability theory as it is needed in current applications – the principles for assigning probabilities by logical analysis of incomplete information – is not present at all in the Kolmogorov system.
As noted in Appendix A, each of his axioms turns out to be, for all practical purposes, derivable from the Polya–Cox desiderata of rationality and consistency. In short, we regard our system of probability as not contradicting Kolmogorov’s; but rather seeking a deeper logical foundation that permits its extension in the directions that are needed for modern applications.
