Decision theory applied to rare events

The history of statistics reveals diverging viewpoints concerning the concrete interpretation of the mathematical subject termed ''probability.'' Indeed, the frequency of rareness of the phenomena involved contribute strong elementsCS; of justification to the selection of such and such an attitude. The theory of the decision intended by some of its promoters (Abraham Wald) to reinforce the bases for conventional statistics appears to have achieved an opposite result, at the same time quite strongly justifying the Bayes' methods (Leonard J. Savage). This can result in removing a strong reluctance to use probabilistic and ''statistical'' methods in the case of rare events. Nevertheless, a close examination of the concepts and axioms of the theory reveals requirements which are likely to be difficult to satisfy within the very definition of rare events. It appears that a collective effort for better satisfying these requirements would be extremely desirable. It could contribute to the improvement of the present situation by providing a better consensus concerning an estimate of the risks