Principio di verosirniglianza e scelta della legge a priori nell inferenza statistica

Abstract

According to a common opinion, if all designs produce proportional likeliLoods, one sbonld make an identical inference about a parameter from the data d irrespective of the design which yields d. This thesis is not surprising in Bayesian approach. In fact, Bayesians support that inference is made in terms of the posterior alone and it is independent of design. On the contrary, the corrected Bayes formula sbows that the posterior depends on the sampling rule s. Namely, in principle, the piece of information about s is relevant for the purpose of inference. Besides, the paradoxical consequences of the irrelevance of sampling rule in statistical inference (both in general and in the case of sampling from finite populations) can be considered as counter-examples against this thesis. In conformity with the sampling rule, a hypothesis h is supported rather than another. In other words, the equiprobability assumption is to be linked to the idea of the impartiality of sampling with respect to the set of the considered hypotheses. In line with such a conception, prior probabilities are determined in an objective way according to the original version of Jeffreys' prior, and the use of Bayes formula as an inductive tool is confirmed (in sampling from finite/infinite populations).