Objective Bayesian intervals: some remarks on Gini's approach

摘要

Some important papers were written by C. Gini in 1939 and 1943, concerning the logic of statistical inference, with a special attention to probability intervals; Gini's approach was strictly objective Bayesian. In this paper it is stressed how some Bayesian scholars have recently elaborated concepts and procedures (reference priors, Bayesian robustness) with the aim of ensuring some kind of objectivity, which was Gini's main worry. A verification of the possible errors that may result from improper choice of the prior, within a regular family of prior distributions, has been made by using prior distributions of the normal and uniform type for the mean of a normal distribution. As expected, gross errors can be made when one tries - without success - in eliciting a very precise prior; on the contrary, a correct result is obtained when the likelihood is much less dispersed than the prior; in this case, however, the Bayesian interval becomes practically coincident with the confidence interval.