Bayes statistics: Part II

The classical statistical methodology has been developed as a tool for dealing with scientific problems. A consequence of this has been, on the one hand, a negative attitude towards prior opinions (or at least towards admitting them), and on the other hand, a certain reluctance against specifying the ultimate goal of the statistical analysis: one has contented oneself with making statements about facts, and left the rest to the applying colleages, or employers. Some modem statisticians have, in spite of supporting in principle the bayesian ideas, tried to stick to these ideals and to bring as much as possible of the classical methodology into the new theoretical structure. For this purpose, they have attempted to let the prior distribution reflect some kind of total ignorance. On the other hand, they have avoided the notion of utility and stopped the analysis at the construction of estimators, confidence regions, and tests; i.e., at what is usually referred to as statistical inference. A notable champion for this program is at present Lindley (1965).