Critical issues in different inferential paradigms

Summary The main issues which characterize the current inferential paradigms are discussed. Emphasis is given to the kind of probability that can be used and to the problem of total or partial conditioning. Through classical examples, the major role of conditioning is stressed. Some trends of the main approaches (frequentist and Bayesian) are illustrated and some comments on the completely predictive approach are also provided. Revised version of an invited paper presented at the Meeting of the Italian Statistical Society onMethodological Developments in the Different Approaches to Statistical Inferences, Cagliari, April 3–5, 1991.