Sul ruolo della probabilità e della verosimiglianza nella programmazione degli esperimenti

Abstract

The first part of this paper investigates the role of probability at the time of planning an experiment, starting from the work of Fisher and the introduction of randomization. The aim is to explore the connections between the choice of the design and the statistical model on one hand and the inferential method employed to analyze the data on the other. There is a special emphasis on the importance of the linear model in the classical theory of Design of Experiment, which has led to Jack Kiefer's theory of optimality. The second part is centred on the use of the likelihood function and of Fisher's information matrix in designing experiments for non linear models, in particular sequential and adaptive experiments; the role of the information derived from the "limit" experiment is considered. The Likelihood Principle is also briefly discussed from the viewpoint of the experimental plan. This paper assumes the frequentist framework, with a short mention of the Bayesian approach in the last paragraph.