Inductive Principles of the Search for Empirical Dependences (Methods Based on Weak Convergence of Probability Measures)

Abstract

This chapter discusses the inductive principles of the search for empirical dependences. Problems of inductive type, when a general law has to be found on the basis of a finite number of observations, are one of the important trends of analysis. To begin investigations in the field of induction, one should first formulate the general model embracing as broad a class as possible of problems classified as inductive. This model will be the problem of expected risk minimization from empirical data. To obtain the conditions of consistency solely in terms of the characteristics of the set as a whole, a stronger concept of consistency is used. In the 1920s, a philosopher, K. Popper, working on induction theory suggested the principle of falsifiability. Popper thought that the necessary condition for the justification of the induction method is a possibility of falsifying the method—the existence of such a set of propositions for which a general rule cannot be found.