Optimum Inductive Methods

The problem of the choice of prior probabilities for Bayesian inferences is considered, with special reference to the theory of inductive probabilities and the analysis of the multinomial inferences provided by Bayesian statistics. Among other things, it is argued that the choice of prior probabilities in a given empirical inquiry should be suitably restricted by specific "contextual constraints" such as the available background knowledge and the cognitive goal of the inquiry, where this goal is assumed to be the achievement of a high degree of verisimilitude. One of the features of the book is it attempts a "coordinated development" of Bayesian statistics, the theory of inductive probabilities, and the verisimilitude theory. The book should be of interest to researchers and readers concerned with Bayesian inference and, more generally, to readers engaged in inductive logic, philosophy of science and statistics.