Optimum Inductive Methods: A Study in Inductive Probability, Bayesian Statistics, and Verisimilitude

ISBN-13: 9780792324607 / Angielski / Twarda / 1993 / 194 str.

Roberto Festa; R. Festa

Opis

This book deals with a basic problem arising within the Bayesian approach 1 to scientific methodology, namely the choice of prior probabilities. The problem will be considered with special reference to some inference methods used within Bayesian statistics (BS) and the so-called theory of inductive 2 probabilities (T/P). In this study an important role will be played by the assumption - defended by Sir Karl Popper and the supporters of the current verisimilitude theory (VT) - that the cognitive goal of science is the achievement of a high degree of truthlikeness or verisimilitude. A more detailed outline of the issues and objectives of the book is given in Section 1. In Section 2 the historical background of the Bayesian approach and the verisimilitude theory is briefly illustrated. In Section 3, the methods used in TIP and BS for making multinomial inference are considered and some conceptual relationships between TIP and BS are pointed out. In Section 4 the main lines of a new approach to the problem of the choice of prior probabilities are illustrated. Lastly, in Section 5 >the structure of the book is described and a first explanation of some technical terms is provided.

Spis treści

1. Introduction. Part I: Inductive Probabilities, Bayesian Statistics, and Verisimilitude. 2. The Theory of Inductive Probabilities: Basic Features and Applications. 3. Bayesian Statistics and Mulinomial Inferences: Basic Features. 4. Bayesian Point Estimation, Verisimilitude, and Immodesty. Part II: De Finetti's Theorem, GC-Systems, and Dirichlet Distributions. 5. Exchangeable Inductive Methods, Bayesian Statistics, and Convergence towards the Truth. 6. GC-Systems and Dirichlet Distributions. Part III: Verisimilitude, Disorder, and Optimum Prior Probabilities. 7. The Choice of Priors Probabilities: the Subjective, Aprioristic, and Contextual Approaches. 8. The Epistemic problem of Optimaility (EPO): a Contextual Approach. 9. The Contextual Approach to EPO: Comparisons with Other Views. 10. Disordered Universes: Diversity Measures in Statistics and the Empirical Sciences. 11. Concluding Remarks. Notes. References. Index of Names. Index of Subjects. List of Requirements and Acronyms.