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

ISBN-13: 9789048143184 / Angielski / Miękka / 2010 / 194 str.

R. Festa

Opis

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 most original features of the book is the attempt at a coordinated development' of Bayesian statistics, the theory of inductive probabilities, and the verisimilitude theory. The book will be of special interest to researchers and readers concerned with Bayesian inference and, more generally, to readers engaged in inductive logic, philosophy of science and statistics.

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.