Optimum Inductive Methods
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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.
Acknowledgments1Introduction1Pt. IInductive Probabilities, Bayesian Statistics, and Verisimilitude2The Theory of Inductive Probabilities: Basic Features and Applications133Bayesian Statistics and Multinomial Inferences: Basic Features204Bayesian Point Estimation, Verisimilitude, and Immodesty38Pt. IIDe Finetti's Theorem, GC-Systems, and Dirichlet Distributions5Exchangeable Inductive Methods, Bayesian Statistics, and Convergence Towards the Truth516GC-Systems and Dirichlet Distributions57Pt. IIIVerisimilitude, Disorder, and Optimum Prior Probabilities7The Choice of Prior Probabilities: The Subjective, Aprioristic, and Contextual Approaches758The Epistemic Problem of Optimality (EPO): A Contextual Approach1039The Contextual Approach to EPO: Comparisons with Other Views12310Disordered Universes: Diversity Measures in Statistics and the Empirical Sciences13911Concluding Remarks150Notes154References177Index of Names185Index of Subjects188
