Optimum Inductive Methods

1. Front Matter

   Pages i-xiii

   PDF

2. Introduction

   1. Introduction

      • Roberto Festa

      Pages 1-9

3. Inductive Probabilities, Bayesian Statistics, and Verisimilitude

   1. Front Matter

      Pages 11-11

      PDF

   2. The Theory of Inductive Probabilities: Basic Features and Applications

      • Roberto Festa

      Pages 13-19

   3. Bayesian Statistics and Multinomial Inferences: Basic Features

      • Roberto Festa

      Pages 20-37

   4. Bayesian Point Estimation, Verisimilitude, and Immodesty

      • Roberto Festa

      Pages 38-47

4. De Finetti’s Theorem, GC-Systems, and Dirichlet Distributions

   1. Front Matter

      Pages 49-49

      PDF

   2. Exchangeable Inductive Methods, Bayesian Statistics, and Convergence Towards the Truth

      • Roberto Festa

      Pages 51-56

   3. GC-systems and Dirichlet Distributions

      • Roberto Festa

      Pages 57-71

5. Verisimilitude, Disorder, and Optimum Prior Probabilities

   1. Front Matter

      Pages 73-73

      PDF

   2. The Choice of Prior Probabilities: The Subjective, Aprioristic, and Contextual Approaches

      • Roberto Festa

      Pages 75-102

   3. The Epistemic Problem of Optimality (EPO): A Contextual Approach

      • Roberto Festa

      Pages 103-122

   4. The Contextual Approach to EPO: Comparisons with Other Views

      • Roberto Festa

      Pages 123-138

   5. Disordered Universes: Diversity Measures in Statistics and the Empirical Sciences

      • Roberto Festa

      Pages 139-149

   6. Concluding Remarks

      • Roberto Festa

      Pages 150-153

6. Back Matter

   Pages 154-194

   PDF

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.

• argue
• bayesian statistics
• knowledge
• logic
• philosophy of science
• probability
• science
• statistics

• Fellow of the Department of Philosophy of Science, University of Groningen, The Netherlands

  Roberto Festa

Policies and ethics