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Theory of Probability: A critical introductory treatment




Theory of Probability: A critical introductory treatment

Bruno de Finetti

ISBN: 978-1-119-28637-0 March 2017 596 Pages



First issued in translation as a two-volume work in 1975, this classic book provides the first complete development of the theory of probability from a subjectivist viewpoint. It proceeds from a detailed discussion of the philosophical mathematical aspects to a detailed mathematical treatment of probability and statistics.

De Finetti’s theory of probability is one of the foundations of Bayesian theory. De Finetti stated that probability is nothing but a subjective analysis of the likelihood that something will happen and that that probability does not exist outside the mind.  It is the rate at which a person is willing to bet on something happening.  This view is directly opposed to the classicist/ frequentist view of the likelihood of a particular outcome of an event, which assumes that the same event could be identically repeated many times over, and the 'probability' of a particular outcome has to do with the fraction of the time that outcome results from the repeated trials.

Foreword ix

Preface xiii

1 Introduction 1

2 Concerning Certainty and Uncertainty 21

3 Prevision and Probability 59

4 Conditional Prevision and Probability 113

5 The Evaluation of Probabilities 153

6 Distributions 187

7 A Preliminary Survey 251

8 Random Processes with Independent Increments 311

9 An Introduction to Other Types of Stochastic Process 393

10 Problems in Higher Dimensions 401

11 Inductive Reasoning; Statistical Inference 421

12 Mathematical Statistics 447

Appendix 475

Index 571