Bruno de Finetti 
Theory of Probability 
A Critical Introductory Treatment

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.

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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

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Bruno de Finetti (1906 – 1985) is today recognized as the greatest Italian applied mathematician of the 20th century. He published extensively and acquired an international reputation in the small world of probability mathematicians. He is noted for his operational subjective conception of probability and for de Finetti’s theorem on exchangeable sequences of random variables.