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This book is based on lectures given at Yale in 1971-1981 to
students prepared with a course in measure-theoretic probability.
It contains one technical innovation-probability distributions in
which the total probability is infinite. Such improper
distributions arise embarras singly frequently in Bayes theory,
especially in establishing correspondences between Bayesian and
Fisherian techniques. Infinite probabilities create interesting
complications in defining conditional probability and limit
concepts. The main results are theoretical, probabilistic
conclusions derived from probabilistic assumptions. A useful theory
requires rules for constructing and interpreting probabilities.
Probabilities are computed from similarities, using a formalization
of the idea that the future will probably be like the past.
Probabilities are objectively derived from similarities, but
similarities are sUbjective judgments of individuals. Of course the
theorems remain true in any interpretation of probability that
satisfies the formal axioms. My colleague David Potlard helped a
lot, especially with Chapter 13. Dan Barry read proof. vii Contents
CHAPTER 1 Theories of Probability 1. 0. Introduction 1 1. 1.
Logical Theories: Laplace 1 1. 2. Logical Theories: Keynes and
Jeffreys 2 1. 3. Empirical Theories: Von Mises 3 1. 4. Empirical
Theories: Kolmogorov 5 1. 5. Empirical Theories: Falsifiable Models
5 1. 6. Subjective Theories: De Finetti 6 7 1. 7. Subjective
Theories: Good 8 1. 8. All the Probabilities 10 1. 9. Infinite
Axioms 11 1. 10. Probability and Similarity 1. 11. References 13
CHAPTER 2 Axioms 14 2. 0. Notation 14 2. 1. Probability Axioms 14
2. 2."
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