The Foundations of StatisticsWith the 1954 publication of his Foundations of Statistics, in which he proposed a basis that takes into account not only strictly objective and repetitive events, but also vagueness and interpersonal differences, Leonard J. Savage opened the greatest controversy in modern statistical thought. His theory of the foundations, connected with the personalistic interpretation of probability, challenged the then dominant frequentist school. In the first seven chapters of his book, Professor Savage is concerned with the foundations at a relatively deep level. To explain and defend his theory of the behavior of a highly idealized person faced with uncertainty, he considers decision making, the sure-thing principle, qualitative and quantitative personal probability, the approach to certainty through experience, symmetric sequences of events, critical comments on personal probability, utility, observations as they affect the decision, and partition problems. In chapters eight through seventeen he discusses statistics proper — the actual devices of the discipline — from the personalistic view. He concentrates on minimax problems and on the theories of estimation and testing. Exercises are included throughout to reinforce and supplement the text. The mathematical techniques used are quite elementary, some calculus and elementary probability theory being presupposed. Understanding of all the material calls for some mathematical maturity on the part of the reader. Professor Savage had reevaluated his position somewhat during the decade and a half since the work was first published. While reaffirming the material in the first seven chapters, he had reconsidered the appropriateness of many frequentistic applications. To explain these recent developments, he added a new preface, new footnotes, and a supplementary 180-item, annotated bibliography. Because of Professor Savage's death, the revisions that he made for this edition are his final analysis of the situation. As he says on page one, "the foundations are the most controversial parts of many, if not all, sciences." In statistics, the foundation of probability is "as controversial a subject as one could name." In 1954, the controversy was very great, and although it has quieted since, the problem has yet to be resolved. A new generation of readers who have missed Savage's analysis have here an opportunity to study firsthand what his important foundation of statistics — personal probability — is, and what it means to statistical thought. |
Contents
Postulates of a personalistic theory of decision End papers | 1 |
PERSONAL PROBABILITY | 27 |
OBSERVATION | 47 |
Copyright | |
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act f Annals of Mathematical apply B₁ basic acts behavior Behrens-Fisher problem bilinear games bility called chapter coin concept conditional conditional probability consequences considered context convex convex set Criterion decision problem defined definition derived act discussion distribution dominates elements equal equivalent example Exercise expected value f and g Finetti finite number formal function gambles hypothesis idea illustrations implies infinite interpretation interval estimation least likelihood ratio likelihood-ratio test linear logic loss loss function lottery Mathematical Statistics max L(f maximin minimax rule minimax theory mixed acts n-tuples notion null objectivistic views observation Paperbound particular partition problems personal probability personalistic view possible postulate preference proba probability measure qualitative probability random variables real numbers seems sequence situation small world sufficient statistics Suppose sure-thing principle symmetry technical testing Theorem theory of personal tion typically utility verbalistic Wald