The Foundations of Statistics
by Leonard J. Savage
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Book Summary Information
Author: Leonard J. SavageEdition: Paperback
Audio: English (Unknown); English (Original Language); English (Published)
Published: 1972-06-01
ISBN: 0486623491
Number of pages: 310
Publisher: Dover Publications
Book Reviews of The Foundations of Statistics
Book Review: L J Savage was never able to deal technically with ambiguity
Summary: 4 Stars
John Maynard Keynes's A Treatise on Probability(1921;TP)was given a five star rating by this reviewer because he dealt clearly and succinctly with what Ellsberg later called "ambiguity".Keynes did not use the terminology of Ellsberg.In the TP Keynes analyzed the problem of ambiguity using the term "weight of the evidence".In the General Theory(GT)Keynes used the term"uncertainty".Keynes defined an index to measure the weight of the evidence,denoted by the variable w.By definition,0<=w<=1(See p.315,TP,chapter 26).Keynes then incorporated w into a decision rule which he called a conventional coefficient of weight and risk c.Given outcome A,the decisionmaker's goal is to maximize cA,as opposed to pA or pU(A),where p equals a probability(p+q=1)and U(A)is a utility function.c=p(1/(1+q)[2w/1+w].Savage did discuss the problem of ambiguity or uncertainty or lack of evidential weight using the term vagueness.Unfortunately,after discussing the problem of vagueness,Savage decided not to deal with this problem technically.Savage's technical analysis of decision making under risk is certainly very interesting.However,his failure to deal with the problem that Keynes had already solved in his TP means that I can only give Savage four stars.
Summary of The Foundations of Statistics
Classic analysis of the subject and the development of personal probability; one of the greatest controversies in modern statistcal thought. New preface and new footnotes to 1954 edition, with a supplementary 180-item annotated bibliography by author. Calculus, probability, statistics, and Boolean algebra are recommended.
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