The Foundations of Statistics

by Leonard J. Savage

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.

Genres: Mathematics, Economics, Philosophy, Reference, Textbooks, Nonfiction

310 pages, Paperback

First published June 1, 1972

About the author

Born 20 November 1917, Leonard Jimmie Savage graduated from the University of Michigan and later worked at the Institute for Advanced Study in Princeton, New Jersey; the University of Chicago; and the Statistical Research Group at Columbia University. Though his thesis advisor was Sumner Myers, he also credited Milton Friedman and W. Allen Wallis as his statistical mentors.

His most noted work was the 1954 book Foundations of Statistics, in which he put forward a theory of subjective and personal probability and statistics which forms one of the strands underlying Bayesian statistics and has applications to game theory.

One of Savage's indirect contributions was his discovery of the work of Louis Bachelier on stochastic models for asset prices and the mathematical theory of option pricing. Savage brought the work of Bachelier to the attention of Paul Samuelson. It was from Samuelson's subsequent writing that random walk (and subsequently Brownian motion) became fundamental to mathematical finance.

In 1951 he introduced the Minimax regret criterion used in decision theory. The Hewitt-Savage zero-one law is (in part) named after him.

Reviews

[Chris · Rating 5 out of 5]

When I was 15 or so years old, I realised probability and statistics were insanely underappreciated subjects in school. These subjects govern effectively EVERYTHING we do. You can't make good decisions without thinking about facts probabilistically. Of course, if you're looking at this book, you already know that.

Today, probability is my full-time job. In the sense that it's everyone's full time job, yes, but also that the services I produce are based on probabilistic analyses.

This book, along with de Finetti's Theory of Probability, has changed the way I approach probability and made me a much better probabilist.

If you, against all odds, don't really know what sort of book you've ended up looking at: this is not your typical book on probability. Most books on probability and statistics take what I call a "frequentist toolbox" style, i.e. a list of recipes for standard frequentist techniques for estimation, testing, and inference.

Savage (and de Finetti, along the same vein) approach the problem instead from the perspective of consequences. How can we define probability in terms of the decisions people make? This gives rise to a subjective, or personal, view of probability. It builds a rich theory on common sense concepts you can observe in real life daily.

It's a very important (and not discussed often enough) perspective that I just can't do justice in a review. I can only recommend reading this book (and de Finetti's Theory of Probability) if you're in any way interested in probability (and you should be!)

[William Schram · Rating 4 out of 5]

The title of this book is a misnomer. There is little of what one would call statistics in this book. Instead, the focus is on probability.

Professor Leonard J Savage explains his views well. He defines the symbols, and that is all I expect from such books.

[Rusty del Norte · Rating 2 out of 5]

Foundations of Statistics is a book that discusses concepts about statistics. Inductive Inference & Axiomatic Concept of Probability are some of the early concepts discussed as well as briefly discussing Extramathematical Properties.

The core concepts deal with 3 classes of Interpretation: 1) Objectivistic, 2) Personalistic, & 3) Necessary. The rest of the book beckons back to these concepts at times. It deals with logical principles & probabilities that come up, including the interesting St. Petersburg Paradox.

However, there are bigger issues with this book. Many of the concepts are not given much discussion. Instead, its based around theoretical concepts & formulas for those theorems. If you want it explained to you in any way, this book will not do that. With so much devoted to theorem examples in the 2nd half of the book, it made for a laborious read that didn't satisfy this reader.

[Don · Rating 5 out of 5]

First half of the book is fabulously valuable and influential.

[Berk · Rating 5 out of 5]

Outstanding book but apparently not without some redundancies:

https://onlinelibrary.wiley.com/doi/a...

[Leonardo]

Citado en Microeconomic Theory Cap.6

[Sarwar Kamal]

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