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E. T. Jaynes

Probability Theory: The Logic of Science Annotated Edition

by E. T. Jaynes (Author), G. Larry Bretthorst (Editor)

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Going beyond the conventional mathematics of probability theory, this study views the subject in a wider context. It discusses new results, along with applications of probability theory to a variety of problems. The book contains many exercises and is suitable for use as a textbook on graduate-level courses involving data analysis. Aimed at readers already familiar with applied mathematics at an advanced undergraduate level or higher, it is of interest to scientists concerned with inference from incomplete information.

ISBN-10

0521592712
ISBN-13

978-0521592710
Edition

Annotated
Publisher

Cambridge University Press
Publication date

June 9, 2003
Language

English
Dimensions

7.25 x 1.5 x 10.25 inches
Print length

753 pages
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Editorial Reviews

Review

"Tantalizing ideas one of the most useful and least familiar applications of Bayesian theory Probability Theory is considerably more entertaining reading than the average statistics textbook the conceptual points that underlie his attacks are often right on."
Science

"This is a work written by a scientist for scientists. As such it is to be welcomed. The reader will certainly find things with which he disagrees, but he will also find much that will cause him to think deeply not only on his usual practice by also on statistics and probability in general. Probability Theory: The Logic of Science is, for both statisticians and scientists, more than just 'recommended reading': It should be prescribed."
Mathematical Reviews

"The rewards of reading Probability Theory can be immense."
Physics Today, Ralph Baierlein

“This is not an ordinary text. It is an unabashed, hard sell of the Bayesian approach to statistics. It is wonderfully down to earth, with hundreds of telling examples. Everyone who is interested in the problems or applications of statistics should have a serious look.”
SIAM News

"The author thinks for himself and writes in a lively way about all sorts of things. It is worth dipping into it if only for vivid expressions of opinion; There are many books on Bayesian statistics, but few with this much color."
Notices of the AMS

Book Description

New and original interpretation of probability theory, with applications to a wide range of subjects.

Product details

Publisher ‏ : ‎ Cambridge University Press; Annotated edition (June 9, 2003)
Language ‏ : ‎ English
Hardcover ‏ : ‎ 753 pages
ISBN-10 ‏ : ‎ 0521592712
ISBN-13 ‏ : ‎ 978-0521592710
Item Weight ‏ : ‎ 3.62 pounds
Dimensions ‏ : ‎ 7.25 x 1.5 x 10.25 inches

Best Sellers Rank: #387,266 in Books (See Top 100 in Books)
- #145 in Statistics (Books)
- #159 in Mathematical Physics (Books)
- #574 in Probability & Statistics (Books)

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4.7 out of 5

130 global ratings

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The greatest book ever written on Statistics!

Reviewed in the United States 🇺🇸 on February 20, 2023

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To me, this is the greatest book ever written on Statistics. I have studied statistics for the past 22 years and I have been teaching statistics for the past 10 years. I only got to know this book a couple of years ago. Many many conceptual issues that I have had in Statistics have been clarified from a careful study of this book. Jaynes had a deep understanding not only of Bayesian Statistics but also of Frequentist Statistics. Everything that he says about Frequentist "Orthodox" Statistics is correct (although often it took me many months to fully understand what he is saying).

The ideas and messages of this book significantly differ from what is taught in pretty much all other statistics books. Here is one example, the Gaussian distribution is heavily used in statistical analysis. Most textbooks are pretty much apologetic about this overuse of the Gaussian distribution and struggle to suggest alternative methods. Jaynes, on the other hand, says (in Chapter 7) that the range of validity for the application of the Gaussian distribution in data analysis is actually "far wider that is usually supposed".

A major highlight of the book is the focus on history. Very careful historical accounts are presented as to how the greats of the field (like Gauss, Laplace, Cox, Fisher etc) approached data analysis. This stuff again cannot be found in any other book in the field. I have been using this book heavily in pretty much anything I teach these days and, as a consequence, teaching statistics has been a much more pleasurable experience than before.

Jaynes apparently originally wanted to write a sequel to this book focussing on more advanced applications. It is a pity that he passed away before he could write the sequel.
I recommend readers to the outstanding books by MacKay and by von der Linden-Dose-von Toussaint for numerous interesting and nontrivial applications of Probability Theory (Bayesian Statistics) to Data Problems.

I would also like to recommend (as sequels to reading Jaynes) the books of David Blower which clarify and complement the ideas of Jaynes. For readers interested in learning more about the various issues, pitfalls and shortcomings of Frequentist "Orthodox" statistics, I would like to recommend the collected works of Dev Basu.

4 people found this helpful

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ACCGTGGTGACA...

A masterpiece of mathematical exposition

Reviewed in the United States 🇺🇸 on December 5, 2009

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I have rarely learned so much from one book. This book is somewhat unusual among mathematical texts in that it is heavy on prose and (compared to other texts) light on equations. However, don't get the idea that it is any less rigorous! It simply focuses on precisely what most math books neglect: exhaustive explanation of the concepts...and to very good effect. Jaynes (and his editor) are possibly the most articulate writers of mathematics I've ever read. If you can read equations like English, you may not appreciate this. The rest of us will.
Summarizing the content: The book very exhaustively demonstrates how Bayesian statistical approaches subsume rather than compete with "orthodox" (sampling theory-derived) statistics. Importantly, it begins by deriving the sum and product rules (which in other texts are typically presented as axioms) from "common sense" considerations. In other words, what is usually treated as "given" in other statistics texts is shown to, in fact, depend on even more fundamental (and, thus, indisputable) considerations of what constitutes rational plausible reasoning. This places the whole endeavor of statistics on firmer ground than any other text I've seen. The book is worth buying for the first few chapters alone, but it just gets better from there.
Jaynes goes on to link Bayes rule to information-theoretic considerations and build up probability as an extended form of logic (as the title implies). In some cases this yields a new and deeper understanding of "orthodox statistical practice." In others it exposes (and explains) the absurdities of strictly frequentist approaches. Again, I have rarely learned so much from one book.
One caveat: It does not at all require a statistics background, but, obviously, some of Jaynes (mildly polemical) discourse will, of course, be lost on you without it.

27 people found this helpful

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the best possible worldview

Reviewed in the United States 🇺🇸 on December 8, 2016

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One of the most important works of the 20th century (or any century) in both philosophy and physics, Jaynes' work lays the foundation for the physical ontology and epistemology of science. This book is the completion of what amounted to a lifetime of effort on Jaynes' part, dating back to the "Mobil Lectures" where he first laid out this approach to knowledge. It follows the world of Richard Cox, who demonstrated that Bayesian probability theory naturally follows from three simple axioms that also serve to establish the connection between evidence and plausible belief.

In my opinion, this book is a required read for anyone who wishes to understand precisely how the scientific worldview is, in a mathematically defensible sense, the best possible worldview, the one that lets us optimally use evidence to develop an interlocked Bayesian network of evidence supported beliefs that can change and evolve as the evidence is accumulated. It also shows the critical connections between physics and statistical mechanics and Shannon's theorem in computational information theory, laying the foundation for a fair bit of modern physics as it demonstrates that physical entropy and information entropy are very much one and the same thing, from a certain point of view.

41 people found this helpful

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Michael Hopkins

THE reference on how to understand probability theory from 1st principles

Reviewed in the United Kingdom 🇬🇧 on April 13, 2012

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Considering this is a weighty book about the fundamentals and history of probability theory, it is actually quite entertaining with humour, stories, an engaging style and vitriolic personal criticism (generally justified) of the people who fought hard to defend their mistaken positions by dismissing the ideas that Jaynes promoted. It can be a little over-wordy, opinionated and pompous in places, and has small sections missing because he unfortunately died before it was completed. It is however an absolute gem that rewards re-reading over an extended period of time, and will make anyone who has to deal with measuring and reasoning about uncertain systems - i.e. all scientists, engineers & economists in my opinion - think differently about what can be done as objectively as possible and how they should extract the maximum amount of information from measured data and make optimal inferences. Modern Bayesian theory is becoming the basis for solving Inverse Problems so if you are in this area then have a look.

His description of probability distributions as "carriers of uncertain information about unknowns" rather than the traditional and flawed classical view of "behaviour of selected summary statistics in the limit of an infinite amount of repeated random events" (whatever that means!) is an indicator of the different perspectives.

Anyone who wants to understand what probability theory actually _is_ at a fundamental level and have their mind opened up to how they can apply it in their area should have a look and strap themselves in for the ride. Highly recommended.

If you want a more compact and introductory book with an applied focus and examples then I strongly recommend Sivia & Skilling:

Data Analysis: A Bayesian Tutorial

11 people found this helpful

tomoftheglen

Five Stars

Reviewed in the United Kingdom 🇬🇧 on July 13, 2017

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Classic tome.

A user

A must-read for researchers in many fields

Reviewed in Germany 🇩🇪 on February 2, 2016

Verified Purchase

Far too many researchers are convinced they have a command of statistics and its underlying probability paradigms because they are familiar with software packages that calculate ANY statistical test they know or believe in or "the one everybody else does in my field". Alas, that leads to sloppy data interpretation and non-insights that should be caught BEFORE the analysis begins.
The logic of science in the title does not deal with history-laden aspects (scu as the emergence and replacement of paradigms) but rather what logic one adopts in natural systems where a large (statistical) noise contribution is present; in such systems, the logic of interpreting experimental outcomes and what constitutes a valid theory is far from easy and straightforward. This book is a good support in such matters.

One person found this helpful

Ramon Crehuet

Un libro que hace pensar

Reviewed in Spain 🇪🇸 on March 31, 2014

Verified Purchase

Soy científico, y nunca había entrado en la visión frecuentista de la probabilidad. Me parecían un conjunto de recetas basadas en unas hipotésis cuestionables. Este libro explica la probabilidad como una extensión de la lógica aristotélica, cuando no hay certezas absolutas. Entra en cuestiones aparentemente filosóficas sobre que base tiene la inducción. Los argumentos son claros y simples.
La mayoría de casos que trata son bastante sencillos, muy tratables analíticamente. Quizás debe ser complementado con algun tratado más aplicado, pero como base de la probabilidad Bayesiana, me parece fantástico.

4 people found this helpful

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Z. G

The content is great, but can the delivery be handled in a better way?

Reviewed in the Netherlands 🇳🇱 on February 3, 2021

Verified Purchase

Love the content of the book (5 stars for the content), but the delivery could have been handled nicely: the corners of the book were damaged. It seems that such cases happened more often in recent years.

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