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Probability Theory: The Logic of Science [Hardcover]

by E. T. Jaynes, G. Larry Bretthorst
4.9 out of 5 stars  See all reviews (27 customer reviews)

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Book Description

June 9, 2003 0521592712 978-0521592710
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.

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Editorial Reviews


"...tantalizing 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."

"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.”

"[T]he 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

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.

Product Details

  • Hardcover: 753 pages
  • Publisher: Cambridge University Press (June 9, 2003)
  • Language: English
  • ISBN-10: 0521592712
  • ISBN-13: 978-0521592710
  • Product Dimensions: 9.8 x 6.7 x 1.7 inches
  • Shipping Weight: 3.5 pounds (View shipping rates and policies)
  • Average Customer Review: 4.9 out of 5 stars  See all reviews (27 customer reviews)
  • Amazon Best Sellers Rank: #85,697 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews
169 of 172 people found the following review helpful
Reading this book is an exhilarating intellectual adventure. I found that it shed light on many mysteries and answered questions that had long troubled me. It contains the clearest exposition of the fundamentals of probability theory that I have ever encountered, and its chatty style is a pleasure to read. Jaynes the teacher collaborates fully with Jaynes the scientist in this book, and at times you feel as if the author is standing before you at the blackboard, chalk in hand, giving you a private lesson. Jaynes's advice on avoiding errors in the application of probability theory -- reinforced in many examples throughout the book -- is by itself well worth the price of the book.
If you deal at all with probability theory, statistics, data analysis, pattern recognition, automated diagnosis -- in short, any form of reasoning from inconclusive or uncertain information -- you need to read this book. It will give you new perspectives on these problems.
The downside to the book is that Jaynes died before he had a chance to finish it, and the editor, although capable and qualified to fill in the missing pieces, was understandably unwilling to inject himself into Jaynes's book. One result is that the quality of exposition suffers in some of the later chapters; furthermore, the author is not in a position to issue errata to correct various minor errors. Volunteer efforts are underway to remedy these problems -- those who buy the book may want to visit the "Unofficial Errata and Commentary" website for it, or check out the etjaynesstudy mailing list at Yahoo groups.
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87 of 88 people found the following review helpful
5.0 out of 5 stars Invaluable June 27, 2003
This book has been on the web in unfinished form for a number of years and has shaped my scientific thinking more than any other book. I believe it constitutes one of the most important scientific texts of the last hundred years. It convincingly shows that "statistics", "statistical inference", "Bayesian inference", "probability theory", "maximum entropy methods" , and "statistical mechanics" are all parts of a large coherent theory that is the unique consistent extension of logic to propositions that have degrees of plausibility attached to them. This is already a theoretical accomplishment of epic proportions. But in addition, the book shows how one actually solves real world problems within this frame work, and in doing so shows what a vastly wider array of problems is addressable within this frame work than in any of the forementioned particular fields.
If you work in any field where on needs to "reason with incomplete information" this book is invaluable.
As others have already mentioned, Jaynes never finished this book. The editor decided to "fill in" the missing parts by putting excercises that, when finished by the reader, provide what (so the editor guesses) Jaynes left out. I find this solution a bit disappointing. The excercises don't take away the impression that holes are left in the text. It would have been better if the editor had written the missing parts and then printed those in different font so as to indicate that these parts were not written by Jaynes. Better still would have been if the editor had invited researchers that are intimately familiar with Jaynes' work and the topic of each of the missing pieces to submit text for the missing pieces.
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63 of 65 people found the following review helpful
From a few common sense requirements, the books starts by deriving basic results such as the product and sum rules, for probabilities defined not in terms of frequencies, but as degrees of plausibility. This was an eye-opener for me, having imbibed the common attitude that such probabilities are 'subjective' and, implicitly, lacking rigor and utility.

Jaynes' knowledge of the history and philosophy of statistics is far deeper than that of most statisticians (including myself). His trenchant style gives the book a narrative drive and cover-to-cover readability that, in my experience, is unique in the field. One such strand is the continual battle between his respect for RA Fisher's abilities, and his exasperation at how wrongheadedly he feels they were channelled. And he doesn't hesitate to take on philosophical heavyweights such as Hume in defending the possibility - - in fact, the necessity - - of inductive inference. However, this style also produces some more bitter fruit, such as the way the author repeatedly likens himself to historical victims of religious persecution.

The book weakens when it turns to applications. Regression with errors in both variables is said to be 'the most common problem of inference faced by experimental scientists' who have 'searched the statistical literature in vain for help on this'. Good points. So why don't the author and editor give us at least a reference for just one of the 'correct solutions' which 'adapt effortlessly' to scientists' needs? And Jaynes' argument that the null hypothesis procedure 'saws off its own limb' would also rule out mathematical proof by reductio ad absurdum.

When estimating periodicities, we're told that 'the eyeball is a more reliable indicator of an effect than an orthodox equal-tails test'.
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Most Recent Customer Reviews
5.0 out of 5 stars knowledge discovery for scientists and engineers
Luckily, I found out this book after reading Keynes' probability book. This is not an elementary book for beginners, though math is not complicated inside. Read more
Published 3 months ago by white rabbit
5.0 out of 5 stars A classic that every serious student of the subject should have
This is a classic and belongs on every serious data scientists bookshelf. It goes beyond just simply teaching statistics and focuses on the thinking one needs to acquire in order... Read more
Published 4 months ago by ram
5.0 out of 5 stars Best. Book. Ever.
Fantastic book. Changed the way I look at many things. Especially the intuitive way that bayesian updating in estimation is explained was helpful. Read more
Published 4 months ago by Christian Stassen
5.0 out of 5 stars Nice presentation of the nuances of probability
I haven't finished reading this book yet, but the chapters I read so far gave me so much understanding of issues that are either obscure or absent in other probability and... Read more
Published 7 months ago by C. Valente
5.0 out of 5 stars A rather integral view on the field of statistics
The book provides an excellent overview of the field of statistics with the old 'frequentist' and the newer Bayesian approach, showing the relationships between the various... Read more
Published 10 months ago by Hans J. Pasman
5.0 out of 5 stars Impressive
This book does an impressive job of replacing ad hoc rules of statistics with rigorous logic, but it is difficult enough to fully understand that most people will only use small... Read more
Published on July 31, 2010 by Peter McCluskey
5.0 out of 5 stars This book will someday replace Oxygen as the thing we breathe
Every scientist should read this book. It deals with the most fundamental question of experimental science: how do we assign plausibility based on data? Read more
Published on April 1, 2010 by Bradley M. Deutsch
5.0 out of 5 stars Most important book ever written in Science
They should give you a PhD just for reading this book. You're going to be that much smarter.
Thank you ET Jaynes for finally providing a satisfactory theory of conditional... Read more
Published on March 7, 2010 by Snapple
5.0 out of 5 stars A masterpiece of mathematical exposition
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. Read more
Published on December 5, 2009 by ACCGTGGTGACA...
5.0 out of 5 stars More clarifying than groundbreaking
Since the frequentist vs. Bayesian controversy is mentioned right in the book, it didn't set off that controversy. A lot of the edition I acquired is out of date. Read more
Published on November 19, 2009 by Marion Delgado
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I am facing the same problem. Some of the exercises are extremely important, and it would be invaluable to have a commented solution. So far, searching for it on Google has been fruitless...
Feb 17, 2010 by Ed. Valle |  See all 2 posts
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