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Probability Theory: The Logic of Science Annotated Edition
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- ISBN-100521592712
- ISBN-13978-0521592710
- EditionAnnotated
- PublisherCambridge University Press
- Publication dateJune 9, 2003
- LanguageEnglish
- Dimensions7.25 x 1.5 x 10.25 inches
- Print length753 pages
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Editorial Reviews
Review
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."
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Book Description
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)
- Customer Reviews:
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Learn more how customers reviews work on AmazonReviewed in the United States on January 7, 2019
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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.
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.
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.
Top reviews from other countries
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
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.
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.
Reviewed in the Netherlands 🇳🇱 on February 3, 2021










