- Hardcover: 753 pages
- Publisher: Cambridge University Press; 1 edition (June 9, 2003)
- Language: English
- ISBN-10: 0521592712
- ISBN-13: 978-0521592710
- Product Dimensions: 6.8 x 1.5 x 9.7 inches
- Shipping Weight: 3.5 pounds (View shipping rates and policies)
- Average Customer Review: 4.9 out of 5 stars See all reviews (40 customer reviews)
- Amazon Best Sellers Rank: #50,064 in Books (See Top 100 in Books)
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Probability Theory: The Logic of Science 1st Edition
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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.
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Top customer reviews
It is true Jaynes' style is caustic against positions that are contrary to his owns. But he is very convincing on the reasons he gives to pinpoint the big holes in the so called "orthodox" school of probability and statistics.
Besides, the book is very lengthy, without being prolix, on its explanations, making it very pedagogical. Constrasting with that, nevertheless, Jaynes sometimes proposes examples that I believe only a mathematician or physicist with specific knowledge of the subject mentioned by the author will be able to follow. But those parts do not impact understanding of the main ideas.
It must be noted also that "Probaility theory: the logic of science" is mainly a theory book. Its goal is to present probability as an extension of deductive logic. It only brings a small number of exercises.
The best thing about this book, at least for me, is having a style that really makes me look forward reading the next page, something very rare for a technical book. In fact, the only other book I came across that had that virtue was the "Feynman Lectures on Physics".
It includes foundations of probability theory (introduced in a conversational and often funny tone), builds very slowly to its conclusions, and deals with most common criticisms of Bayesian analysis and MaxEnt methods, often based on misunderstandings. Also included are examples of applications, and places where Jaynes leaves the door open to further development. After all, this field is far from complete.
This book is a manifesto. It embodies a sense of urgency and righteousness ever-present in scientific revolution. Such a sense is not misplaced here.
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.