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Title: Probability Theory : The Logic of Science by E. T. Jaynes, G. Larry Bretthorst ISBN: 0-521-59271-2 Publisher: Cambridge University Press Pub. Date: 10 April, 2003 Format: Hardcover Volumes: 1 List Price(USD): $65.00 |
Average Customer Rating: 5 (7 reviews)
Rating: 5
Summary: Ontological and Epistomological Probability
Comment: I read this book before it was published; I downloaded it from a WU website. It has been of immense use to me in my career, it is a very practical book. Other reviews that say Dr. Jaynes' ideas are at odds with traditional measure theoretic probability are mistaken. Dr. Jaynes is a true Baysian. A Baysian is one who believes that probabilities do not model serendipity in nature, but do model subjective certainty. The Bayesian concept of probability is epistomological, i.e. the uncertainty is in our minds, not in objective reality. Traditional probability takes the reverse view: probabilities model unpredictable events, they are a model of objective reality like any science, i.e. probabilities are ontological. The trick is to realize the two are not mutually exclusive! There can be true ontological randomness in nature, and our minds can have uncertainty from incomplete knowledge as well. Probability theory as a branch of mathematics makes no claim what it models. The beauty is that probabiltity distributions integrate the two seamlessly. Thus, it is perfectly valid to put a distribution on an unknown parameter, epistomologically unknown, and derive that distribution from an experiment with, presumably, ontological randomness. Dr. Jaynes' book is well worth reading for the many case studies he presents. His background as a physicist is key to understanding some of the esoteric philisophical points.
Rating: 5
Summary: The most important book on probability theory in decades
Comment: 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.
Rating: 5
Summary: Truthful
Comment: it offers a mathematical discussion of probability
from the point of view of information theory. It argues
against the frequentist approach. The author is absolutely
right: probability has meaning only as incomplete
knowledge (but still objective). Any frequentist approach
is problematic. A real diamond.
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Title: Algebra of Probable Inference by Richard T. Cox ISBN: 080186982X Publisher: Johns Hopkins Univ Pr Pub. Date: February, 2002 List Price(USD): $19.95 |
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Title: A Philosophical Essay on Probabilities by Marquis de Laplace ISBN: 0486288757 Publisher: Dover Pubns Pub. Date: 18 January, 1996 List Price(USD): $11.95 |
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Title: Data Analysis: A Bayesian Tutorial (Oxford Science Publications) by D. S. Sivia ISBN: 0198518897 Publisher: Oxford University Press Pub. Date: July, 1996 List Price(USD): $45.00 |
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Title: Bayesian Data Analysis, Second Edition by Andrew Gelman, John B. Carlin, Hal S. Stern, Donald B. Rubin ISBN: 158488388X Publisher: CRC Press Pub. Date: 29 July, 2003 List Price(USD): $59.95 |
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Title: The Foundation of Statistics by Leonard J. Savage ISBN: 0486623491 Publisher: Dover Pubns Pub. Date: 01 June, 1972 List Price(USD): $14.95 |
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