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Probability Theory: The Logic of Science [Englisch] [Gebundene Ausgabe]

G. Larry Bretthorst , E. T. Jaynes
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10. April 2003
The standard rules of probability can be interpreted as uniquely valid principles in logic. In this book, E. T. Jaynes dispels the imaginary distinction between 'probability theory' and 'statistical inference', leaving a logical unity and simplicity, which provides greater technical power and flexibility in applications. This book goes beyond the conventional mathematics of probability theory, viewing the subject in a wider context. New results are discussed, along with applications of probability theory to a wide variety of problems in physics, mathematics, economics, chemistry and biology. It contains many exercises and problems, and is suitable for use as a textbook on graduate level courses involving data analysis. The material is aimed at readers who are already familiar with applied mathematics at an advanced undergraduate level or higher. The book will be of interest to scientists working in any area where inference from incomplete information is necessary.

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  • Gebundene Ausgabe: 753 Seiten
  • Verlag: Cambridge University Press (10. April 2003)
  • Sprache: Englisch
  • ISBN-10: 0521592712
  • ISBN-13: 978-0521592710
  • Größe und/oder Gewicht: 25 x 17 x 4 cm
  • Durchschnittliche Kundenbewertung: 5.0 von 5 Sternen  Alle Rezensionen anzeigen (1 Kundenrezension)
  • Amazon Bestseller-Rang: Nr. 43.950 in Fremdsprachige Bücher (Siehe Top 100 in Fremdsprachige Bücher)
  • Komplettes Inhaltsverzeichnis ansehen

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'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

'This book could be of interest to scientists working in areas where inference of incomplete information should be made.' Zentralblatt MATH

'… 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. The annotated References and Bibliography are particularly good for this.' Notices of the American Mathematical Society

Über das Produkt

A comprehensive introduction to the role of probability theory in general scientific endeavour. This book provides an original interpretation of probability theory, showing the subject to be an extension of logic, and presenting new results and applications. Ideal for scientists working in any area involving inference from incomplete information.

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5.0 von 5 Sternen Interessant, kohärent und kontrovers 7. Mai 2014
Format:Gebundene Ausgabe|Verifizierter Kauf
Dieses Buch ermöglicht ein zusammenhängendes Verständnis von "Wahrscheinlichkeit" im Kontext experimenteller Wissenschaften. Dabei steht das Buch eindeutig auf der Bayesischen Seite und lässt keine Möglichkeit aus, die Irrtümer der Frequentisten aufzuzeigen. Man sollte nicht alles als "herrschende Meinung" betrachten; wer diese Warnung berücksichtigt, kann ein Gedankengebäude genießen, welches ganz anders ist als viele Bücher in der "Anwendung", welche nur lose zusammenhängende statistische Tests beschreiben.
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Die hilfreichsten Kundenrezensionen auf (beta) 4.9 von 5 Sternen  27 Rezensionen
173 von 176 Kunden fanden die folgende Rezension hilfreich
5.0 von 5 Sternen The most important book on probability theory in decades 29. August 2003
Von Kevin S. Van Horn - Veröffentlicht auf
Format:Gebundene Ausgabe
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.
90 von 91 Kunden fanden die folgende Rezension hilfreich
5.0 von 5 Sternen Invaluable 27. Juni 2003
Von brainowner - Veröffentlicht auf
Format:Gebundene Ausgabe
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. The editor could then have chosen from these to provide a "best guess" for what Jaynes might have written.
Finally, there is the issue of Jaynes' writing style. This is of course largely a matter of taste. I personally like his writing style very much because it is clear, and not as stifly formal as most science texts. However, some readers may find his style too belligerent and polemic.
64 von 66 Kunden fanden die folgende Rezension hilfreich
4.0 von 5 Sternen usually insightful, sometimes annoying, always challenging 10. Mai 2005
Von Neal Alexander - Veröffentlicht auf
Format:Gebundene Ausgabe
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'. So why not show us the data of the example used, to let us use our eyes? In fact, there's only one graph of empirical data in all the book's 600+ pages.

Several convincing arguments are presented for the use of the Jeffreys (reciprocal) prior for scale parameters, including scale independence. However, just when I was ready to go and use it, there's a warning against the use of improper priors except as 'as a well-defined limit of a sequence of proper priors'. A few pages later a uniform prior is used for the mean of a Gaussian, with no such justification as a limit, which makes it far from clear what exactly is being recommended.

I could give a lot more space to the book's many other insights, and several other annoyances. Instead, I'll finish now by recommending it to anyone interested in the foundations and practice of statistical analysis.
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5.0 von 5 Sternen Ontological and Epistomological Probability 25. Februar 2004
Von "walleke" - Veröffentlicht auf
Format:Gebundene Ausgabe
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.
53 von 58 Kunden fanden die folgende Rezension hilfreich
4.0 von 5 Sternen Flawed gems 16. Oktober 2007
Von Carl - Veröffentlicht auf
Format:Gebundene Ausgabe
First off, I can in good conscience only recommend this book to experts who already have a deep understanding of both Bayesian and frequentist probability theory. The most useful function of this book is to illuminate puzzling features of probability theory that niggle at the minds of experts. If you don't already understand the subject at a fairly deep level, Jaynes will only leave you confused. (I could not imagine the torment of someone trying to learn probability and statistics for the first time from this book!)

Expect little in the way of examples or practical solutions here. Jaynes is concerned more with fundamentals and philosophy. Phil Gregory's textbook, although overly fond of Mathematica, is a better intro to practical applications. What examples there are tend to be highly idealized, with a high amount of tedious calculation.

Jaynes died with his book in an unfinished state. What he needed was an editor, but what he got instead was a hagiographer. Rather than inject himself into Jaynes' work, the editor instead has left all of the flaws, incomplete explanations, and many out-and-out mistakes in place. This was a bad mistake. Too many important points are left as exercises to the reader.

Jaynes himself is highly infuriating on a number of points. He repeatedly argues for a Haldane prior as a non-informative prior for a binomial distribution, but doesn't come to grips with the fact that this improper prior gives absurd results in some limits, whereas the more commonly used and more robust Jeffreys prior is ignored. Jeffreys priors themselves are scarcely mentioned in most places, while discussion of how to apply KL information measures to construct non-informative priors is completely missing. Jaynes' commentary on the state of quantum mechanics will strike most physicists as misguided as at best.

I find it ironic that I have mostly negative things to say about a book that I rank at 4 out of 5. The trouble is that this could have been the greatest single book ever written on the subject if it only had better editing, fewer polemics, and a more practical bent. I find myself mourning for what this book could have been. What it actually is, however, is a great probability text from a Bayesian perspective. It contains many gems, but you have to wade through a lot to find them.
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