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Probability Theory: The Logic of Science: Principles and Elementary Applications Vol 1 Hardcover – 10 Apr 2003

4.6 out of 5 stars 7 customer reviews

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Product details

  • Hardcover: 753 pages
  • Publisher: Cambridge University Press; 1st Ed. (U.K.) edition (10 April 2003)
  • Language: English
  • ISBN-10: 0521592712
  • ISBN-13: 978-0521592710
  • Product Dimensions: 17.4 x 3.9 x 24.7 cm
  • Average Customer Review: 4.6 out of 5 stars  See all reviews (7 customer reviews)
  • Amazon Bestsellers Rank: 374,172 in Books (See Top 100 in Books)

Product Description

Going beyond the conventional mathematics of probability theory, this study views the subject in a w....


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Format: Hardcover
A fragmentary edition of this book was published online in 1994, and has already been an academic "underground hit". The subject matter (probability as the only consistent, universal logic of uncertain inference) is relevant to nearly every field in science where evidence has to be assessed.
Edwin Jaynes was a great scientific writer and his breadth of learning, concern for real-world applications and wit clearly show through in this book. His comments on opposing views are very harsh by academic standards, but Jaynes' writing shows up how bland and how disconnected from real-world problems the academic writing on Bayesianism usually is.
This book combines two principles and shows how they can produce a Bayesian mathematical system which illuminates and unifies problems of reasoning and decision. His examples are sometimes delightfully original and range from court-room decisions to complex engineering problems.
The first principle is the Cox Proof, explained at length in Chapter 2. Probability is normally justified in terms of rational betting behaviour or in terms of sensible preferences between options. The Cox Proof, by contrast, derives probability from consistency constraints on the form of a system of inference. Hence non-probabilistic systems (such as those in orthodox statistics or fuzzy logic) are inconsistent; a very important result.
The other principle is the idea that one's expectations have an information content, which can be measured using the mathematics of Information Theory. Ideally, your beliefs should contain no more information than what is allowed by the evidence you have so far. Spelled out mathematically, this gives what is known as the Maximum Entropy (or "maxent") principle.
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Format: Hardcover
The book quotes Bernoulli (1713): "I cannot conceal the fact here that in the [application of probability theory], I foresee many things happening which can cause one to be badly mistaken if he does not proceed cautiously.", and indeed shows that throughout the history of probability theory this has happened all too often.
Jaynes starts with some deceptively simple requirements for the rules of reasoning in the face of uncertainty. He then proceeds systematically and with confident ease, to deduce the rules and practice of probability theory, showing along the way how to avoid the controversies and paradoxes usually associated with this field. He shows that these rules are the only consistent ones and any method that violates them is necessarily inconsistent.
The bulk of the book is about inference, or inverse probability problems. It is therefore highly recommended for all users of probability theory for inference. (This specifically includes engineers working on all types of automatic speech processing.) The reader is freed from the restrictive frequency interpretation of probability and can then start to develop a deep understanding of inference.
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Format: Hardcover
This is a book that puts all other textbooks on Bayesian statistics to shame. Whereas these books avoid the discussion about the interpretation of probability, and hide in the technical aspects of Bayesian statistics, Probability Theory by Jaynes has this interpretation as its main topic. Jaynes shows that probability can be used to say how plausible something is. He starts from a few very basic desiderata and then uses Cox Proof to derive the usual expressions for probabilities. The rest of the book is a showcase of how this interpretation leads to a more natural, simpler, and more powerful form of statistics than the frequency interpretation.

Jaynes discusses a large number of problems, compares various approaches to them, and shows their strengths and weaknesses. He does this in a highly engaging style; one learns how to apply the techniques of Bayesian statistics almost as if in passing. I found the problems not only very interesting, sometimes they even made me smile. For example, in chapter 5 he uses extra-sensory perception as an application of Bayesian statistics on hypothesis testing with more than two hypotheses. He argues that if an experiment shows that ESP is much more likely than random chance, people will still not accept its existence. The reason is that there is a third possibility, which is that there is something wrong with the experiment. If this possibility has a higher prior probability than ESP, then it will retain this higher probability no matter what the outcome of the experiment.

I became interested in Bayesian statistics, because I was trying to do model selection based on results of quantum chemical calculations. As these calculations are perfectly reproducible, a frequency interpretation of probability makes no sense.
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Format: Hardcover Verified Purchase
Considering this is a weighty book about the fundamentals and history of probability theory, it is actually quite entertaining with humour, stories, an engaging style and vitriolic personal criticism (generally justified) of the people who fought hard to defend their mistaken positions by dismissing the ideas that Jaynes promoted. It can be a little over-wordy, opinionated and pompous in places, and has small sections missing because he unfortunately died before it was completed. It is however an absolute gem that rewards re-reading over an extended period of time, and will make anyone who has to deal with measuring and reasoning about uncertain systems - i.e. all scientists, engineers & economists in my opinion - think differently about what can be done as objectively as possible and how they should extract the maximum amount of information from measured data and make optimal inferences. Modern Bayesian theory is becoming the basis for solving Inverse Problems so if you are in this area then have a look.

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
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