Probability Theory: The Logic of Science: Principles and Elementary Applications Vol 1 Hardcover – 10 Apr 2003
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Going beyond the conventional mathematics of probability theory, this study views the subject in a w....
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Top Customer Reviews
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.Read more ›
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.
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.Read more ›
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
Most Recent Customer Reviews
This book got very good reviews on amazon, so I got curious and bought it. I read about 90% of it over the past months. Read morePublished on 7 Nov. 2012 by L&H
If you think that probability has to be a long run frequency, read this book and think again. It is a page-turner of a book that explains that probability theory is best seen as an... Read morePublished on 19 Feb. 2012 by J C.
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