 Trade In this Item for up to £24.65
Get an extra £5 when you trade in books worth £10 or more until June 30, 2012. Trade in Probability Theory: The Logic of Science: Principles and Elementary Applications Vol 1 for an Amazon.co.uk gift card of up to £24.65, which you can then spend on millions of items across the site. Trade-in values may vary (terms apply). Find more products eligible for trade-in.
|
Frequently Bought Together
Product details
|
More About the Author
Product Description
Review
'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
Product Description
Suppose some dark night a policeman walks down a street, apparently deserted. Read the first page
Concordance
Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
Tags Customers Associate with This Product(What's this?)Click on a tag to find related items, discussions, and people.
|
Sell a Digital Version of This Book in the Kindle Store
What Other Items Do Customers Buy After Viewing This Item?
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.
As a doctoral student in the philosophy of science, I found this the most useful source about induction, probability and statistics. Even though a lot of the maths was too advanced for me, Jaynes puts the mathematical proofs in context and explains why they are so important for science.
If more philosophers would read the first few chapters of this book, then a lot of collective misconceptions about probability would be cleared up and a lot of "new" discoveries would be shown to be already part of Jaynes' sophisticated system. AI researchers interested in the representation of uncertainty will also find it essential.
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. Almost all books on Bayesian statistics that I looked at were highly technical, but did not really tell me how to apply Bayesian statistics to my relatively simple problems. Only when I found Data Analysis by Sivia did I learn what I needed. That book was not only very useful in itself, it also pointed me to Jaynes's great book.
Listmania!
|
|
Look for similar items by category
- Books > Science & Nature > Engineering & Technology > Engineering Physics
- Books > Science & Nature > Experiments, Instruments & Measurements > Methods
- Books > Science & Nature > Mathematics > Probability & Statistics
- Books > Science & Nature > Physics > Mathematical
- Books > Science & Nature > Physics > Methods
- Books > Science & Nature > Popular Science > Maths
- Books > Science & Nature > Popular Science > Physics
- Books > Scientific, Technical & Medical
Look for similar items by subject
Feedback
- Would you like to update product info or give feedback on images?
- I am the Author, and I want to comment on my book.
- I am the Publisher, and I want to comment on this book.
|
