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.
Probability Theory
and over 1.5 million other books are available for Amazon Kindle . Learn more
| |||||||||||||||
 Trade In this Item for up to £19.25
Trade in Probability Theory: The Logic of Science: Principles and Elementary Applications Vol 1 for an Amazon.co.uk gift card of up to £19.25, which you can then spend on millions of items across the site. Trade-in values may vary (terms apply). Special Offer until June 30, 2013: Receive an additional £5 promotional Gift Card, when you trade-in at least £10 worth of books. Learn more
|
Book Description
Frequently Bought Together
Product details
Would you like to update product info or give feedback on images?
|
More About the Author
Discover books, learn about writers, and more.
Product Description
Review
'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
'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
Book Description
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.
Inside This Book
(Learn More)
First Sentence
Suppose some dark night a policeman walks down a street, apparently deserted. Read the first page
Front Cover | Copyright | Table of Contents | Excerpt | Index
Suppose some dark night a policeman walks down a street, apparently deserted. Read the first page
Explore More
Concordance
Browse Sample PagesConcordance
Front Cover | Copyright | Table of Contents | Excerpt | Index
What Other Items Do Customers Buy After Viewing This Item?
Customer Reviews
Most Helpful Customer Reviews
23 of 23 people found the following review helpful
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.
... Read more ›11 of 11 people found the following review helpful
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.
6 of 6 people found the following review helpful
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.... Read more ›
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 ›
3 of 3 people found the following review helpful
5.0 out of 5 stars
THE reference on how to understand probability theory from 1st principles
13 April 2012
Format:Hardcover|Amazon 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.... 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.... Read more ›
Would you like to see more reviews about this item?
›
Go to Amazon.com to see all 22 reviews
4.8 out of 5 stars
Were these reviews helpful?
Let us know
Most Recent Customer Reviews
2.0 out of 5 stars
Too many words, too little content
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 more
Published 7 months ago by L&H
5.0 out of 5 stars
See the light!
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 more
Published 16 months ago by Jeremy
5.0 out of 5 stars
This book changed my life !
I know, while this sentence adorn most self-helf books, it is a claim rarely made for a textbook on statistics. Read more
Published on 5 Jun 2009 by Frederic J. Pont
Customer Discussions
|
This product's forum
Search Customer Discussions
|
Related forums
|
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
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.
|
