| Probability Theory: The Logic of Science (Vol 1) |  | Author: E. T. Jaynes
Creator: G. Larry Bretthorst
Publisher: Cambridge University Press
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Rating:  22 reviews
Media: Hardcover
Pages: 758
Number Of Items: 1
Shipping Weight (lbs): 3.5
Dimensions (in): 10 x 7.2 x 1.6
ISBN: 0521592712
Dewey Decimal Number: 519.2
EAN: 9780521592710
ASIN: 0521592712
Publication Date: June 9, 2003
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Product Description
Going beyond the conventional mathematics of probability theory, this study views the subject in a wider context. It discusses new results, along with applications of probability theory to a variety of problems. The book contains many exercises and is suitable for use as a textbook on graduate-level courses involving data analysis. Aimed at readers already familiar with applied mathematics at an advanced undergraduate level or higher, it is of interest to scientists concerned with inference from incomplete information.
Book Description
Going beyond the conventional mathematics of probability theory, this study views the subject in a wider context. It discusses new results, along with applications of probability theory to a variety of problems. The book contains many exercises and is suitable for use as a textbook on graduate level courses involving data analysis. Aimed at readers already familiar with applied mathematics at an advanced undergraduate level or higher, it is of interest to scientists concerned with inference from incomplete information.
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Showing reviews 1-5 of 22
Impressive July 31, 2010
Peter McCluskey (San Bruno, CA USA)
This book does an impressive job of replacing ad hoc rules of statistics with rigorous logic, but it is difficult enough to fully understand that most people will only use small parts of it.
He emphasizes that probability theory consists of logical reasoning about the imperfect information we have, and repeatedly rants against the belief that probabilities or randomness represent features of nature that exist independent of our knowledge. Even something seemingly simple such as a toss of an ordinary coin cannot have some objectively fixed frequency unless concepts such as "toss" are specified in unreasonable detail. What we think of as randomness is best thought of as a procedure for generating results of which we are ignorant.
He derives his methods from a few simple axioms which appear close to common sense, and don't look much like they are specifically designed to produce statistical rules.
He is careful to advocate Bayesian methods for an idealized robot, and avoids addressing questions of whether fallible humans should sometimes do something else. In particular, his axiom that the robot should never ignore information is a goal that will probably reduce the quality of human reasoning in some cases where there's too much information for humans to handle well.
I'm convinced that when his methods can be properly applied and produce different results than frequentist methods do, we should reject the frequentist results. But it's not obvious how easy it is to apply his methods properly, nor is it obvious whether he has accurately represented the beliefs of frequentists (who I suspect often don't think clearly enough about the issues he raises to be clearly pinned down).
He does a good job of clarifying the concept of "induction", showing that we shouldn't try to make it refer to some simple and clearly specified rule, but rather we should think of it as a large set of rules for logical reasoning, much like the concept of "science".
This book will someday replace Oxygen as the thing we breathe April 1, 2010
Bradley M. Deutsch (Rochester, NY)
Every scientist should read this book. It deals with the most fundamental question of experimental science: how do we assign plausibility based on data? What if we have very little data? What if we have none?
It includes foundations of probability theory (introduced in a conversational and often funny tone), builds very slowly to its conclusions, and deals with most common criticisms of Bayesian analysis and MaxEnt methods, often based on misunderstandings. Also included are examples of applications, and places where Jaynes leaves the door open to further development. After all, this field is far from complete.
This book is a manifesto. It embodies a sense of urgency and righteousness ever-present in scientific revolution. Such a sense is not misplaced here.
Most important book ever written in Science March 7, 2010
Snapple
They should give you a PhD just for reading this book. You're going to be that much smarter.
Thank you ET Jaynes for finally providing a satisfactory theory of conditional probability. Now I finally can kick all the heavy-baggage measure theory definitions into the bin, which on the one hand are useless for an engineer as you don't want to carry around the sigma-field formalism for each new problem you're working on, but on the other hand you feel helpless to apply probability calculus without it because it's the only formal definition of conditional probability (unless you consider the tautological P(A|B) := P(AB)/P(B) a foundation..)
Thank you for ridding me of the frequentist viewpoint, which other Bayesian books have not achieved because their theory was flawed as well.
Everything is falling into place now. No wonder Statistics is so hard, because it is..wrong. You either absolve yourself of a foundation and merrily apply rules, or you waste a lot of time twisting your mind to fit each new problem into the unreasonable frequentist assumptions.
A masterpiece of mathematical exposition December 5, 2009
ACCGTGGTGACA... (Seattle, WA USA)
1 out of 1 found this review helpful
I have rarely learned so much from one book. This book is somewhat unusual among mathematical texts in that it is heavy on prose and (compared to other texts) light on equations. However, don't get the idea that it is any less rigorous! It simply focuses on precisely what most math books neglect: exhaustive explanation of the concepts...and to very good effect. Jaynes (and his editor) are possibly the most articulate writers of mathematics I've ever read. If you can read equations like English, you may not appreciate this. The rest of us will.
Summarizing the content: The book very exhaustively demonstrates how Bayesian statistical approaches subsume rather than compete with "orthodox" (sampling theory-derived) statistics. Importantly, it begins by deriving the sum and product rules (which in other texts are typically presented as axioms) from "common sense" considerations. In other words, what is usually treated as "given" in other statistics texts is shown to, in fact, depend on even more fundamental (and, thus, indisputable) considerations of what constitutes rational plausible reasoning. This places the whole endeavor of statistics on firmer ground than any other text I've seen. The book is worth buying for the first few chapters alone, but it just gets better from there.
Jaynes goes on to link Bayes rule to information-theoretic considerations and build up probability as an extended form of logic (as the title implies). In some cases this yields a new and deeper understanding of "orthodox statistical practice." In others it exposes (and explains) the absurdities of strictly frequentist approaches. Again, I have rarely learned so much from one book.
One caveat: It does not at all require a statistics background, but, obviously, some of Jaynes (mildly polemical) discourse will, of course, be lost on you without it.
More clarifying than groundbreaking November 20, 2009
Marion Delgado (Eugene OR)
Since the frequentist vs. Bayesian controversy is mentioned right in the book, it didn't set off that controversy. A lot of the edition I acquired is out of date. The supplementary readings recommended by Jaynes make it much more worthwhile, especially examples and worked-out problems.
As Jaynes predicted, it's still entirely relevant 10 years later. Not much was altered posthumously. The reason it's going to get nothing but good reviews is that it's an overview, not an argument on a controversy or a textbook.
Showing reviews 1-5 of 22
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