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Probability Theory: The Logic of Science Hardcover – Jun 9 2003
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"...tantalizing ideas...one of the most useful and least familiar applications of Bayesian theory...Probability Theory [is] considerably more entertaining reading than the average statistics textbook...the conceptual points that underlie his attacks are often right on."
"This is a work written by a scientist for scientists. As such it is to be welcomed. The reader will certainly find things with which he disagrees, but he will also find much that will cause him to think deeply not only on his usual practice by also on statistics and probability in general. Probability Theory: the Logic of Science is, for both statisticians and scientists, more than just 'recommended reading': it should be prescribed."
"...the rewards of reading Probability Theory can be immense."
Physics Today, Ralph Baierlein
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.
"[T]he 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...There are many books on Bayesian statistics, but few with this much color."
Notices of the AMS
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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To frequentist statisticians, probability theory is the study of relative frequencies or of proportions of a population; those are "probabilities".
To Bayesian statisticians, probability theory is the study of degrees of belief. Bayesians may assign probability 1/2 to the proposition that there was life on Mars a billion years ago; frequentists will not do that because they cannot say that there was life on Mars a billion years ago in precisely half of all cases -- there are no such "cases".
To _subjective_ Bayesians, probability theory is about subjective degrees of belief. A subjective degree of belief is merely how sure you happen to be.
"Noninformative" _objective_ Bayesians assign "noninformative" probability distributions when they deal with uncertain propositions or uncertain quantities, and replace them with "informative" distributions only when they update them because of "data". "Data", in this sense, consists of the outcomes of random experiments.
"Informative" _objective_ Bayesians -- a rare species -- ask what degree of belief in an uncertain proposition is logically necessitated by whatever information one has, and they don't necessarily require that information to consist of outcomes of random experiments.
Jaynes is an "informative" objective Bayesian. This book is his defense of that position and his account of how it is to be used.
"Pure" mathematicians will not find that this book resembles that branch of "pure" mathematics that they call probability theory.
Jaynes rails against those he disagrees with at great length. Often he is right.Read more ›
If you deal at all with probability theory, statistics, data analysis, pattern recognition, automated diagnosis -- in short, any form of reasoning from inconclusive or uncertain information -- you need to read this book. It will give you new perspectives on these problems.
The downside to the book is that Jaynes died before he had a chance to finish it, and the editor, although capable and qualified to fill in the missing pieces, was understandably unwilling to inject himself into Jaynes's book. One result is that the quality of exposition suffers in some of the later chapters; furthermore, the author is not in a position to issue errata to correct various minor errors. Volunteer efforts are underway to remedy these problems -- those who buy the book may want to visit the "Unofficial Errata and Commentary" website for it, or check out the etjaynesstudy mailing list at Yahoo groups.
This book develops probability theory from first principles as an extension of deductive logic. In deductive logic, propositions can have only three possible truth values: true, false, and irremediable uncertainty. Therefore, the goal of the book is to describe a consistent extended logic that assigns real numbers to the plausibility of propositions. The requirements for such a system are derived from five simple desiderata, which serve as the postulates of this theory - and it turns out that *any* such system is equivalent to probability theory, to within a monotonic transformation.
Probability theory is then developed through applications to problems which grow more and more complex. The author demonstrates its use in direct sampling problems and so-called inverse problems, aka Bayesian probability. He derives procedures for multiple hypothesis testing, parameter estimation, and significance testing, and shows that although there are close connections between probability and frequency of occurrence in a large number of trials, no probability is *simply* a frequency.
Following this, the author presents solutions to the problem of assigning prior probabilities, and develops decision theory as an adjunct to probability theory. The author then compares and contrasts mainstream or "orthodox" statistical theory with probability theory as extended logic, and (perhaps unsurprisingly) finds severe deficiencies in the orthodox methods. The final chapters concern even more advanced applications.
Readers should be well versed in simple calculus and multivariate calculus; some familiarity with convolution integrals and finite combinatorics is also an asset, but not essential.Read more ›
Most recent customer reviews
I read this book before it was published; I downloaded it from a WU website. It has been of immense use to me in my career, it is a very practical book. Other reviews that say Dr. Read morePublished on Feb. 24 2004
it offers a mathematical discussion of probability
from the point of view of information theory. It argues
against the frequentist approach. Read more
This book has been on the web in unfinished form for a number of years and has shaped my scientific thinking more than any other book. Read morePublished on June 27 2003 by brainowner
Jaynes' work on probability has inspired many students and academics over the years. Jaynes advocates probability as a degree of belief. Read morePublished on June 17 2003 by Ali Abbas
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