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. I believe it constitutes one of the most important scientific texts of the last hundred years. It convincingly shows that "statistics", "statistical inference", "Bayesian inference", "probability theory", "maximum entropy methods" , and "statistical mechanics" are all parts of a large coherent theory that is the unique consistent extension of logic to propositions that have degrees of plausibility attached to them. This is already a theoretical accomplishment of epic proportions. But in addition, the book shows how one actually solves real world problems within this frame work, and in doing so shows what a vastly wider array of problems is addressable within this frame work than in any of the forementioned particular fields.
If you work in any field where on needs to "reason with incomplete information" this book is invaluable.

As others have already mentioned, Jaynes never finished this book. The editor decided to "fill in" the missing parts by putting excercises that, when finished by the reader, provide what (so the editor guesses) Jaynes left out. I find this solution a bit disappointing. The excercises don't take away the impression that holes are left in the text. It would have been better if the editor had written the missing parts and then printed those in different font so as to indicate that these parts were not written by Jaynes. Better still would have been if the editor had invited researchers that are intimately familiar with Jaynes' work and the topic of each of the missing pieces to submit text for the missing pieces. The editor could then have chosen from these to provide a "best guess" for what Jaynes might have written.

Finally, there is the issue of Jaynes' writing style. This is of course largely a matter of taste. I personally like his writing style very much because it is clear, and not as stifly formal as most science texts. However, some readers may find his style too belligerent and polemic.

To "pure" mathematicians, probability theory is measure theory in spaces of measure 1. To the extent to which you remain a "pure" mathematician, this book will be incomprehensible to you.

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. But often he simply misunderstands them. For example, writing in the 1990s, he said that pure mathematicians reject the use of Dirac's delta function and its derivatives, and related topics. That is nonsense; the delta function has long been considered highly respectable, and required material in the graduate curriculum. Unfortunately Jaynes's misunderstandings may cause some others to misunderstand him when he is right. Statisticians are more informed than "pure" mathematicians and will disagree with Jaynes for better reasons. _Some_ statisticians will agree with him.

Jaynes has many flaws, made all the more annoying by the fact that we need to overlook them in order to understand him. His message is important.

Outline

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.

Math Requirements

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. In isolated places, the author uses or refers to the calculus of variations and the theory of function spaces (in this case Hilbert spaces); but lack of familiarity with these branches of mathematics will not seriously hamper the reader.

Critical Review

This book represents a major step forward in the understanding of what probability theory is and how to use it. In particular, a lack of solutions to the problem of prior probabilities is the main reason that for the past 100 years, mainstream probability theory was taught as a theory of frequencies instead of as an extenstion of logic; therefore, having solutions to the problem of assigning priors in a textbook is a great step forward in the development of probability theory.

The book is a pleasure to read, with a text-to-equation ratio that is uncharacteristically high for a textbook of probability theory. That is not to say that the equations are simplistic; on the contrary, solutions to quite challenging problems are presented. In addition, the author's polemics against orthodox theory are quite entertaining (and convincing); he wields an acerbic pen when describing the efforts of those who actively reject probability theory as extended logic.

One negative feature of the book is its incompleteness: the author passed away before finishing the book, so occasionally large chunks of planned text are missing. The editor has cleverly mitigated this flaw by inserting "Editor's Problem Boxes", which challenge the reader to fill in the missing text. Still, as one reads the book, one gets the vaguely disquieting feeling that the author wanted to include much, much more information, but didn't have the chance.

The careers suggested by the author were limited and unimaginative. Pass on it, there are much better career books out there for both romantic and creative types!

I consider myself a romantic. I'm about to graduate from college, and I have no idea what I'm going to do with my life. When I saw this book in my school's job placement office, I thought it looked like something I should read--careers for romantics! I'm romantic and I'm looking for a career. How perfect!

Sadly, this book is far from perfect. Many of the careers in this book--most of the careers, actually--don't appeal to me at all. Why would I want to be a wedding coordinator when I don't even want a wedding of my own? Romance doesn't always mean marriage. The only career in here that is a possibility for me is to be a romance novelist (mainly because that's what I plan on doing), but the book told me nothing that I didn't already know. Something I was hoping to find in this book was what I can do to support myself before my books start selling... but this had none of that. Other possible careers--like writing love letters for a living, seemed highly unlikely as viable careers. I don't think that many people want to buy letters that someone else wrote--especially not enough to make a living off of. I need to make a living. This book did not help me at all.

This book may be a springboard to a whole new professional life! With insider interviews and insightful descriptions of careers and jobs in more than a dozen industries, career book author Blythe Camenson will get those creative what-ifs going in your brain.

Not just a resource book for romantic people, but a resource book for creative people, entrepreneurial people, and people who seek fulfillment from work, this book could be your ticket to a whole new lifework. With essays from people in various careers, you'll get an insider's look at the pros and cons of different types of jobs, many of them fun.

One of the advantages to the careers in this book is that most of them do not require lengthy training or expensive education, but rather creative talent, desire, and skills that are learned on the job.

I recommend this book to those who seek their destiny, rather than "default" employment. The book is encouraging and inspirational. Ideas will be percolating in your head in no time at all.

Eve Paludan, author of 3 editions of Romance Writer's Pink Pages