This is a great, great book that I'm absolutely ecstatic to see back in print. I was introduced to it when I was in graduate school (mathematics) and rooming in the house of a physics professor who swore by Richard Threlkeld Cox's account of subjective probability. I haven't had a copy of it in my hand for nearly twenty years; I happened across this page today and ordered it at once. So pardon me while I gush:

What Cox accomplishes in this deceptively slim volume is amazing. He places Bayesian probability theory on an axiomatic foundation, as a natural extension of Boolean logic, identifying probabilities with degrees of subjective belief in propositions rather than directly with frequencies of events (though he also argues that the subjectivist interpretation accords with the frequentist interpretation whenever the latter makes sense at all).

Essentially, he shows that the ordinary laws of probability theory are normative laws of thought that apply to degrees of belief in propositions, and that we have to conform to them if we want to think consistently.

If you like math and logic books, you'll find this one eminently readable; I haven't seen it in years and yet I still remember the stunning clarity of Cox's rigorous exposition.

This is the book that originally sold me on Bayesianism. If you have any interest in this subject at all, grab this one while it's available.

This book contains the fundamental argument justifying Laplace's original theory of probability. Laplace justified his theory by basic intuitive considerations, which left it open to attack on philosophical grounds. Here, R. T. Cox shows how Laplace's theory is the logical consequence of two very simple, almost unavoidable axioms.

Cox begins the book by discussing his axioms, and then expressing them as functional equations. The solution of these functional equations develops the theory to the point at which Laplace began his own development.

(In general, the probability of a proposition is conditional on the truth of some other proposition. An item of particular interest here is that while most Bayesian expositions call this a priori true proposition "prior information", Cox calls this proposition the "hypothesis". This term seems to me to be more sensible, because we are rarely absolutely certain about our prior information. We take our "prior information" to be true, not because we are certain it is true, but as a conjectural point of departure for the subsequent calculation.)

Cox continues the development of the theory by relating the notion of probability to information entropy. He gives a definition for systems of propositions and shows how entropy is related to the uncertainty as to which of the propositions in the defining set of the system is true. (By hypothesis, at least one proposition in the defining set is true.)

Cox finishes the book with a section on expectation. He shows here how the theory he has developed encompasses all of the standard results of expectations found in other theories of probability.

This book looks deceptively thin, but packs the punch of a ten-pound textbook. It requires multiple passes (or, perhaps, one pass, closely read) in order to get all of the information out of it. It is definitely an exposition of an algebra, that is to say, an abstract symbolic method of calculation. Sometimes Cox gives concrete examples to illustrate the abstract reasoning, and sometimes he doesn't. Where he doesn't, the reader is left to puzzle out the concrete consequences of the abstract reasoning. I'm not sure if this is good or bad, but I'm leaning towards good, even though it does make my brain hurt.

That Gian-Carlo Rota and I both admired this book largely
explains why I have my present position at MIT. But I
cannot write book reviews the way Rota did.

Why should the conventional sum and product rules of
probability hold when probabilities are assigned, not
to *events* that are *random* according to their
relative frequencies of occurrence, nor to subsets of
populations as proportions of the whole, but rather
to *propositions* that are *uncertain* according to the
degree to which the evidence supports them? The tenet
that the same rules should apply to such "degrees of
belief," whether they are "subjective" probabilities or
"logical" probabilities, is the essence of Bayesianism.
The relative merits of Bayesian and frequentist methods of
statistical inference have been debated for decades. But
seldom is the question with which I started this paragraph
addressed. Several answers to that question have been
proposed. Richard Cox's book embodies one of them.

Many writers on foundations of statistical inference are
callously imprecise about the kind of topic dealt with
in this book. Cox is their antipode, writing not only
clearly, but supremely efficiently, beautifully, perhaps
sometimes poetically, about functional differential
equations and about delicate philosophical questions.

Cox also deals with the relationship between entropy and
distributive lattices. Shannon entropy is to distributive
lattices as probability is to Boolean algebras. I do not
think Cox was familiar with standard work on lattice theory.
He never uses the word "lattice," nor other standard
lattice-theory nomenclature.

The second edition is much like the first and is at least a year behind the original schedule. See my review of the first edition to understand why this is a classical. The promised advances in missing data are included and a new author Haegerty has been added. The missing data chapter is three times longer than in the first edition. They cover what they promised. They also mention some of the econometrics literature including the work of Nobel Laureate James Heckman but admit in the preface that they do not know that literature very well and hence do not cover it in depth.

In the past two years Verbeke and Molenberghs have produced a highly competitive book that deals in detail with pattern mixture models and other missing data methodology but curiously Diggle et al. do not reference it even though they do cite some of Molenberghs work.

When this book came out in 1994 there was a great need to look differently at clinical data on subjects. Typically such data would have repeated measurements over time for many subjects but for only a few time points (say three to five). Standard analysis of variance methods do not properly account for within patient correlation between measurements. Time series analysis generally is good for treating long series (but usually only one or a few). In the clinical setting we often are considering hundreds of patients over short time intervals. This book is clearly written for intermediate level statistics students.

The field is important and rapidly developing. Though slightly dated the book is still an excellent introduction to the subject and a very good reference. However, a second edition is in the works and should be out in about one year. I recently took a short course from the authors and I know that the second edition will have some nice features including the latest advances for dealing with missing data and ways to combined the information from time to event data with the repeated measures data. It may be that if longitudinal data analysis is important to you, read the first edition at your favorite university library and save your money for the second edition.

The book includes some nice treatment of the important but often neglected topic of sample size determination.

This book was written by three very prestigious authors, two of which work at The Johns Hopkins University(Dr. Liang and Dr. Zeger), and Dr. Diggle, who is working in England. These three are very well known and respected characters in their field of work, and this book is an excellent reflection upon the research and work they have done over the years. Watch out! the key word is: GEE

Overview

This book was the textbook used at the University of Wisconsin-Madison for the graduate course in Bayesian Decision and Control I during the fall of 2001 and 2002. It strikes a good balance between theory and practical example, making it ideal for a first course in Bayesian theory at an intermediate-advanced graduate level. Its emphasis is on Bayesian modeling and to some degree computation.

Prerequisites

While no Bayesian theory is assumed, it is assumed that the reader has a background in mathematical statistics, probability and continuous multi-variate distributions at a beginning or intermediate graduate level. The mathematics used in the book is basic probability and statistics, elementary calculus and linear algebra.

Intended audience

This book is primarily for graduate students, statisticians and applied researchers who wish to learn Bayesian methods as opposed to the more classical frequentist methods.

Material covered

It covers the fundamentals starting from first principles, single-parameter models, multi-parameter models, large sample inference, hierarchical models, model checking and sensitivity analysis, study design, regression models, generalized linear models, mixture models and models for missing data. In addition it covers posterior simulation and integration using rejection sampling and importance sampling. There is one chapter on Markov chain simulation (MCMC) covering the generalized Metropolis algorithm and the Gibbs sampler.

Over 38 models are covered, 33 detailed examples from a wide range of fields (especially biostatistics). Each of the 18 chapter has a bibliographic note at the end. There are two appendixes: A) a very helpful list of standard probability distributions and B) outline of proofs of asymptotic theorems.

Sixteen of the 18 chapters end with a set of exercises that range from easy to quite difficult. Most of the students in my fall 2001 class used the statistical language R to do the exercises.

The book's emphasis is on applied Bayesian analysis. There are no heavy advanced proofs in the book. While the proofs of the basic algorithms are covered there are no algorithms written in pseudo code...Additional books of related interest

1) Statistical Decision Theory and Bayesian Analysis, James Berger, second edition. Emphasis on decision theory and more difficult to follow than Gelman's book. Covers empirical and hierarchical Bayes analysis. More philosophical challenging than Gelman's book.

2) Monte Carlo Statistical Methods, Robert and Casella. Very mathematically oriented book. Does a good job of covering MCMC.

3) Monte Carlo Methods in Bayesian Computation, Ming-Hui Chen, Qi-Man Shao, Joseph George Ibrahim. An enormous number of algorithms related to MCMC not covered elsewhere. If you need MCMC and need an algorithm to implement MCMC this is the book to read.

4) Monte Carlo Strategies in Scientific Computing, Jun S. Liu. Covers a wide range of scientific disciplines and how Monte Carlo methods can be used to solve real world problems. Includes hot topics such as bioinformatics. Very concise. Well written, but requires effort to understand as so many different topics are covered. This book is my most often borrowed book on Monte Carlo methods. Jun S. Liu is a big gun at Harvard.

5) Probabilistic Networks and Expert Systems. Cowell, Dawid, Lauritzen, Spiegelhalter. Covers the theory and methodology of building Bayesian networks (probabilistic networks).

This is a well written text that is fast becoming a classic reference. It contains a wealth of good applications. It is one of the new books that presents the growing use of Bayesian methods in practice since the advancement of Markov Chain Monte Carlo approach. It includes a whole chapter the Markov chain approach to computation. Other strengths of the book include the chapter on missing data and the chapter that provides expert advice.

Another text in the CRC series Markov Chain Monte Carlo in Practice by Gilks, Richardson and Spiegelhalter provides more detail on these methods along with many applications including some Bayesian ones.

First, I must admit a bias: I frequently work with one of the authors (Gelman), and I think highly of his work and statistical judgment.

This book's biggest strength is its introduction of most of the important ideas in Bayesian statistics through well-chosen examples. These are examples are not contrived: many of them came up in research by the authors over the past several years. Most examples follow a logical progression that was probably used in the original research: a simple model is fit to data; then areas of model mis-fit are sought, and a revised model is used to address them. This brings up another strength of the book: the discussion and treatment of measures of model fit (and sensitivity of inferences) is lucid and enlightening.

Some readers may wish the computational methods were spelled out more fully: this book will help you choose an appropriate statistical model, and the ways to look for serious violations of it, but it will take a bit of work to convert the ideas into computational algorithms. This is not to say that the computational methods aren't discussed, merely that many of the details are left to the reader. The reader expecting pseudo-code programs will be disappointed.

All in all, I recommend this book for anyone who applies statistical models to data, whether those models are Bayesian or not. I especially recommend it for researchers who are curious about Bayesian methods but do not see the point of them---Chapter 5, and particularly section 5.5 (an example chosen from educational testing), beautifully addresses this issue.

Recently there have been a wealth of good books published on Bayesian methods and the Markov chain Monte Carlo approach to its implementation. For the beginner Berry's introductory book is a good place to start.

Bernardo and Smith are experts in the field who have participated in many of the Bayesian conferences held in Valencia and much of that lterature is contained in this book. They originally wrote the book in 1993 (with a publication date of January 1994). This paperback edition is not a revision but rather a reprinting with corrections. The original hardcover edition was very expensive and this paperback edition makes the text more affordable and should greatly expand the list of Bayesian specialists and other statisticians and practitioners that read it.

The authors intent was to extend the classical work of Bruno deFinetti who popularized the Bayesian approach with his two classic probability books. One of the authors was involved in translating deFinetti's books into English and they are both well familiar with it. In this book they offer an extension to the area of statistical inference.

The beauty of deFinetti is the logical and systematic nature of the presentation but he did not extend this to statistical practice. These authors maintain the systematic approach and review the probability axioms but then go on to cover statistical modelling including how models are approached through concepts of exchangeability, invariance, sufficency and partial exchangeability. The chapter on inference covers the Bayesian paradigm, the use of conjugate families, asymptotic methods, multiparameter problems and the thorny issues with nuisance parameters. It also includes a number of methods of numerical approximation including Markov chain Monte Carlo (MCMC) methods.

The authors deliberately left the coverage of computational methods brief as they planned a second volume to cover it in detail. But in the preface to the new paperback edition they admit that they have abandon this plan due to the evolution of MCMC methods as the dominant numerical approach and the wealth of new texts that adequately cover the topic.

I suggest that this text is the new bible for Bayesian statistics because I think it replaces the old bibles, Lindley's two volumes (some may argue for Savage's book). This is fitting as both authors attest to being students and disciples of Dennis Lindley. The reason I think it is worthy of bible status is because it covers the foundations in systematic detail, is current and very complete. The text contains references from 1763 (Bayes' original treatise) to 1993 covering an incredible 66 pages of the text. With 20 plus references per page that means over 1320 references!

This is an intermediate level text that requires advanced calculus but not measure theory. Emphasis is on concepts and not mathematical proofs. The authors also provide an overview of the non-Bayesian forms of statistical inference in Appendix B. The authors confront the controversial issues in each chapter. Bayesian statistical methods are treated in the framework of decision theory and ideas from information theory take on a central role.

This book provides a thorough introduction to Bayesian theory and decision analysis. It presents a coherent defense of the subjective view of probability that is driving many new technologies, including probabilistic graphical models, data mining, information retrieval and machine learning, as well as, classical problems such as control and econometrics. It is therefore a must for students and practitioners in these fields. The new, reasonably priced, paper-back version makes the book suitable for university courses on model selection, conjugate analysis or Bayesian statistics in general.

This excellent book presents the foundations of the Bayesian approach to uncertainty in systematic way. Statistical inference is treated as a decision problem which, the authors argue, should be solved on the basis of a subjective probability measure. The emphasis is on ideas rather than technical details and every chapter ends with a detailed discussion of specially important subjects. The list of references is so comprehensive that they alone provide a good reason to buy the book. An absolute must for any true Bayesian, and a perhaps even more necessary book for the yet unconvinced non-Bayesian.

Schumacker and Lomax make for a good first course in SEM. Although they are somewhat less technical than Bollen (1989), they are a little more up-to-date, and very good reading for a beginning student of SEM. I found the sections on confirmatory factor analysis and identification very useful.

This is a very good book about SEM for the beginners and advanced. The book gives a clear and concise principles and examples about SEM. This book definitely enables the readers clearly understand the subject.

The authors present remarkably the basic principles and concepts underlying SEQ, but also give numerous notions about technical aspects. An Excellent book, even for people who are not very keen on statistical writings.

Great book !! Statistical analysis ? When to use what ? How to interpret ? You won't ask these questions after you read this book. Full of examples. I am teaching marketing research and I strongly recommend this book to every business student who wants to learn the basics of bivariate analysis. I also encourage the author for second edition which will cover more examples or maybe even multivariate data analysis !

As a business student, I took the required two semesters of stats and did pretty well. Yet I never understood why, if, or when I was using the correct or most conclusive test to support the data. I always felt that something was missing. This book gives you the confidence to continue the research knowing that the method used to support your conclusion is the most appropriate for the data collected. The definitions are complete and the examples are varied. This book is great if your at a stand still on how to define your problem to meet the desired criteria of a statisical test. It definitely relieves the intimidation factor.

After reading Bivariate Data Analysis I would like to offer the following as a review: First of its kind. Offers information not otherwise available. Easy to read and understand. Interesting charts, examples, and experiments Great choice for students doing research work.

An excellent yet concise encyclopedy of surprisingly wide range of statistical topics, very dense and ballanced text. Exhaustive descriptions and definitions on few lines of text with good referrences. I can hardly think of basic or advanced statistical terms not included here. Thanks.

Brian Everitt is a well known statistician and author. This dictionary was prepared by a scholar and includes many famous statistician as well as statistical terms. It provides concise and accurate descriptions and in many cases also includes pictures and formulae. Literature references are often mentioned. Particularly useful to biostatisticians. It is an excellent reference document.

I bought this book to celebrate passing my Master's course. It's worth every penny. There is hardly a Statistical term that one might want to refer to that is not defined in it. Just occasionally there is a definition which could be a bit more precise, e.g. the definition of hazard as a probability rather than its differential coefficient. Nevertheless, an excellently comprehensive book and a very worthwhile addition to anyone's library.

If you decide to do any gambling, even a few bucks on your state lottery, consider the price of this book as your first bet. Orkin presents the real odds of most popular gambling games, at least one 'sure fire system' (yes there is such a thing, but you need deep pockets and have to be satisified with a pretty low rate of return), and the effects of the 'house edge'in an entertaining manner and with just a minimum of math. In fact, skipping the math in the book does nothing to reduce the book's usefulness nor your reading enjoyment.

Read this if you think gambling is a solution to money problems. In fact, after going through this highly readable and entertaining book you may be tempted to skip the lottery tickets and put the money in casino stock instead!

Casino math for the non-mathematician. If you really want to understand the math, it will take some effort to follow if you haven't dealt with probability and statistics in a while or ever. However, I am so tired of people presenting schemes on how to win at craps, roulette, etc: Martingale, anti-Martingale, D'Alembert, contra-D'Alembert, ad nauseam. No matter how you weight a negative expected return, the sum of the series is still expected to be negative. The risk to people who use these schemes unwittingly to gain a series of small "wins" is the guarantee of a single huge loss somewhere in the future - the longer you put it off, the larger it will be. If you didn't understand what you just read and want to, this book is for you. The writing is brisk, bordering on entertaining (if you're into this sort of thing) and not nearly as dull as you'd expect. The previous reviewer covered which games were presented so I won't repeat. Like Stanford Wong, this author's math is accurate - unlike many, many other authors.

Mike Orkin's book explains the real odds for all the common casino games, and in the process, shows you it is generally better to leave your money in your own pocket, and just watch. Games covered include roulette, craps, Keno, slots machines, sports betting, blackjack, lotteries and horse races. A great chapter on the Prisoner's Dilemma is included, and covers thecomplex issue of when it is best to be a snicth, and when it is best to be quiet.

This book is very unique. Basic statistical concepts are clearly presented but only those concepts that are important in clinical trials. The author presents all the issues with clinical trials including ethical issues with some historical perspective. Principles of randomization and statistical design are clearly presented. It offers discussion of Bayesian techniques and meta-analyses, cross-over designs and group sequential methods (interim analyses). For statisticians doing clinical research like myself, this is a valuable reference source.

The amount of knowledge and the scope of this book are the exact need for the first contact with clinical trials. Yet, it is not a simple or superficial text. Instead, it not only will guide the reader through the basics of trials (and there is so much that is not basic in it) but the author points the reader to hundreds of papers and books that are landmarks. I regard this book itself as one of these landmarks!

Covers many aspects of trials (particularly facets of design and analysis)not yet covered by other books, eg randomisation with minimisation, and meta-analysis of trial results. Readable, applicable, practical, good references, well structured.