This seems to be the best book out there for learning Bayesian statistics. The book is well written and usually quite clear. I think it be better organized, and pointers to programming examples would be welcomed, especially in the introductory computation section.

I am an engineer, and unfortunately for me, this book is geared towards social scientists. However, no other bayesian statistics books currently teach from an engineering perspective, so this is your best be if you are an engineer.

This book does assume a good deal of familarity with mathematical statistics, which many engineers do not have. However, it is possible to get though it by looking this up on wikipedia.

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. It is one of the best books ever written on the practical aspects of modern Bayesian analysis. I know one of the authors very well (Hal Stern) and am familiar with the fine research work of the others. Don Rubin brings a wealth of knowledge and experience in statistical methods and Bayesian analysis to the table. He is also the inventor of the Bayesian bootstrap.

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.

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.

This book is a very comprehensive treatment of Bayesian data analysis. However, it is not well-written. I find Lancaster's book to be much more well-written and interesting to read.

This book is a very comprehensive treatment of Bayesian data analysis. However, it is not well-written. I find Lancaster's book to be much more well-written and interesting to read.

Gelman's book is an excellent and complete introduction to Bayesian methods. It covers a number of topics not touched by other intros I've read, and focuses much more on regression and ANOVA than other texts.

There are two downsides, coming from someone in psychology. First, the book seems to hover between an introductory text and a more advanced one. The topics covered are mostly introductory, but the examples aren't always entirely easy to follow. A tighter integration with the R and Bugs code would help. Perhaps a section at the end of the chapters containing a code example for each topic would be ideal. It's not that the topics themselves are necessarily opaque, but Gelman moves too fast at times, making it hard to think in terms of notation, theory, experimental design AND code at the same time (for those of us constantly thinking about how this affects our own research).

Second, as a general rule, this book is outside the ken of most psychologists. This is unfortunate since the methods are ideal for our discipline, and since many psychologists already perceive a large barrier of entry to statistics. As a psychologist with minimal undergraduate training in stats, I would (and did) start with a standard statistics book like Casella and Berger, and then move on to a gentler introduction to Bayesian methodology, like _Bayesian Methods: A Social and Behavioral Sciences Approach_ by Jeff Gill. Also, you can barely do anything in this book with SPSS so you'll have to learn R and Bugs.

Yes, it is an introduction to Bayesian methods. That means you have to have a very good understanding of classical statistics (at the level of Casella and Berger would be optimal) and then be willing to use the WinBugs program to further your knowledge. A great book.

[1] A good introductory book, but definitely not a bible of Bayesian analysis.
[2] The example-based introduction may be a try of new generation of Bayesian. Many people, especially the beginners, may like this style.
[3] Some of the authors are good at programming in BUGS, R, etc, so the part of MCMC methods seems worthy to skim through.
[4] The book is suitable for the undergraduate and the first year graduate level.

[1] A good introductory book, but definitely not a bible of Bayesian analysis.
[2] The example-based introduction may be a try of new generation of Bayesian. Many people, especially the beginners, may like this style.
[3] Some of the authors are good at programming in BUGS, R, etc, so the part of MCMC methods seems worthy to skim through.
[4] The book is suitable for the undergraduate and the first year graduate level.

I read the other reviews and agree with them to some extent. This is
a good introduction to applied Bayesian analysis. Lots of
good examples, illustrations and exercises.

If you are the kind of person who learns by way of examples, then
this might be the text book for you. If you are looking for the
bigger picture, then you will be lost here. There is very little in the way
of theory. Why is this the right method? What is gained theoretically
over a frequentist method? What are the theoretical properties of the
proposed approach? To a large extent these kinds of questions remain a mystery.
In terms of flexibility an applied Bayesian approach has some decided
advantages. However, in terms of theory
it's almost as if the authors want you to believe that once
you adopt the Bayesian approach then the benefits of averaging
by way of using a prior will always be the right thing to do.

You could argue that advanced questions like this are better suited for
a more advanced text book. I tend to ask more out of a book.

Note, this is a review of the first edition.

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 (model checking and sensitivity analysis are especially well covered), 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 Monte Carlo 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.