Customer Reviews

Bayesian Data Analysis, Second Edition (Chapman & Hall/CRC Texts in Statistical Science)

5 star:		(8)
4 star:		(3)
3 star:		(4)
2 star:		(2)
1 star:		(0)

 

 

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).

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.

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.

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.

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.

I used this book for an introductory graduate course in Bayesian Data Analysis. I found aspects of the book to be needlessly confusing due to a lack of mathematical clarity in the text. The mathematical level of this book is very low. However, the book proceeds to perform Bayesian data analysis using multivariate normal theory and generalized linear models, without developing any background. It seems contradictory to assume such a low mathematical level, but also assume that the reader knows particular results from multivariate normal theory and glm. The verbal orientation of the book can be frustrating, especially since a verbal description could adequately suggest more than one model formulation. I would not recommend this book as a text book. This book seems best served as an auxiliary book for examples. If you want to learn Bayesian statistics, you need to buy "The Bayesian Choice: From Decision-Theoretic Foundations to Computational Implementation" by Christian P. Robert. Robert's book is the correct place to start.

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.

I've read many, many books on Bayesian analysis at this point. Gelman's book is head-and-shoulders above the rest as an introduction to Bayesian analysis. His book does an outstanding job of introducing the model and the motivation behind the parameters from a very intuitive perspective. Many other Bayesian statisticians seem to enjoy the formulation of the problem so much (count myself as one of them) that they get lost in the beauty of the math and it becomes difficult to effectively convey why the model was selected and how to infer the parameters.

Gelman's book is the first book I've read that strikes a balance between the formulation and the explanation.

This book is not for those looking for the theoretical motivation behind Bayesian analysis, or those interested in absorbing the bounds of asymptotic performance, etc. Christian Robert's "The Bayesian Choice", or his other co-authored books, is a much better place for those who have already gotten their minds around Bayesian statistics and want to explore the gory details.

I don't dock Gelman's book for the limited amount of formal propositions/theorems/proofs because I feel that there are plenty of other decent books that do that well. But Gelman's book fills a much-needed gap for those interesting in starting out in Bayesian statistics.

The book introduces the basis of bayesian statistics. There are lots of examples and many applications realized by R software or WinBugs.
Topcis about hierarcical models and MonteCarlo markov Chain method are explained clearly.
I think that a minus prerequisite is a good knowledge of classical stastical inference, stastical models and software packaging as R, stata or Win Bugs.

This book, more than any statistics book that i've read, is full of beautiful heuristic commentary which is also useful to a practitioner.
I've found that an excellent supplement is "Bayesian Modeling Using WinBugs" by Ntzoufras. Gelman et al. provide wordy but enlightening explanations of Bayesian concepts with just the right amount of Math for someone that wants get their hands dirty and analyze some data with competance. The book is full examples with nice discussions from someone with a deep understanding of statistical inference. What these examples sometime lack is details of how the results were got.

This is where Ntzoufras comes in.

Ntzoufras complements Gelman perfectly by offering a book full of detailed examples with a lot of R and WinBugs code.
Jim Albert's book, "Bayesian Computation with R" is also a very good supplement to Part III of Gelman et al. as is Albert's LearnBayes R package.

Gelman has also co-written an R package called "arms" which can also supplement some of this book.