Brad Carlin and Tom Louis recently came out with a third edition of their book, originally called Bayes and Empirical Bayes Methods for Data Analysis with a plain green cover, now called Bayesian Methods for Data Analysis with a red cover with graphs on it. In title and appearance they are thus converging to our book. They even use the “Bugs code” and “R code” marginal notation that is in my book with Jennifer (see Carlin and Louis, page 178, for example).

What’s fun, though, is how *different* their book is from ours. I highly recommend that anyone interested in Bayesian statistics buy their book as well as Bayesian Data Analysis. This review focuses on the features of Brad’s and Tom’s book that differ from ours.

Their approach to *modeling* is similar to ours: building up hierarchical models from basic building blocks such as the normal and Poisson distributions, and letting the details of the model be driven by the problem structure and the data at hand.

Their approach to *fitting* models is similar to ours, basically, relying on Gibbs and Metropolis, with a nod to simpler methods such as direct sampling rejection sampling (as conceptual aids and as components in more elaborate sampling schemes) and to more complicated methods such as hybrid MCMC for those hard problems that Brad and I try to avoid.

Their approach to *checking* models differs from ours. We are proponents of fitting a model, checking it by comparing data to predictive simulations under the fitted model, and then altering the model as necessary to account for serious discrepancies with observed data. Carlin and Louis follow a more mainstream Bayesian approach of model selection and model averaging using Bayes factors (posterior probabilities of different models being true, conditional on a discrete space of possible models).

Beyond this, their book has many strengths, including R and Bugs code, many real examples, and theoretical discussions of Bayesian experimental design and frequentist/empirical-Bayes inference. As noted above, the book as a whole overlaps remarkably little with ours, despite their having an applied and philosophical perspective that is close to ours.

Now some minor comments (things to fix in the next printing or the next edition). I didn’t try to catch everything; I just opened the book to the middle and started noting things.

p.162: Table 3.5 should be a time-series plot. You can put the raw numbers on the web.

p.177, Figure 4.5: What happened here??

pp.294-295: Tables 6.4-6.6 should be graphs (with n on the x-axis).

pp.296-297: You gotta either make these graphs more readable or supply a magnifying glass for those readers over the age of 40.

p.298: Table 6.7 should be a table^H^H^H^H^Hfigure.

p.301: Figure 6.8 looks weird. Why isn’t this in the usual “typewriter” font you used for Bugs code in the rest of the book?

p.337: You gotta be kidding.

OK, you get the picture. I won’t go over every page….

Finally, my only serious criticism. I don’t like Appendix B on decision theory. I think this sort of decision theory (quadratic loss functions and the like) is both less interesting and less important than actual decision analysis (where the costs represent dollars, lives, etc.). We make this point on page 543 of Bayesian Data Analysis (second edition). For their next edition, I hope Brad and Tom replace their Appendix C with something like our chapter 22 (but with their own examples, of course).

**Summary**

I like this book a lot. It’s not the book that I would’ve written, and that’s a good thing. Buying Carlin and Louis along with our book will give you two perspectives on applied Bayesian statistics as it is practiced in the 21st century. Compared to our book, Carlin and Louis offer the following:

– Discussion of the debates over Bayesianism within the statistical community, culminating in chapter 5, which covers the links between Bayes, empirical Bayes, and frequentist methods of evaluating statistical procedures.

– A crisp presentation of Bayesian computation (chapter 5), which offers a different perspective than ours.

– A chapter on experimental design including several biomedical examples. This chapter should be useful to a lot of people, I think.

– Near the end of the book, discussion of several classes of models–longitudinal analysis, survival analysis, spatial models, clinical trials, and others–where I often think, “What’s would a Bayesian do here?”

I don’t think Carlin and Louis have made our own Bayesian Data Analysis obsolete but I do think their book is a great complement to ours, with a slightly different perspective, strong coverage of the theoretical issues of point and interval estimation, and a bunch of compelling biomedical examples.

"Table 6.7 should be a table."

Isn't it?

Andrew: Thanks very much for your kind and favorable review; my student Laura Hatfield alerted me to its existence. Naturally I'm thrilled you basically like the book and I'll make sure Tom sees your review as well.

Hal has already kidded me that by dropping "empirical Bayes" from the title and adding a picture to the front cover, we now have a book that looks very similar to BDA! But really the reason for dropping the "EB" was we heard from the publisher that the phrase was frightening away a few potential buyers from comp sci and other non-statistical fields. Plus it's just an admission of the reality that modern Bayesian data analysis is mostly fully Bayesian and done via MCMC these days, and approximate methods like EB are no longer "core material". Still the Ch 5 comparison of Bayes, EB, and frequentism is important and I'm glad you like this part.

Yes indeed I did steal your "BUGS code" marginal notation from your book with Jennifer; I thought it was an excellent idea! More generally, I now teach a course here at Minnesota where the audience is MS-level guys in stat and biostat, and PhD-level guys in other fields, most of whom need to learn some hierarchical modeling so they can analyze data for their dissertations. So I wanted to get some BUGS and R code in the book right away in Ch 2, rather than making them wait until after I'd gone thru all the MCMC algorithms and details. This is a fairly major difference from your book, since you make the student do a lot of easy models to get started and don't let them do any MCMC until Ch 10 or 11, I believe — halfway thru the book. We wanted to get them up and running a little quicker (understanding the risks that this entails).

In this MS-level class I cover just the first four chapters in the book, and then pick a few goodies from elsewhere in the book (clinical trials, spatial, etc) to finish up. Meanwhile your gifted former student Cavan Reilly teaches our PhD-level Bayes class, in which he covers the whole of the book and probably supplements with a little Bernardo and Smith, since our book is not heavy on the theorems by any stretch.

re: tables to figures in the HW problems, sure I guess so; the coal mine data and rat weight data tables are holdovers from the old green book days when the data weren't also sitting there on the web for the student to download. Certainly a plot of the coal mine data would make abundantly clear where the changepoint happened ;) re: the tables in the clinical trials chapter, here I'm afraid this is standard operating procedure in this area; these clinical trials statisticians have an incredible tolerance for "table pain"; the protocols are filled with them. re: Fig 6.8, sure, we should have put that in typewriter font like the others, instead of in its own "figure".

finally re: your serious criticism (you don't like decision theory), you and I have had this discussion before so we won't have it again now. Moreover I would prefer to let Tom have a go at it since this is basically his material! We did at least get it out of the body of the book after the first edition, because we found it was freaking out too many people and was not central to the presentation (at least at the MS level). But decision theory is how we "keep score" on which procedures are good and which are not, so the Ch 5 presentation needs it to some extent. Again I'll let Tom comment further.

Finally if I may be permitted one tiny advert/shout out here, Laura has been working incredibly hard on a solutions manual for CL3, and it will be available for any instructor adopting the book for the Spring 2009 semester. I'm talking solutions for *every single problem* in the book. The instructor will also get files with the R and/or BUGS code for every problem requiring it, so s/he won't have to retype all that and can check our answers and maybe do a few tweaks of his/her own. Only a student of Laura's intestinal fortitude could have pulled this off (and with only minor help and nitpicking from me).

We hope this further enhances the book's usefulness as a text and a self-study device.

Thanks again for the kind review. BDA remains the "industry standard" in the field and if we can sell half as many copies as you already have, we'll be thrilled.

Andrew, Thank you for taking the time to evaluate C&L3 and posting your comments. Brad has replied to most of them; I'll rejoin on Appendix B: Decision Theory. The material isn't intended to be a comprehensive treatment of a context-connected decision analysis. We included the material to provide some guidance on how to develop procedures that address non-standard, inferential goals such as ranking and histograms (see 7.1) and not as a recipe for life.