Customer Reviews

Bayesian Statistics: An Introduction

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3 star:		(1)
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This is a simple and easy-to-read introduction to the basics of Bayesian statistics, for someone with some previous exposure to statistical methods and theory. Lee does not try to do too much with this book. It's not too taxing on the brain, uses simple and easy-to-follow notation, and has a helpful appendix of common statistical distributions. I like the emphasis on conjugate priors, which are the mathematically most tractable Bayesian models that are often not treated fully in other texts. (Someone still needs to write the definitive text on conjugate Bayesian models.)

The book is limited in scope, a strength if you're just getting started on this topic, but will frustrate once you get into this stuff. There are plenty of other good books that go beyond the basics once you're ready.

Although only the second edition is listed, I have read only the first 1989 edition and my review is for that edition. Lee wrote this book with the goal of teaching an introductory course in Bayesian statistics to his students at York University. He wanted a text that was more mathematical and deatiled than Lindley (1965) but not quite at the level of Box and Tiao.
This text achieves that goal. It was published at the time when MCMC methods were only starting to be appreciated. So the wider use of general prior distributions and hierarchical models does not yet enter into this book. I would assume that the second edition published in 1997 was written to remedy this shortcoming but I have not seen if it does.

But for the time it was a good intermediate text.

This book has a clean selection of materials as an introduction to bayesian statistics. It is quite readable. Two problems however: 1) the formula derivation and reasoning often have intermediate steps skipped. You need to think for a while for derivations and his texts. In particular, you need to figure out by yourself which theorem or previous results that the derivation is based on. 2) typos. the 3rd printing still has typos not listed in the author's page, not too many but not trivial either.

Anyway, I still recommand this book because no better introductory bayesian book found yet.

Lee's book is an introductory text to the Bayesian statistics; as such it does a good job;

The notations are not usual, as remarked by another reviewer, but it is definitely not a show-stopper; on a first reading; on a second reading however, after getting acquainted with classical notations used in other textbooks, Lee's notations do indeed disturb;

Lee updates the errata and offers solutions to all exercises; both can be found on Lee's web site [...]

It is classical in the sense that linear (in the unknown parameters) and non-linear regression and model comparison are not handled; those topics are hardly ever addressed in introductory textbooks, which is quite frustrating for engineers. Pattern Recognition and Machine Learning (Information Science and Statistics) by Bishop would be a good companion to bridge the gap.

The book has also true weaknesses:
- the introduction is rather aimed at mathematicians; no exposition, detailed or not, on all the applications (image reconstruction, spectrum analysis, model comparison, ...) where Bayesian statistics have shown tremendous benefits; I think the best introduction was written by Sivia in Data Analysis: A Bayesian Tutorial (though Sivia's book cannot be considered to be an introductory text); As an engineer, this is the kind of motivations I would expect in the first pages, and that is desperately missing;
- the treatment of the EM algorithm is difficult to understand; Duda et al. in Pattern Classification (2nd Edition) offer a simple enlightening worked-out example to illustrate how the EM works; again, it would have been great if Lee had included such examples for illustration; another very good coverage of the EM at both an introductory and advanced level can be found again in Bishop's Pattern Recognition and Machine Learning (Information Science and Statistics);
- the third edition brings a coverage of Monte Carlo methods (Gibbs sampler and Metropolis-Hastings algorithm); I think, this new addition should be either revamped or withdrawn since it is extremely cryptic, to say the least; the paper of Casella and George "Explaining the Gibbs Sampler" available on the net is much clearer and well-written;
- the principle of maximum entropy to assign probabilities is not treated;
- curiously, there is not a single reference to the seminal works of Jaynes;
- after reading the book, it was not clear to me why to use a Jeffreys prior for a Gaussian distribution; in this respect, Bayesian Logical Data Analysis for the Physical Sciences: A Comparative Approach with Mathematica® Support presented a clearer view on this topic;

This book appears to have all the basics for Bayesian Statistics, but the notation is very different from most statistics texts. For example, theta is usually the mean, as opposed to the standard mu, and phi is the variance, as opposed to sigma^2. It's also not a light read, although most graduate level mathematics/engineering texts arent as well.