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Statistical Decision Theory and Bayesian Analysis (Springer Series in Statistics) 2nd Edition
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"The outstanding strengths of the book are its topic coverage, references, exposition, examples and problem sets... This book is an excellent addition to any mathematical statistician's library."
(Bulletin of the Am. Mathematical Soc.)
About the Author
James O. Berger teaches at the Institute of Statistics and Decision Sciences, Duke University.
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This book covers decision theory and Bayesian statistics in much depth. While it is a high-level text oriented towards researchers and people with strong backgrounds, it is clear enough that someone learning this material for the first time would have little trouble with it. It provides ample review and clear exposition of key mathematical and statistical concepts such as sufficiency, convexity. Its exposition of invariance (with respect to groups of transformations) is both the clearest and most rigorous I have found in any statistics text. In my opinion, there are no weak or unclear sections in the book, and the difficulty level does not rise disproportionately in later chapters the way it does in many books on similar subjects.
This book is rich with examples, and the examples are mostly of a practical nature, in contrast to the "toy" mathematical examples that dominate many books written at this advanced level. The exercises are diverse and extensive, and have a good gradient of difficult level for building both technical skill and depth of understanding. The exercises are more carefully worded and constructed than is typical for books at this level. Most of the typos have been caught and corrected in the revised edition.
This is an old book. The author, in his philosophy, was arguably well ahead of his time. The ideas contained in this book are highly modern. However, the use of computers in statistics has changed since this book was written. This book is a book on theory and will teach you how to do things by hand. I do not see this as a weakness at all, but one should be aware of it when considering this book. But, as the other author noted, it will not teach you algorithms, numerical techniques, or how to use a statistical computing package.
I think this book would make an outstanding textbook for a course in statistical decision theory or Bayesian statistics. It would also be useful as a supplement for a course in statistical inference. Perhaps more importantly, it is very useful for self-study. I think this book would make an excellent addition to any statistician's collection--and it would certainly be useful to people working in more practical settings, such as business, science, or social science. If you are going to buy any one advanced, theoretical book on statistics, this would be the one to buy.
 Its mathematics is precise and fascinating.
 The philosophy of Bayesian statistics is well discussed.
 It's worthy to read it many times.
 At the time of its publication, the revolutionary computational statistics was still in gestation. So, it is unfair to criticize its lack of numerical simulation, etc. As a comlement, some pragmatistic books are recommended, such as J. Liu's book on MCMC methods, Tanner's Tools for Statistical Inference, etc.