Monte Carlo Statistical Methods (Springer Texts in Statistics) [Hardcover]

Christian Robert (Author), George Casella (Author)

Book Description

Publication Date: July 28, 2004 | ISBN-10: 0387212396 | ISBN-13: 978-0387212395 | Edition: 2nd

We have sold 4300 copies worldwide of the first edition (1999).

This new edition contains five completely new chapters covering new developments.

Editorial Reviews

Review

From the reviews:

MATHEMATICAL REVIEWS

"Although the book is written as a textbook, with many carefully worked out examples and exercises, it will be very useful for the researcher since the authors discuss their favorite research topics (Monte Carlo optimization and convergence diagnostics) going through many relevant references…This book is a comprehensive treatment of the subject and will be an essential reference for statisticians working with McMC."

From the reviews of the second edition:

"Only 2 years after its first edition this carefully revised second edition accounts for the rapid development in this field...This book can be highly recommended for students and researchers interested in learning more about MCMC methods and their background." Biometrics, March 2005

"This is a comprehensive book for advanced graduate study by statisticians." Technometrics, May 2005

"This excellent text is highly recommended..." Short Book Reviews of the ISI, April 2005

"This book provides a thorough introduction to Monte Carlo methods in statistics with an emphasis on Markov chain Monte Carlo methods. … Each chapter is concluded by problems and notes. … The book is self-contained and does not assume prior knowledge of simulation or Markov chains. …. on the whole it is a readable book with lots of useful information." (Søren Feodor Nielsen, Journal of Applied Statistics, Vol. 32 (6), August, 2005)

"This revision of the influential 1999 text … includes changes to the presentation in the early chapters and much new material related to MCMC and Gibbs sampling. The result is a useful introduction to Monte Carlo methods and a convenient reference for much of current methodology. … The numerous problems include many with analytical components. The result is a very useful resource for anyone wanting to understand Monte Carlo procedures. This excellent text is highly recommended … ." (D.F. Andrews, Short Book Reviews, Vol. 25 (1), 2005)

"You have to practice statistics on a desert island not to know that Markov chain Monte Carlo (MCMC) methods are hot. That situation has caused the authors not only to produce a new edition of their landmark book but also to completely revise and considerably expand it. … This is a comprehensive book for advanced graduate study by statisticians." (Technometrics, Vol. 47 (2), May, 2005)

"This remarkable book presents a broad and deep coverage of the subject. … This second edition is a considerably enlarged version of the first. Some subjects that have matured more rapidly in the five years following the first edition, like reversible jump processes, sequential MC, two-stage Gibbs sampling and perfect sampling have now chapters of their own. … the book is also very well suited for self-study and is also a valuable reference for any statistician who wants to study and apply these techniques." (Ricardo Maronna, Statistical Papers, Vol. 48, 2006)

"This second edition of ‘Monte Carlo Statistical Methods’ has appeared only five years after the first … the new edition aims to incorporate recent developments. … Each chapter includes sections with problems and notes. … The style of the presentation and many carefully designed examples make the book very readable and easily accessible. It represents a comprehensive account of the topic containing valuable material for lecture courses as well as for research in this area." (Evelyn Buckwar, Zentrablatt MATH, Vol. 1096 (22), 2006)

"This is a useful and utilitarian book. It provides a catalogue of modern Monte carlo based computational techniques with ultimate emphasis on Markov chain Monte Carlo (MCMC) … . an excellent reference for anyone who is interested in algorithms for various modes of Markov chain (MC) methodology … . a must for any researcher who believes in the importance of understanding what goes on inside of the MCMC ‘black box.’ … I recommend the book to all who wish to learn about statistical simulation." (Wesley O. Johnson, Journal of the American Statistical Association, Vol. 104 (485), March, 2009)

From the Back Cover

Monte Carlo statistical methods, particularly those based on Markov chains, are now an essential component of the standard set of techniques used by statisticians. This new edition has been revised towards a coherent and flowing coverage of these simulation techniques, with incorporation of the most recent developments in the field. In particular, the introductory coverage of random variable generation has been totally revised, with many concepts being unified through a fundamental theorem of simulation

There are five completely new chapters that cover Monte Carlo control, reversible jump, slice sampling, sequential Monte Carlo, and perfect sampling. There is a more in-depth coverage of Gibbs sampling, which is now contained in three consecutive chapters. The development of Gibbs sampling starts with slice sampling and its connection with the fundamental theorem of simulation, and builds up to two-stage Gibbs sampling and its theoretical properties. A third chapter covers the multi-stage Gibbs sampler and its variety of applications. Lastly, chapters from the previous edition have been revised towards easier access, with the examples getting more detailed coverage.

This textbook is intended for a second year graduate course, but will also be useful to someone who either wants to apply simulation techniques for the resolution of practical problems or wishes to grasp the fundamental principles behind those methods. The authors do not assume familiarity with Monte Carlo techniques (such as random variable generation), with computer programming, or with any Markov chain theory (the necessary concepts are developed in Chapter 6). A solutions manual, which covers approximately 40% of the problems, is available for instructors who require the book for a course.

Christian P. Robert is Professor of Statistics in the Applied Mathematics Department at Université Paris Dauphine, France. He is also Head of the Statistics Laboratory at the Center for Research in Economics and Statistics (CREST) of the National Institute for Statistics and Economic Studies (INSEE) in Paris, and Adjunct Professor at Ecole Polytechnique. He has written three other books and won the 2004 DeGroot Prize for The Bayesian Choice, Second Edition, Springer 2001. He also edited Discretization and MCMC Convergence Assessment, Springer 1998. He has served as associate editor for the Annals of Statistics, Statistical Science and the Journal of the American Statistical Association. He is a fellow of the Institute of Mathematical Statistics, and a winner of the Young Statistician Award of the Société de Statistique de Paris in 1995.

George Casella is Distinguished Professor and Chair, Department of Statistics, University of Florida. He has served as the Theory and Methods Editor of the Journal of the American Statistical Association and Executive Editor of Statistical Science. He has authored three other textbooks: Statistical Inference, Second Edition, 2001, with Roger L. Berger; Theory of Point Estimation, 1998, with Erich Lehmann; and Variance Components, 1992, with Shayle R. Searle and Charles E. McCulloch. He is a fellow of the Institute of Mathematical Statistics and the American Statistical Association, and an elected fellow of the International Statistical Institute. 

Product Details

• Hardcover: 675 pages
• Publisher: Springer; 2nd edition (July 28, 2004)
• Language: English
• ISBN-10: 0387212396
• ISBN-13: 978-0387212395
• Product Dimensions: 9.7 x 6.2 x 1.7 inches
• Shipping Weight: 2.1 pounds (View shipping rates and policies)
• Average Customer Review: 3.9 out of 5 stars  See all reviews (9 customer reviews)
• Amazon Best Sellers Rank: #91,047 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

59 of 59 people found the following review helpful:

5.0 out of 5 stars Does something necessary, does it well., December 9, 2002

By A Customer

This review is from: Monte Carlo Statistical Methods (Hardcover)

This text may or may not be the best book on MC for a particular application; to be honest, it's the only book on MC I own.

However, I did peruse a number of texts before I bought this one, and I am very pleased with my decision. To me, this book does something that seems necessary but is relatively uncommon: it gives a detailed, modern, comprehensive introduction to MC methods per se. There are other texts that might have one of those characteristics, but they seem to either not have all of them: they either are not modern, not comprehensive, not introductory, or are not concerned with Monte Carlo per se.

Many other excellent texts, for example, are largely oriented toward Bayesian implementations, or general integration, but not both.

I would highly recommend this book as an excellent introduction to MC methods as a general computational tool.

49 of 50 people found the following review helpful:

4.0 out of 5 stars great coverage of Monte Carlo MCMC and its Bayesian applications, February 9, 2008

By 

Michael R. Chernick "statman31147" (Holland PA) - See all my reviews
(REAL NAME)   

This review is from: Monte Carlo Statistical Methods (Hardcover)

Monte Carlo methods are old. They can be traced back to Buffon's needle problem in the 17th century. However meaningful application had to wait for the invention of digital computers in the 20th century. Much of the development took place in the 1940s and 50s for military and nuclear engineering application. The Hastings - Metropolis algorithm of the 1950s has had a rebirth in the 1990s with the application of Markov Chain Monte Carlo methods to imaging problems and many Bayesian problems.

The authors of this book are Bayesians and present Bayesian methods in the very first chapter. The book is intended to be a course text on Monte Carlo methods. I judge the level to be intermediate to advanced (first or second year graduate level). The first chapter introduces statistical and numerical problems that Monte Carlo methods can solve. It includes a discussion of bootstrap methods in the notes at the end of the chapter. Chapters 2 and 3 introduce standard topics including methods for generating pseudo-random numbers and various variance reduction techniques. Chapter 4 is an introduction to Markov Chains. Markov Chains are commonly a topic in introductory courses on stochastic processes. The authors presuppose that the reader has no knowledge of Markov Chains. So they develop the essential aspects of the theory needed in the application of Markov Chain Monte Carlo methods (MCMC). Chapter 5 then deals with optimization problems discussing simulated annealing, stochastic approximation and the EM algorithm. Chapters 6 - 8 deal with topic in MCMC methods. The final chapter deals with applications to missing data models. The topics are very current and important to statisticians. The theory is covered very well. Many interesting examples are provided throughout the book. A number of these are presented in the problems section at the end of the chapters. It also contains a very extensive bibliography.

23 of 23 people found the following review helpful:

5.0 out of 5 stars Comprehensive and detailed, April 7, 2006

By 

Reader in Statistics (Rochester, NY) - See all my reviews

This review is from: Monte Carlo Statistical Methods (Springer Texts in Statistics) (Hardcover)

I own both versions of this book. The authors have made significant amount of changes and enrichments in the second edition. Many recent developments in this field, such as perfect sampling, trans-dimensional MCMC and sequential Monte Carlo are covered in certain details. The level of this book is intermediate to advanced, and I used this book for the 3rd year Ph.D. students. My only disappointment is the examples are not up to my expectation. However, the problems at the back of each chapter include some interesting applications.

I highly recommend this book to anyone who wants to understand and apply MCMC and other Monte Carlo methods.