Product Description

Monte Carlo statistical methods, particularly those based on Markov chains, have now matured to be part of the standard set of techniques used by statisticians. This book is intended to bring these techniques into the classroom, being a self-contained logical development of the subject. This is a textbook intended for a second year graduate course. We do not assume that the reader has any familiarity with Monte Carlo techniques (such as random variable generation), or with any Markov chain theory. Chapters 1-3 are introductory, first reviewing various statistical methodologies, then covering the basics of random variable generation and Monte Carlo integration. Chapter 4 is an introduction to Markov chain theory, and Chapter 5 provides the first application of Markov chains to optimization problems. Chapters 6 and 7 cover the heart of MCMC methodology, the Metropolis-Hastings algorithm and the Gibbs sampler. Finally, Chapter 8 presents methods for monitoring convergence of the MCMC methods, while Chapter 9 shows how these methods apply to some statistical settings which cannot be processed otherwise. Each chapter concludes with a section of notes that serve to enhance the discussion in the chapters. Christian P. Robert is Professor of Statistics in the Mathematics Department at the University of Rouen, 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 Lecturer at Ecole Polytechnique. In addition to many papers on Bayesian statistics, simulation, and decision theory, he has written three other books, including The Bayesian Choice, Springer 1994. He also edited Discretization and MCMC Convergence Assessment, Springer 1998. He has served as associate editor for the Annals of Statistics 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 the Liberty Hyde Bailey Professor of Biological Statistics in the College of Agriculture and Life Sciences at Cornel University. He is active in many aspects on both theoretical and applied statistics, and has served as the Theory and Methods Editor of the Journal of the American Statistical Association. He has authored three other textbooks: Statistical Inference, 1990, with Roger L. Berger; Variance Components, 1992, with Shayle R. Searle and Charles E. McCulloch; and Theory of Point Estimation, 1998, with Erich Lehmann. 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

• Amazon Sales Rank: #133268 in Books
• Published on: 2005-07-26
• Original language: English
• Number of items: 1
• Binding: Hardcover
• 645 pages

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)

Customer Reviews

Does something necessary, does it well.
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.

Modern text on Monte Carlo with a Bayesian Perspective
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.

great coverage of Monte Carlo MCMC and its Bayesian applications
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.