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| Monte Carlo Statistical Methods (Springer Texts in Statistics)
Hardcover
Edition: 2nd
Author: Christian P. Robert, George Casella
Publisher: Springer
Release Date: 2005-07-26
ISBN-10: 0387212396
ISBN-13: 9780387212395
List Price: $99.00
Average Customer Rating:
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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.
great coverage of Monte Carlo MCMC and its Bayesian applications
| Customer Rating:  | 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.
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Comprehensive but hard to read
| Customer Rating: | | There is no doubts this text is a comprehensive study of Monte Carlo methods with an impressive number of examples. However, I must say it is hard to read for someone who is beginning to work with Monte Carlo methods. I highly recommend the book by Sobol (A primer for the Monte Carlo Method) which I think it remains to be the best introduction to the subject. After reading and enjoying this primer you will be ready to take full advantage of Robert and Casella's book. |
Comprehensive and detailed
| Customer Rating: | 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.
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Monte Carlo Statistical Methods (by Christian P. Robert)
| Customer Rating: | | It is a fantastic book for Monte Carlo Methods |
Review of the Monte Carlo Statistical Methods book
| Customer Rating: | | A good book, with a really interesting mathematical treatement to different simulation techniques, but a little bit complicated in some aspects. |
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