Monte Carlo Statistical Methods

1. Front Matter

   Pages i-xxi

   PDF

2. Introduction

   • Christian P. Robert, George Casella

   Pages 1-34

3. Random Variable Generation

   • Christian P. Robert, George Casella

   Pages 35-70

4. Monte Carlo Integration

   • Christian P. Robert, George Casella

   Pages 71-138

5. Markov Chains

   • Christian P. Robert, George Casella

   Pages 139-191

6. Monte Carlo Optimization

   • Christian P. Robert, George Casella

   Pages 193-230

7. The Metropolis—Hastings Algorithm

   • Christian P. Robert, George Casella

   Pages 231-283

8. The Gibbs Sampler

   • Christian P. Robert, George Casella

   Pages 285-361

9. Diagnosing Convergence

   • Christian P. Robert, George Casella

   Pages 363-413

10. Implementation in Missing Data Models

    • Christian P. Robert, George Casella

    Pages 415-450

11. Back Matter

    Pages 451-509

    PDF

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 class­ room, being (we hope) a self-contained logical development of the subject, with all concepts being explained in detail, and all theorems, etc. having detailed proofs. There is also an abundance of examples and problems, re­ lating the concepts with statistical practice and enhancing primarily the application of simulation techniques to statistical problems of various dif­ ficulties. 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. We do assume that the reader has had a first course in statistical theory at the level of Statistical Inference by Casella and Berger (1990). Unfortu­ nately, a few times throughout the book a somewhat more advanced no­ tion is needed. We have kept these incidents to a minimum and have posted warnings when they occur. While this is a book on simulation, whose actual implementation must be processed through a computer, no requirement is made on programming skills or computing abilities: algorithms are pre­ sented in a program-like format but in plain text rather than in a specific programming language. (Most of the examples in the book were actually implemented in C, with the S-Plus graphical interface.

• MCMCM
• Markov Chain Monte Carlo Methods
• Monte Carlo method
• mathematical statistics
• random variable
• statistical inference
• statistics

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 highlyrecommended … ." (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 whatgoes 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)

• Laboratoire de Statistique, CREST-INSEE, Paris Cedex 14, France

  Christian P. Robert

• Dept. de Mathematique UFR des Sciences, Universite de Rouen, Mont Saint Aignan cedex, France

  Christian P. Robert

• Biometrics Unit, Cornell University, Ithaca, USA

  George Casella

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