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Title: Monte Carlo Statistical Methods by Christian P. Robert, George Casella ISBN: 0-387-98707-X Publisher: Springer Verlag Pub. Date: 13 August, 1999 Format: Hardcover Volumes: 1 List Price(USD): $94.00 |
Average Customer Rating: 4.67 (3 reviews)
Rating: 5
Summary: Useful and Clear
Comment: I have a graduate level physics and mathematics background really enjoyed the clear descriptions as a useful and ever-needed review.
Monte Carlo experts who want to apply their knowlege to finance should also read: "Options, Futures, and Other Derivatives (5th Edition) by John Hull; and "Credit Derivatives" (2nd Edition) by Janet Tavakoli.
Rating: 5
Summary: Does something necessary, does it well.
Comment: 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.
Rating: 4
Summary: Modern text on Monte Carlo with a Bayesian Perspective
Comment: 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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Title: Monte Carlo Methods in Bayesian Computation (Springer Series in Statistics) by Ming-Hui Chen, Qi-Man Shao, Joseph George Ibrahim ISBN: 0387989358 Publisher: Springer Verlag Pub. Date: January, 2000 List Price(USD): $89.95 |
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Title: Markov Chain Monte Carlo in Practice by W. R. Gilks, S. Richardson, D. J. Spiegelhalter ISBN: 0412055511 Publisher: CRC Press Pub. Date: 01 December, 1995 List Price(USD): $79.95 |
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Title: Monte Carlo Strategies in Scientific Computing by Jun S. Liu ISBN: 0387952306 Publisher: Springer Verlag Pub. Date: 26 June, 2001 List Price(USD): $74.95 |
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Title: Bayesian Data Analysis, Second Edition by Andrew Gelman, John B. Carlin, Hal S. Stern, Donald B. Rubin ISBN: 158488388X Publisher: CRC Press Pub. Date: 29 July, 2003 List Price(USD): $59.95 |
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Title: Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference by Dani Gamerman ISBN: 0412818205 Publisher: CRC Press Pub. Date: 01 October, 1997 List Price(USD): $59.95 |
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