Monte Carlo Statistical Methods (Springer Texts in Statistics)

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. Written as a self-contained logical development of the subject, this book will be suitable as an introduction to the field or as a textbook intended for a seconcl-year graduate course. The reader is not assumed to have any familiarity with Monte Carlo techniques (such as random variable generation), or with any Markov chain theory. Chapters 1 to 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 that cannot be processed otherwise. Each chapter concludes with a section of notes that serve to enhance the discussion in the chapters.