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 second-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 methdology, 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.
