Monte Carlo Strategies in Scientific Computing

This book provides a self-contained and up-to-date treatment of the Monte Carlo method and develops a common framework under which various Monte Carlo techniques can be "standardized" and compared. Given the interdisciplinary nature of the topics and a moderate prerequisite for the reader, this book should be of interest to a broad audience of quantitative researchers such as computational biologists, computer scientists, econometricians, engineers, probabilists, and statisticians. It can also be used as the textbook for a graduate-level course on Monte Carlo methods. Many problems discussed in the later chapters can be potential thesis topics for master's or Ph.D. students in statistics or computer science departments.

The Monte Carlo method is a computer-based statistical sampling approach for solving numerical problems concerned with a complex system. The methodology was initially developed in the field of statistical physics during the early days of electronic computing (1945 to 1955) and has now been adopted by researchers in almost all scientific fields. The fundamental idea for constructing Markov-chain-based Monte Carlo algorithms was introduced in the 1950s. This idea was later extended to handle more and more complex physical systems. In the 1980s, statisticians and computer scientists developed Monte Carlo-based algorithms for a wide variety of integration and optimization tasks. In the 1990s, the method began to play an important role in computational biology. Over the past fifty years, researchers in diverse scientific fields have studied the Monte Carlo method and contributed to its development. Today, a large number of scientists and engineers employ Monte Carlotechniques as an essential tool in their work. For such scientists, there is a need to keep up to date with recent advances in Monte Carlo methodologies.

About the Author:
Jun S. Liu is a professor in the Department of Statistics at Harvard University