Monte Carlo simulation has become one of the most important tools in all fields of science. Simulation methodology relies on a good source of numbers that appear to be random. These "pseudorandom" numbers must pass statistical tests just as random samples would. Methods for producing pseudorandom numbers and transforming those numbers to simulate samples from various distributions are among the most important topics in statistical computing. This book surveys techniques of random number generation and the use of random numbers in Monte Carlo simulation. The book covers basic principles, as well as newer methods such as parallel random number generation, nonlinear congruential generators, quasi Monte Carlo methods, and Markov chain Monte Carlo. The best methods for generating random variates from the standard distributions are presented, but also general techniques useful in more complicated models and in novel settings are described. The emphasis throughout the book is on practical methods that work well in current computing environments. The book includes exercises and can be used as a test or supplementary text for various courses in modern statistics. It could serve as the primary test for a specialized course in statistical computing, or as a supplementary text for a course in computational statistics and other areas of modern statistics that rely on simulation. The book, which covers recent developments in the field, could also serve as a useful reference for practitioners. Although some familiarity with probability and statistics is assumed, the book is accessible to a broad audience. The second edition is approximately 50% longer than the first edition. It includes advances in methods for parallel random number generation, universal methods for generation of nonuniform variates, perfect sampling, and software for random number generation.
Since the term “random ?eld’’ has a variety of different connotations, ranging from agriculture to statistical mechanics, let us start by clarifying that, in this book, a random ?eld is a stochastic process, usually taking values in a Euclidean space, and de?ned over a parameter space of dimensionality at least 1. Consequently, random processes de?ned on countable parameter spaces will not 1 appear here. Indeed, even processes on R will make only rare appearances and, from the point of view of this book, are almost trivial. The parameter spaces we like best are manifolds, although for much of the time we shall require no more than that they be pseudometric spaces. With this clari?cation in hand, the next thing that you should know is that this book will have a sequel dealing primarily with applications. In fact, as we complete this book, we have already started, together with KW (Keith Worsley), on a companion volume [8] tentatively entitled RFG-A,or Random Fields and Geometry: Applications. The current volume—RFG—concentrates on the theory and mathematical background of random ?elds, while RFG-A is intended to do precisely what its title promises. Once the companion volume is published, you will ?nd there not only applications of the theory of this book, but of (smooth) random ?elds in general.
Random Generation of Trees is about a field on the crossroads between computer science, combinatorics and probability theory. Computer scientists need random generators for performance analysis, simulation, image synthesis, etc. In this context random generation of trees is of particular interest. The algorithms presented here are efficient and easy to code. Some aspects of Horton--Strahler numbers, programs written in C and pictures are presented in the appendices. The complexity analysis is done rigorously both in the worst and average cases. Random Generation of Trees is intended for students in computer science and applied mathematics as well as researchers interested in random generation.
This book explores the remarkable connections between two domains that, a priori, seem unrelated: Random matrices (together with associated random processes) and integrable systems. The relations between random matrix models and the theory of classical integrable systems have long been studied. These appear mainly in the deformation theory, when parameters characterizing the measures or the domain of localization of the eigenvalues are varied. The resulting differential equations determining the partition function and correlation functions are, remarkably, of the same type as certain equations appearing in the theory of integrable systems. They may be analyzed effectively through methods based upon the Riemann-Hilbert problem of analytic function theory and by related approaches to the study of nonlinear asymptotics in the large N limit. Associated with studies of matrix models are certain stochastic processes, the "Dyson processes", and their continuum diffusion limits, which govern the spectrum in random matrix ensembles, and may also be studied by related methods. Random Matrices, Random Processes and Integrable Systems provides an in-depth examination of random matrices with applications over a vast variety of domains, including multivariate statistics, random growth models, and many others. Leaders in the field apply the theory of integrable systems to the solution of fundamental problems in random systems and processes using an interdisciplinary approach that sheds new light on a dynamic topic of current research.
Exploring random maintenance models, this book provides an introduction to the implementation of random maintenance, and it is one of the first books to be written on this subject. It aims to help readers learn new techniques for applying random policies to actual reliability models, and it provides new theoretical analyses of various models including classical replacement, preventive maintenance and inspection policies. These policies are applied to scheduling problems, backup policies of database systems, maintenance policies of cumulative damage models, and reliability of random redundant systems.Reliability theory is a major concern for engineers and managers, and in light of Japan’s recent earthquake, the reliability of large-scale systems has increased in importance. This also highlights the need for a new notion of maintenance and reliability theory, and how this can practically be applied to systems.Providing an essential guide for engineers and managers specializing in reliability maintenance and quality control, this book provides a useful resource for those with doubts carrying out maintenance of new and large systems. It is also intended for graduate students and researchers interested in operations research, statistics, industrial engineering and management science.
Exploring random maintenance models, this book provides an introduction to the implementation of random maintenance, and it is one of the first books to be written on this subject. It aims to help readers learn new techniques for applying random policies to actual reliability models, and it provides new theoretical analyses of various models including classical replacement, preventive maintenance and inspection policies. These policies are applied to scheduling problems, backup policies of database systems, maintenance policies of cumulative damage models, and reliability of random redundant systems.Reliability theory is a major concern for engineers and managers, and in light of Japan’s recent earthquake, the reliability of large-scale systems has increased in importance. This also highlights the need for a new notion of maintenance and reliability theory, and how this can practically be applied to systems.Providing an essential guide for engineers and managers specializing in reliability maintenance and quality control, this book provides a useful resource for those with doubts carrying out maintenance of new and large systems. It is also intended for graduate students and researchers interested in operations research, statistics, industrial engineering and management science.
The book includes recipes and treatments for a variety of diseases and illnesses common in early 19th Century London. It also provides an insight into the Medical Profession working at that time, and is an important social commentary.
