This book presents a unified theory of rare event simulation and the variance reduction technique known as importance sampling from the point of view of the probabilistic theory of large deviations. This perspective allows us to view a vast assortment of simulation problems from a unified single perspective. It gives a great deal of insight into the fundamental nature of rare event simulation. Until now, this area has a reputation among simulation practitioners of requiring a great deal of technical and probabilistic expertise. This text keeps the mathematical preliminaries to a minimum with the only prerequisite being a single large deviation theory result that is given and proved in the text. Large deviation theory is a burgeoning area of probability theory and many of the results in it can be applied to simulation problems. Rather than try to be as complete as possible in the exposition of all possible aspects of the available theory, the book concentrates on demonstrating the methodology and the principal ideas in a fairly simple setting. The book contains over 50 figures and detailed simulation case studies covering a wide variety of application areas including statistics, telecommunications, and queueing systems. James A. Bucklew holds the rank of Professor with appointments in the Department of Electrical and Computer Engineering and in the Department of Mathematics at the University of Wisconsin-Madison. He is a Fellow of the Institute of Electrical and Electronics Engineers and the author of Large Deviation Techniques in Decision, Simulation, and Estimation
CONTENT
1. Random Number Generation -- 2. Stochastic Models -- 3. Large Deviation Theory -- 4. Importance Sampling -- 5. The Large Deviation Theory of Importance Sampling Estimators -- 6. Variance Rate Theory of Conditional Importance Sampling Estimators -- 7. The Large Deviations of Bias Point Selection -- 8. Chernoffโs Bound and Asymptotic Expansions -- 9. Gaussian Systems -- 10. Universal Simulation Distributions -- 11. Rare Event Simulation for Level Crossing and Queueing Models -- 12. Blind Simulation -- 13. The (Over-Under) Biasing Problem in Importance Sampling -- 14. Tools and Techniques for Importance Sampling -- A. Convex Functions and Analysis -- B. A Covering Lemma -- C. Pseudo-Random Number Generator Programs -- References
SUBJECT
Statistics
Computer communication systems
Computer simulation
Operations research
Management science
Probabilities
Applied mathematics
Engineering mathematics
Statistics
Statistics for Engineering
Physics
Computer Science
Chemistry and Earth Sciences
Simulation and Modeling
Probability Theory and Stochastic Processes
Computer Communication Networks
Operations Research
Management Science
Appl.Mathematics/Computational Methods of Engineering
