Rare Event Simulation Using Monte Carlo Methods
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Rare Event Simulation using Monte Carlo Methods
In a probabilistic model, a rare event is an event with a very small probability of occurrence. The forecasting of rare events is a formidable task but is important in many areas. For instance a catastrophic failure in a transport system or in a nuclear power plant, the failure of an information processing system in a bank, or in the communication network of a group of banks, leading to financial losses. Being able to evaluate the probability of rare events is therefore a critical issue. Monte Carlo Methods, the simulation of corresponding models, are used to analyze rare events. This book sets out to present the mathematical tools available for the efficient simulation of rare events. Importance sampling and splitting are presented along with an exposition of how to apply these tools to a variety of fields ranging from performance and dependability evaluation of complex systems, typically in computer science or in telecommunications, to chemical reaction analysis in biology or particle transport in physics. Graduate students, researchers and practitioners who wish to learn and apply rare event simulation techniques will find this book beneficial.
Introduction to Rare Event Simulation
Author: James Bucklew
language: en
Publisher: Springer Science & Business Media
Release Date: 2004-03-11
This book is an attempt to present 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 framework allows us to view a vast assortment of simulation problems from a single unified perspective. It gives a great deal of insight into the fundamental nature of rare event simulation. Unfortunately, this area has a reputation among simulation practitioners of requiring a great deal of technical and probabilistic expertise. In this text, I have tried to keep the mathematical preliminaries to a minimum; the only prerequisite is a single large deviation theorem dealing with sequences of Rd valued random variables. (This theorem and a proof are given 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, I have tried to concentrate on demonstrating the methodology and the principal ideas in a fairly simple setting. Madison, Wisconsin 2003 James Antonio Bucklew Contents 1. Random Number Generation . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . 1.1 Uniform Generators. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Nonuniform Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.2.1 The Inversion Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.2.2 The Acceptance---Rejection Method . . . . . . . . . . . . 10 . . . . . 1.3 Discrete Distributions . . . . . . . . . . . . . . . . . . . . . . . . 13 . . . . . . . . . . . 1.3.1 Inversion by Truncation of a Continuous Analog. . . . . . 14 1.3.2 Acceptance---Rejection . . . . . . . . . . . . . . . . . . . . 15 . . . . . . . . .
Estimation of Rare Event Probabilities in Complex Aerospace and Other Systems
Rare event probability (10-4 and less) estimation has become a large area of research in the reliability engineering and system safety domains. A significant number of methods have been proposed to reduce the computation burden for the estimation of rare events from advanced sampling approaches to extreme value theory. However, it is often difficult in practice to determine which algorithm is the most adapted to a given problem.Estimation of Rare Event Probabilities in Complex Aerospace and Other Systems: A Practical Approach provides a broad up-to-date view of the current available techniques to estimate rare event probabilities described with a unified notation, a mathematical pseudocode to ease their potential implementation and finally a large spectrum of simulation results on academic and realistic use cases. Provides a broad overview of the practical approach of rare event methods. Includes algorithms that are applied to aerospace benchmark test cases Offers insight into practical tuning issues