Rare Event Simulation Using Monte Carlo Methods

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Rare Event Simulation Using Monte Carlo Methods

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Author : Gerardo Rubino
language : en
Publisher: John Wiley & Sons
Release Date : 2009-03-18

Rare Event Simulation Using Monte Carlo Methods written by Gerardo Rubino and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-03-18 with Mathematics categories.

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

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Author : James Bucklew
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-03-11

Introduction To Rare Event Simulation written by James Bucklew and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-03-11 with Business & Economics categories.

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

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Author : Jerome Morio
language : en
Publisher: Woodhead Publishing
Release Date : 2015-11-16

Estimation Of Rare Event Probabilities In Complex Aerospace And Other Systems written by Jerome Morio and has been published by Woodhead Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-16 with Technology & Engineering categories.

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

An Introduction To Sequential Monte Carlo

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Author : Nicolas Chopin
language : en
Publisher: Springer Nature
Release Date : 2020-10-01

An Introduction To Sequential Monte Carlo written by Nicolas Chopin and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-01 with Mathematics categories.

This book provides a general introduction to Sequential Monte Carlo (SMC) methods, also known as particle filters. These methods have become a staple for the sequential analysis of data in such diverse fields as signal processing, epidemiology, machine learning, population ecology, quantitative finance, and robotics. The coverage is comprehensive, ranging from the underlying theory to computational implementation, methodology, and diverse applications in various areas of science. This is achieved by describing SMC algorithms as particular cases of a general framework, which involves concepts such as Feynman-Kac distributions, and tools such as importance sampling and resampling. This general framework is used consistently throughout the book. Extensive coverage is provided on sequential learning (filtering, smoothing) of state-space (hidden Markov) models, as this remains an important application of SMC methods. More recent applications, such as parameter estimation of these models (through e.g. particle Markov chain Monte Carlo techniques) and the simulation of challenging probability distributions (in e.g. Bayesian inference or rare-event problems), are also discussed. The book may be used either as a graduate text on Sequential Monte Carlo methods and state-space modeling, or as a general reference work on the area. Each chapter includes a set of exercises for self-study, a comprehensive bibliography, and a “Python corner,” which discusses the practical implementation of the methods covered. In addition, the book comes with an open source Python library, which implements all the algorithms described in the book, and contains all the programs that were used to perform the numerical experiments.

The Cross Entropy Method

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Author : Reuven Y. Rubinstein
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-07-28

The Cross Entropy Method written by Reuven Y. Rubinstein and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-07-28 with Business & Economics categories.

Rubinstein is the pioneer of the well-known score function and cross-entropy methods. Accessible to a broad audience of engineers, computer scientists, mathematicians, statisticians and in general anyone, theorist and practitioner, who is interested in smart simulation, fast optimization, learning algorithms, and image processing.

Introducing Monte Carlo Methods With R

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Author : Christian Robert
language : en
Publisher: Springer Science & Business Media
Release Date : 2010

Introducing Monte Carlo Methods With R written by Christian Robert and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Computers categories.

This book covers the main tools used in statistical simulation from a programmer’s point of view, explaining the R implementation of each simulation technique and providing the output for better understanding and comparison.

Reaction Rate Theory And Rare Events

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Author : Baron Peters
language : en
Publisher: Elsevier
Release Date : 2017-03-22

Reaction Rate Theory And Rare Events written by Baron Peters and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-22 with Technology & Engineering categories.

Reaction Rate Theory and Rare Events bridges the historical gap between these subjects because the increasingly multidisciplinary nature of scientific research often requires an understanding of both reaction rate theory and the theory of other rare events. The book discusses collision theory, transition state theory, RRKM theory, catalysis, diffusion limited kinetics, mean first passage times, Kramers theory, Grote-Hynes theory, transition path theory, non-adiabatic reactions, electron transfer, and topics from reaction network analysis. It is an essential reference for students, professors and scientists who use reaction rate theory or the theory of rare events. In addition, the book discusses transition state search algorithms, tunneling corrections, transmission coefficients, microkinetic models, kinetic Monte Carlo, transition path sampling, and importance sampling methods. The unified treatment in this book explains why chemical reactions and other rare events, while having many common theoretical foundations, often require very different computational modeling strategies. - Offers an integrated approach to all simulation theories and reaction network analysis, a unique approach not found elsewhere - Gives algorithms in pseudocode for using molecular simulation and computational chemistry methods in studies of rare events - Uses graphics and explicit examples to explain concepts - Includes problem sets developed and tested in a course range from pen-and-paper theoretical problems, to computational exercises

Markov Chain Monte Carlo Simulations And Their Statistical Analysis With Web Based Fortran Code

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Author : Bernd Albert Berg
language : en
Publisher: World Scientific Publishing Company
Release Date : 2004-10-01

Markov Chain Monte Carlo Simulations And Their Statistical Analysis With Web Based Fortran Code written by Bernd Albert Berg and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-10-01 with Science categories.

This book teaches modern Markov chain Monte Carlo (MC) simulation techniques step by step. The material should be accessible to advanced undergraduate students and is suitable for a course. It ranges from elementary statistics concepts (the theory behind MC simulations), through conventional Metropolis and heat bath algorithms, autocorrelations and the analysis of the performance of MC algorithms, to advanced topics including the multicanonical approach, cluster algorithms and parallel computing. Therefore, it is also of interest to researchers in the field. The book relates the theory directly to Web-based computer code. This allows readers to get quickly started with their own simulations and to verify many numerical examples easily. The present code is in Fortran 77, for which compilers are freely available. The principles taught are important for users of other programming languages, like C or C++.

Handbook Of Monte Carlo Methods

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Author : Dirk P. Kroese
language : en
Publisher: John Wiley & Sons
Release Date : 2013-06-06

Handbook Of Monte Carlo Methods written by Dirk P. Kroese and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-06 with Mathematics categories.

A comprehensive overview of Monte Carlo simulation that explores the latest topics, techniques, and real-world applications More and more of today’s numerical problems found in engineering and finance are solved through Monte Carlo methods. The heightened popularity of these methods and their continuing development makes it important for researchers to have a comprehensive understanding of the Monte Carlo approach. Handbook of Monte Carlo Methods provides the theory, algorithms, and applications that helps provide a thorough understanding of the emerging dynamics of this rapidly-growing field. The authors begin with a discussion of fundamentals such as how to generate random numbers on a computer. Subsequent chapters discuss key Monte Carlo topics and methods, including: Random variable and stochastic process generation Markov chain Monte Carlo, featuring key algorithms such as the Metropolis-Hastings method, the Gibbs sampler, and hit-and-run Discrete-event simulation Techniques for the statistical analysis of simulation data including the delta method, steady-state estimation, and kernel density estimation Variance reduction, including importance sampling, latin hypercube sampling, and conditional Monte Carlo Estimation of derivatives and sensitivity analysis Advanced topics including cross-entropy, rare events, kernel density estimation, quasi Monte Carlo, particle systems, and randomized optimization The presented theoretical concepts are illustrated with worked examples that use MATLAB®, a related Web site houses the MATLAB® code, allowing readers to work hands-on with the material and also features the author's own lecture notes on Monte Carlo methods. Detailed appendices provide background material on probability theory, stochastic processes, and mathematical statistics as well as the key optimization concepts and techniques that are relevant to Monte Carlo simulation. Handbook of Monte Carlo Methods is an excellent reference for applied statisticians and practitioners working in the fields of engineering and finance who use or would like to learn how to use Monte Carlo in their research. It is also a suitable supplement for courses on Monte Carlo methods and computational statistics at the upper-undergraduate and graduate levels.

Machine Learning Optimization And Data Science

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Author : Giuseppe Nicosia
language : en
Publisher: Springer Nature
Release Date : 2021-01-07

Machine Learning Optimization And Data Science written by Giuseppe Nicosia and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-07 with Computers categories.

This two-volume set, LNCS 12565 and 12566, constitutes the refereed proceedings of the 6th International Conference on Machine Learning, Optimization, and Data Science, LOD 2020, held in Siena, Italy, in July 2020. The total of 116 full papers presented in this two-volume post-conference proceedings set was carefully reviewed and selected from 209 submissions. These research articles were written by leading scientists in the fields of machine learning, artificial intelligence, reinforcement learning, computational optimization, and data science presenting a substantial array of ideas, technologies, algorithms, methods, and applications.