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Markov Chain Importance Sampling With Applications To Rare Event Probability Estimation
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Book Synopsis Introduction to Rare Event Simulation by : James Bucklew
Download or read book Introduction to Rare Event Simulation written by James Bucklew and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. It allows us to view a vast assortment of simulation problems from a unified single perspective.
Book Synopsis Rare Event Simulation using Monte Carlo Methods by : Gerardo Rubino
Download or read book Rare Event Simulation using Monte Carlo Methods written by Gerardo Rubino and published by John Wiley & Sons. This book was released on 2009-03-18 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Estimation of Rare Event Probabilities in Complex Aerospace and Other Systems by : Jerome Morio
Download or read book Estimation of Rare Event Probabilities in Complex Aerospace and Other Systems written by Jerome Morio and published by Woodhead Publishing. This book was released on 2015-11-16 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Markov Chains and Dependability Theory by : Gerardo Rubino
Download or read book Markov Chains and Dependability Theory written by Gerardo Rubino and published by Cambridge University Press. This book was released on 2014-06-12 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dependability metrics are omnipresent in every engineering field, from simple ones through to more complex measures combining performance and dependability aspects of systems. This book presents the mathematical basis of the analysis of these metrics in the most used framework, Markov models, describing both basic results and specialised techniques. The authors first present both discrete and continuous time Markov chains before focusing on dependability measures, which necessitate the study of Markov chains on a subset of states representing different user satisfaction levels for the modelled system. Topics covered include Markovian state lumping, analysis of sojourns on subset of states of Markov chains, analysis of most dependability metrics, fundamentals of performability analysis, and bounding and simulation techniques designed to evaluate dependability measures. The book is of interest to graduate students and researchers in all areas of engineering where the concepts of lifetime, repair duration, availability, reliability and risk are important.
Book Synopsis Handbook of Monte Carlo Methods by : Dirk P. Kroese
Download or read book Handbook of Monte Carlo Methods written by Dirk P. Kroese and published by John Wiley & Sons. This book was released on 2013-06-06 with total page 627 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Handbooks in Operations Research and Management Science: Simulation by : Shane G. Henderson
Download or read book Handbooks in Operations Research and Management Science: Simulation written by Shane G. Henderson and published by Elsevier. This book was released on 2006-09-02 with total page 693 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Handbook is a collection of chapters on key issues in the design and analysis of computer simulation experiments on models of stochastic systems. The chapters are tightly focused and written by experts in each area. For the purpose of this volume "simulation refers to the analysis of stochastic processes through the generation of sample paths (realization) of the processes. Attention focuses on design and analysis issues and the goal of this volume is to survey the concepts, principles, tools and techniques that underlie the theory and practice of stochastic simulation design and analysis. Emphasis is placed on the ideas and methods that are likely to remain an intrinsic part of the foundation of the field for the foreseeable future. The chapters provide up-to-date references for both the simulation researcher and the advanced simulation user, but they do not constitute an introductory level 'how to' guide. Computer scientists, financial analysts, industrial engineers, management scientists, operations researchers and many other professionals use stochastic simulation to design, understand and improve communications, financial, manufacturing, logistics, and service systems. A theme that runs throughout these diverse applications is the need to evaluate system performance in the face of uncertainty, including uncertainty in user load, interest rates, demand for product, availability of goods, cost of transportation and equipment failures.* Tightly focused chapters written by experts* Surveys concepts, principles, tools, and techniques that underlie the theory and practice of stochastic simulation design and analysis* Provides an up-to-date reference for both simulation researchers and advanced simulation users
Book Synopsis The Cross-Entropy Method by : Reuven Y. Rubinstein
Download or read book The Cross-Entropy Method written by Reuven Y. Rubinstein and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Introducing Monte Carlo Methods with R by : Christian Robert
Download or read book Introducing Monte Carlo Methods with R written by Christian Robert and published by Springer Science & Business Media. This book was released on 2010 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis An Introduction to Sequential Monte Carlo by : Nicolas Chopin
Download or read book An Introduction to Sequential Monte Carlo written by Nicolas Chopin and published by Springer Nature. This book was released on 2020-10-01 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Analysis and Approximation of Rare Events by : Amarjit Budhiraja
Download or read book Analysis and Approximation of Rare Events written by Amarjit Budhiraja and published by Springer. This book was released on 2019-08-10 with total page 577 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents broadly applicable methods for the large deviation and moderate deviation analysis of discrete and continuous time stochastic systems. A feature of the book is the systematic use of variational representations for quantities of interest such as normalized logarithms of probabilities and expected values. By characterizing a large deviation principle in terms of Laplace asymptotics, one converts the proof of large deviation limits into the convergence of variational representations. These features are illustrated though their application to a broad range of discrete and continuous time models, including stochastic partial differential equations, processes with discontinuous statistics, occupancy models, and many others. The tools used in the large deviation analysis also turn out to be useful in understanding Monte Carlo schemes for the numerical approximation of the same probabilities and expected values. This connection is illustrated through the design and analysis of importance sampling and splitting schemes for rare event estimation. The book assumes a solid background in weak convergence of probability measures and stochastic analysis, and is suitable for advanced graduate students, postdocs and researchers.
Author :Vladimir V. Kalashnikov Publisher :Springer Science & Business Media ISBN 13 :9401716935 Total Pages :285 pages Book Rating :4.4/5 (17 download)
Book Synopsis Geometric Sums: Bounds for Rare Events with Applications by : Vladimir V. Kalashnikov
Download or read book Geometric Sums: Bounds for Rare Events with Applications written by Vladimir V. Kalashnikov and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book reviews problems associated with rare events arising in a wide range of circumstances, treating such topics as how to evaluate the probability an insurance company will be bankrupted, the lifetime of a redundant system, and the waiting time in a queue. Well-grounded, unique mathematical evaluation methods of basic probability characteristics concerned with rare events are presented, which can be employed in real applications, as the volume also contains relevant numerical and Monte Carlo methods. The various examples, tables, figures and algorithms will also be appreciated. Audience: This work will be useful to graduate students, researchers and specialists interested in applied probability, simulation and operations research.
Book Synopsis Machine Learning: Theory and Applications by :
Download or read book Machine Learning: Theory and Applications written by and published by Newnes. This book was released on 2013-05-16 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: Statistical learning and analysis techniques have become extremely important today, given the tremendous growth in the size of heterogeneous data collections and the ability to process it even from physically distant locations. Recent advances made in the field of machine learning provide a strong framework for robust learning from the diverse corpora and continue to impact a variety of research problems across multiple scientific disciplines. The aim of this handbook is to familiarize beginners as well as experts with some of the recent techniques in this field.The Handbook is divided in two sections: Theory and Applications, covering machine learning, data analytics, biometrics, document recognition and security. - Very relevant to current research challenges faced in various fields - Self-contained reference to machine learning - Emphasis on applications-oriented techniques
Book Synopsis Mechanical Engineering in Uncertainties From Classical Approaches to Some Recent Developments by :
Download or read book Mechanical Engineering in Uncertainties From Classical Approaches to Some Recent Developments written by and published by John Wiley & Sons. This book was released on 2021-05-11 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: Considering the uncertainties in mechanical engineering in order to improve the performance of future products or systems is becoming a competitive advantage, sometimes even a necessity, when seeking to guarantee an increasingly high safety requirement. Mechanical Engineering in Uncertainties deals with modeling, quantification and propagation of uncertainties. It also examines how to take into account uncertainties through reliability analyses and optimization under uncertainty. The spectrum of the methods presented ranges from classical approaches to more recent developments and advanced methods. The methodologies are illustrated by concrete examples in various fields of mechanics (civil engineering, mechanical engineering and fluid mechanics). This book is intended for both (young) researchers and engineers interested in the treatment of uncertainties in mechanical engineering.
Book Synopsis Safety and Reliability of Complex Engineered Systems by : Luca Podofillini
Download or read book Safety and Reliability of Complex Engineered Systems written by Luca Podofillini and published by CRC Press. This book was released on 2015-09-03 with total page 730 pages. Available in PDF, EPUB and Kindle. Book excerpt: Safety and Reliability of Complex Engineered Systems contains the Proceedings of the 25th European Safety and Reliability Conference, ESREL 2015, held 7-10 September 2015 in Zurich, Switzerland. It includes about 570 papers accepted for presentation at the conference. These contributions focus on theories and methods in the area of risk, safety and
Book Synopsis Importance Sampling by : Rajan Srinivasan
Download or read book Importance Sampling written by Rajan Srinivasan and published by Springer Science & Business Media. This book was released on 2002-06-01 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: This research monograph deals with fast stochastic simulation based on im portance sampling (IS) principles and some of its applications. It is in large part devoted to an adaptive form of IS that has proved to be effective in appli cations that involve the estimation of probabilities of rare events. Rare events are often encountered in scientific and engineering processes. Their charac terization is especially important as their occurrence can have catastrophic consequences of varying proportions. Examples range from fracture due to material fatigue in engineering structures to exceedance of dangerous levels during river water floods to false target declarations in radar systems. Fast simulation using IS is essentially a forced Monte Carlo procedure designed to hasten the occurrence of rare events. Development of this simu lation method of analysis of scientific phenomena is usually attributed to the mathematician von Neumann, and others. Since its inception, MC simula tion has found a wide range of employment, from statistical thermodynamics in disordered systems to the analysis and design of engineering structures characterized by high complexity. Indeed, whenever an engineering problem is analytically intractable (which is often the case) and a solution by nu merical techniques prohibitively expensive computationally, a last resort to determine the input-output characteristics of, or states within, a system is to carry out a simulation.
Book Synopsis Reliability and Safety of Cable-Supported Bridges by : Naiwei Lu
Download or read book Reliability and Safety of Cable-Supported Bridges written by Naiwei Lu and published by CRC Press. This book was released on 2021-06-17 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bridge design and construction technologies have experienced remarkable developments in recent decades, and numerous long-span bridges have been built or are under construction all over the world. Cable-supported bridges, including cable-stayed bridges and suspension bridges, are the main type of these long-span bridges, and are widely used in highways crossing gorges, rivers, and gulfs, due to their superior structural mechanical properties and beautiful appearance. However, cable-supported bridges suffer from harsh environmental effects and complex loading conditions, such as heavier traffic loads, strong winds, corrosion effects, and other natural disasters. Therefore, the lifetime safety evaluation of these long-span bridges considering the rigorous service environments is an essential task. Features: Presents a comprehensive explanation of system reliability evaluation for all aspects of cable-supported bridges. Includes a comprehensive presentation of the application of system reliability theory in bridge design, safety control, and operational management. Addresses fatigue reliability, dynamic reliability and seismic reliability assessment of bridges. Presents a complete investigation and case study in each chapter, allowing readers to understand the applicability for real-world scenarios. Reliability and Safety of Cable-Supported Bridges provides a comprehensive application and guidelines for system reliability techniques in cable-supported bridges. Serving as a practical educational resource for both undergraduate and graduate level students, practicing engineers, and researchers, it also intends to provide an intuitive appreciation for probability theory, statistical methods, and reliability analysis methods.
Book Synopsis Stochastic Simulation: Algorithms and Analysis by : Søren Asmussen
Download or read book Stochastic Simulation: Algorithms and Analysis written by Søren Asmussen and published by Springer Science & Business Media. This book was released on 2007-07-14 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sampling-based computational methods have become a fundamental part of the numerical toolset of practitioners and researchers across an enormous number of different applied domains and academic disciplines. This book provides a broad treatment of such sampling-based methods, as well as accompanying mathematical analysis of the convergence properties of the methods discussed. The reach of the ideas is illustrated by discussing a wide range of applications and the models that have found wide usage. The first half of the book focuses on general methods; the second half discusses model-specific algorithms. Exercises and illustrations are included.
