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Author : Hock Peng Chan
Publisher :
ISBN 13 :
Total Pages : 34 pages
Book Rating : 4.:/5 (632 download)
Download or read book Efficient Importance Sampling for Monte Carlo Evaluation of Exceedance Probabilities written by Hock Peng Chan and published by . This book was released on 2005 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Malvin H. Kalos
Publisher : John Wiley & Sons
ISBN 13 : 3527626220
Total Pages : 215 pages
Book Rating : 4.5/5 (276 download)
Download or read book Monte Carlo Methods written by Malvin H. Kalos and published by John Wiley & Sons. This book was released on 2009-06-10 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to Monte Carlo methods seeks to identify and study the unifying elements that underlie their effective application. Initial chapters provide a short treatment of the probability and statistics needed as background, enabling those without experience in Monte Carlo techniques to apply these ideas to their research. The book focuses on two basic themes: The first is the importance of random walks as they occur both in natural stochastic systems and in their relationship to integral and differential equations. The second theme is that of variance reduction in general and importance sampling in particular as a technique for efficient use of the methods. Random walks are introduced with an elementary example in which the modeling of radiation transport arises directly from a schematic probabilistic description of the interaction of radiation with matter. Building on this example, the relationship between random walks and integral equations is outlined. The applicability of these ideas to other problems is shown by a clear and elementary introduction to the solution of the Schrödinger equation by random walks. The text includes sample problems that readers can solve by themselves to illustrate the content of each chapter. This is the second, completely revised and extended edition of the successful monograph, which brings the treatment up to date and incorporates the many advances in Monte Carlo techniques and their applications, while retaining the original elementary but general approach.
Author : Malvin H. Kalos
Publisher : Wiley-VCH
ISBN 13 :
Total Pages : 216 pages
Book Rating : 4.3/5 (91 download)
Download or read book Monte Carlo Methods, Volume 1 written by Malvin H. Kalos and published by Wiley-VCH. This book was released on 1986-10-29 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to Monte Carlo Methods seeks to identify and study the unifying elements that underlie their effective application. It focuses on two basic themes. The first is the importance of random walks as they occur both in natural stochastic systems and in their relationship to integral and differential equations. The second theme is that of variance reduction in general and importance sampling in particular as a technique for efficient use of the methods. Random walks are introduced with an elementary example in which the modelling of radiation transport arises directly from a schematic probabilistic description of the interaction of radiation with matter. Building on that example, the relationship between random walks and integral equations is outlined. The applicability of these ideas to other problems is shown by a clear and elementary introduction to the solution of the Schrodinger equation by random walks. The detailed discussion of variance reduction includes Monte Carlo evaluation of finite-dimensional integrals. Special attention is given to importance sampling, partly because of its intrinsic interest in quadrature, partly because of its general usefulness in the solution of integral equations. One significant feature is that Monte Carlo Methods treats the "Metropolis algorithm" in the context of sampling methods, clearly distinguishing it from importance sampling. Physicists, chemists, statisticians, mathematicians, and computer scientists will find Monte Carlo Methods a complete and stimulating introduction.
Author : John Michael Hammersley
Publisher :
ISBN 13 :
Total Pages : 194 pages
Book Rating : 4.3/5 (91 download)
Download or read book Monte Carlo Methods written by John Michael Hammersley and published by . This book was released on 1965 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Rajan Srinivasan
Publisher : Springer Science & Business Media
ISBN 13 : 3662050528
Total Pages : 252 pages
Book Rating : 4.6/5 (62 download)
Download or read book Importance Sampling written by Rajan Srinivasan and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 252 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.
Author : Arnaud Doucet
Publisher : Springer Science & Business Media
ISBN 13 : 1475734379
Total Pages : 590 pages
Book Rating : 4.4/5 (757 download)
Download or read book Sequential Monte Carlo Methods in Practice written by Arnaud Doucet and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: Monte Carlo methods are revolutionizing the on-line analysis of data in many fileds. They have made it possible to solve numerically many complex, non-standard problems that were previously intractable. This book presents the first comprehensive treatment of these techniques.
Author : Reuven Y. Rubinstein
Publisher : John Wiley & Sons
ISBN 13 : 1118612353
Total Pages : 177 pages
Book Rating : 4.1/5 (186 download)
Download or read book Fast Sequential Monte Carlo Methods for Counting and Optimization written by Reuven Y. Rubinstein and published by John Wiley & Sons. This book was released on 2013-11-13 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive account of the theory and application of Monte Carlo methods Based on years of research in efficient Monte Carlo methods for estimation of rare-event probabilities, counting problems, and combinatorial optimization, Fast Sequential Monte Carlo Methods for Counting and Optimization is a complete illustration of fast sequential Monte Carlo techniques. The book provides an accessible overview of current work in the field of Monte Carlo methods, specifically sequential Monte Carlo techniques, for solving abstract counting and optimization problems. Written by authorities in the field, the book places emphasis on cross-entropy, minimum cross-entropy, splitting, and stochastic enumeration. Focusing on the concepts and application of Monte Carlo techniques, Fast Sequential Monte Carlo Methods for Counting and Optimization includes: Detailed algorithms needed to practice solving real-world problems Numerous examples with Monte Carlo method produced solutions within the 1-2% limit of relative error A new generic sequential importance sampling algorithm alongside extensive numerical results An appendix focused on review material to provide additional background information Fast Sequential Monte Carlo Methods for Counting and Optimization is an excellent resource for engineers, computer scientists, mathematicians, statisticians, and readers interested in efficient simulation techniques. The book is also useful for upper-undergraduate and graduate-level courses on Monte Carlo methods.
Author : Gerardo Rubino
Publisher : Wiley
ISBN 13 : 047074541X
Total Pages : 278 pages
Book Rating : 4.4/5 (77 download)
Download or read book Rare Event Simulation using Monte Carlo Methods written by Gerardo Rubino and published by Wiley. 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.
Author : Malvin H. Kalos
Publisher : Wiley-VCH
ISBN 13 : 9780471898399
Total Pages : 208 pages
Book Rating : 4.8/5 (983 download)
Download or read book Monte Carlo Methods written by Malvin H. Kalos and published by Wiley-VCH. This book was released on 1986-10-29 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to Monte Carlo Methods seeks to identify and study the unifying elements that underlie their effective application. It focuses on two basic themes. The first is the importance of random walks as they occur both in natural stochastic systems and in their relationship to integral and differential equations. The second theme is that of variance reduction in general and importance sampling in particular as a technique for efficient use of the methods. Random walks are introduced with an elementary example in which the modelling of radiation transport arises directly from a schematic probabilistic description of the interaction of radiation with matter. Building on that example, the relationship between random walks and integral equations is outlined. The applicability of these ideas to other problems is shown by a clear and elementary introduction to the solution of the Schrodinger equation by random walks. The detailed discussion of variance reduction includes Monte Carlo evaluation of finite-dimensional integrals. Special attention is given to importance sampling, partly because of its intrinsic interest in quadrature, partly because of its general usefulness in the solution of integral equations. One significant feature is that Monte Carlo Methods treats the "Metropolis algorithm" in the context of sampling methods, clearly distinguishing it from importance sampling. Physicists, chemists, statisticians, mathematicians, and computer scientists will find Monte Carlo Methods a complete and stimulating introduction.
Author : University of Florida. Statistical Laboratory
Publisher :
ISBN 13 :
Total Pages : 408 pages
Book Rating : 4.3/5 (91 download)
Download or read book Symposium on Monte Carlo Methods written by University of Florida. Statistical Laboratory and published by . This book was released on 1956 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Xiaowei Zhang
Publisher : Stanford University
ISBN 13 :
Total Pages : 129 pages
Book Rating : 4.F/5 ( download)
Download or read book Computing Rare-event Probabilities for Affine Models and General State Space Markov Processes written by Xiaowei Zhang and published by Stanford University. This book was released on 2011 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rare-event simulation concerns computing small probabilities, i.e. rare-event probabilities. This dissertation investigates efficient simulation algorithms based on importance sampling for computing rare-event probabilities for different models, and establishes their efficiency via asymptotic analysis. The first part discusses asymptotic behavior of affine models. Stochastic stability of affine jump diffusions are carefully studied. In particular, positive recurrence, ergodicity, and exponential ergodicity are established for such processes under various conditions via a Foster-Lyapunov type approach. The stationary distribution is characterized in terms of its characteristic function. Furthermore, the large deviations behavior of affine point processes are explicitly computed, based on which a logarithmically efficient importance sampling algorithm is proposed for computing rare-event probabilities for affine point processes. The second part is devoted to a much more general setting, i.e. general state space Markov processes. The current state-of-the-art algorithm for computing rare-event probabilities in this context heavily relies on the solution of a certain eigenvalue problem, which is often unavailable in closed form unless certain special structure is present (e.g. affine structure for affine models). To circumvent this difficulty, assuming the existence of a regenerative structure, we propose a bootstrap-based algorithm that conducts the importance sampling on the regenerative cycle-path space instead of the original one-step transition kernel. The efficiency of this algorithm is also discussed.
Author : Jun S. Liu
Publisher : Springer Science & Business Media
ISBN 13 : 0387763716
Total Pages : 350 pages
Book Rating : 4.3/5 (877 download)
Download or read book Monte Carlo Strategies in Scientific Computing written by Jun S. Liu and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a self-contained and up-to-date treatment of the Monte Carlo method and develops a common framework under which various Monte Carlo techniques can be "standardized" and compared. Given the interdisciplinary nature of the topics and a moderate prerequisite for the reader, this book should be of interest to a broad audience of quantitative researchers such as computational biologists, computer scientists, econometricians, engineers, probabilists, and statisticians. It can also be used as a textbook for a graduate-level course on Monte Carlo methods.
Author :
Publisher :
ISBN 13 :
Total Pages : 24 pages
Book Rating : 4.:/5 (227 download)
Download or read book Importance Sampling for Sums of Random Variables With Regularly Varying Tails written by and published by . This book was released on 2006 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: Importance sampling is a variance reduction technique for efficient estimation of rare-event probabilities by Monte Carlo. For random variables with heavy tails there is little consensus on how to choose the change of measure used in importance sampling. In this paper we study dynamic importance sampling schemes for sums of independent and identically distributed random variables with regularly varying tails. The number of summands can be random but must be independent of the summands. For estimating the probability that the sum exceeds a given threshold, we explicitly identify a class of dynamic importance sampling algorithms with bounded relative errors. In fact, these schemes are nearly asymptotically optimal in the sense that the second moment of the corresponding importance sampling estimator can be made as close as desired to the minimal possible value.
Author : Neal Noah Madras
Publisher : Springer Science & Business
ISBN 13 : 9780821829783
Total Pages : 116 pages
Book Rating : 4.8/5 (297 download)
Download or read book Lectures on Monte Carlo Methods written by Neal Noah Madras and published by Springer Science & Business. This book was released on 2002 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: Monte Carlo methods form an experimental branch of mathematics that employs simulations driven by random number generators. These methods are often used when others fail, since they are much less sensitive to the ``curse of dimensionality'', which plagues deterministic methods in problems with a large number of variables. Monte Carlo methods are used in many fields: mathematics, statistics, physics, chemistry, finance, computer science, and biology, for instance. This book is an introduction to Monte Carlo methods for anyone who would like to use these methods to study various kinds of mathematical models that arise in diverse areas of application. The book is based on lectures in a graduate course given by the author. It examines theoretical properties of Monte Carlo methods as well as practical issues concerning their computer implementation and statistical analysis. The only formal prerequisite is an undergraduate course in probability. The book is intended to be accessible to students from a wide range of scientific backgrounds. Rather than being a detailed treatise, it covers the key topics of Monte Carlo methods to the depth necessary for a researcher to design, implement, and analyze a full Monte Carlo study of a mathematical or scientific problem. The ideas are illustrated with diverse running examples. There are exercises sprinkled throughout the text. The topics covered include computer generation of random variables, techniques and examples for variance reduction of Monte Carlo estimates, Markov chain Monte Carlo, and statistical analysis of Monte Carlo output.
Author : David Ardia
Publisher :
ISBN 13 :
Total Pages : 44 pages
Book Rating : 4.:/5 (129 download)
Download or read book To Bridge, to Warp or to Wrap? A Comperative Study of Monte Carlo Methods for Efficient Evaluation of Marginal Likelihood written by David Ardia and published by . This book was released on 2015 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt: Important choices for efficient and accurate evaluation of marginal likelihoods by means of Monte Carlo simulation methods are studied for the case of highly non-elliptical posterior distributions. We focus on the situation where one makes use of importance sampling or the independence chain Metropolis-Hastings algorithm for posterior analysis. A comparative analysis is presented of possible advantages and limitations of different simulation techniques; of possible choices of candidate distributions and choices of target or warped target distributions; and finally of numerical standard errors. The importance of a robust and flexible estimation strategy is demonstrated where the complete posterior distribution is explored. In this respect, the adaptive mixture of Student-t distributions of Hoogerheide et al.(2007) works particularly well. Given an appropriately yet quickly tuned candidate, straightforward importance sampling provides the most efficient estimator of the marginal likelihood in the cases investigated in this paper, which include a non-linear regression model of Ritter and Tanner (1992) and a conditional normal distribution of Gelman and Meng (1991). A poor choice of candidate density may lead to a huge loss of efficiency where the numerical standard error may be highly unreliable.
Author : Christian Robert
Publisher : Springer Science & Business Media
ISBN 13 : 1475730713
Total Pages : 522 pages
Book Rating : 4.4/5 (757 download)
Download or read book Monte Carlo Statistical Methods written by Christian Robert and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: We have sold 4300 copies worldwide of the first edition (1999). This new edition contains five completely new chapters covering new developments.
Author : Tze Leung Lai
Publisher : Springer Science & Business Media
ISBN 13 : 0387778268
Total Pages : 363 pages
Book Rating : 4.3/5 (877 download)
Download or read book Statistical Models and Methods for Financial Markets written by Tze Leung Lai and published by Springer Science & Business Media. This book was released on 2008-07-25 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: The idea of writing this bookarosein 2000when the ?rst author wasassigned to teach the required course STATS 240 (Statistical Methods in Finance) in the new M. S. program in ?nancial mathematics at Stanford, which is an interdisciplinary program that aims to provide a master’s-level education in applied mathematics, statistics, computing, ?nance, and economics. Students in the programhad di?erent backgroundsin statistics. Some had only taken a basic course in statistical inference, while others had taken a broad spectrum of M. S. - and Ph. D. -level statistics courses. On the other hand, all of them had already taken required core courses in investment theory and derivative pricing, and STATS 240 was supposed to link the theory and pricing formulas to real-world data and pricing or investment strategies. Besides students in theprogram,thecoursealso attractedmanystudentsfromother departments in the university, further increasing the heterogeneity of students, as many of them had a strong background in mathematical and statistical modeling from the mathematical, physical, and engineering sciences but no previous experience in ?nance. To address the diversity in background but common strong interest in the subject and in a potential career as a “quant” in the ?nancialindustry,thecoursematerialwascarefullychosennotonlytopresent basic statistical methods of importance to quantitative ?nance but also to summarize domain knowledge in ?nance and show how it can be combined with statistical modeling in ?nancial analysis and decision making. The course material evolved over the years, especially after the second author helped as the head TA during the years 2004 and 2005.
