Download or read book Importance Sampling and Stratification Techniques for Multivariate Models with Low dimentional Structures written by Yoshihiro Taniguchi and published by . This book was released on 2017 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many problems in finance and risk management involve the computation of quantities related to rare-event analysis. As many financial problems are high-dimensional, the quan- tities of interest rarely have analytical forms and therefore they must be approximated using numerical methods. Plain Monte Carlo (MC) is a versatile simulation-based numer- ical technique suitable to high-dimensional problems as its estimation error converges to zero at a rate independent of the dimension of the problem. The weakness of plain MC is the high computational cost it requires to obtain estimates with small variance. This issue is especially severe for rare-event simulation as a very large number, often over millions, of samples are required to obtain an estimate with reasonable precision. In this thesis, we develop importance sampling (IS) and stratified sampling (SS) schemes for rare-event simulation problems to reduce the variance of the plain MC estimators. The main idea of our approach is to construct effective proposal distributions for IS and partitions of the sample space for SS by exploiting the low-dimensional structures that exist in many financial problems. More specifically, our general approach is to identify a low-dimensional transformation of input variables such that the transformed variables are highly correlated with the output, and then make the rare-event more frequent by twisting the distribution of the transformed variables by using IS and/or SS. In some cases, SS is used instead of IS as SS is shown to give estimators with smaller variance. In other cases, IS and SS are used together to achieve greater variance reduction than when they are used separately. Our proposed methods are applicable to a wide range of problems because they do not assume specific types of problems or distribution of input variables and because their performance does not degrade even in high dimension. Furthermore, our approach serves as a dimension reduction technique, so it enhances the effectiveness of quasi-Monte Carlo sampling methods when combined together. This thesis considers three types of low-dimensional structures in increasing order of generality and develops IS and SS methods under each structural assumption, along with optimal tuning procedures and sampling algorithms under specific distributions. The assumed low-dimensional structures are as follows: the output takes a large value when at least one of the input variables is large; a single-index model where the output depends on the input variables mainly through some one-dimensional projection; and a multi-index model where the output depends on the input mainly through a set of linear combinations. Our numerical experiments find that many financial problems possess one of the assumed low-dimensional structure. When applied to those problems in simulation studies, our proposed methods often give variance reduction factors of over 1,000 with little additional computational costs compared to plain MC.

Download or read book Importance Sampling Methods with Multiple Sampling Distributions written by Wentao Li and published by . This book was released on 2013 with total page 91 pages. Available in PDF, EPUB and Kindle. Book excerpt: The complexity of integrands in modern scientific, industrial and financial problems increases rapidly with the development of data collection technologies. Monte Carlo method is widely used for complicated integration. In Monte Carlo integration, it is a natural and flexible method to consider multiple simulation mechanisms instead of one to address different aspects of the integrand. New methods are needed to combine the multiple mechanisms efficiently. Monte Carlo integration methods are reviewed, with focus on importance sampling methods (IS) and sequential Monte Carlo methods (SMC). The former is commonly used for low-dimension problems. The latter is a variation of IS, which has been developed to be a new branch itself in the recent two decades, and promising for high- dimension problems with sequential nature. For IS, techniques for combining multiple proposal distributions have been well developed, including Owen and Zhou (2000) and Tan (2004). Important implementation issues are needed to be resolved, including the allocation of sample budgets and the selection of proposals. A two-stage procedure is proposed to optimize the sample allocation, and although little theoretical investigation has been done for such a two-stage procedure in literatures, its optimality among current approaches is theoretically justified. The choice of the first stage sample size is also discussed through investigating the high order performance of estimators. About the construction of proposals, suggestions are given to approximate the perfect case. For SMC, only the plain vanilla combination of multiple proposals has been used in literatures. A novel SMC filtering scheme is proposed to combine the multiple proposals through the control variates approach in Tan (2004). Control variates are used in both resampling and estimation. The new algorithm is shown to be asymptotically more efficient than the direct use of multiple proposals and control variates. The guidance for selecting multiple proposals and control variates is also given. Numerical studies of the AR(1) model observed with noise and the stochastic volatility model with AR(1) dynamics show that the new algorithm can significantly improve over the bootstrap filter and auxiliary particle filter.

Download or read book An adaptive importance sampling procedure written by Stanford University. Systems Optimization Laboratory and published by . This book was released on 1981 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: Monte Carlo calculations often require generation of a random sample of n-dimensional points drawn from a specified multivariate probability distribution. We present an importance sampling technique that can often greatly improve the efficiency of an acceptance/rejection generating method. The importance sampling function is defined as piecewise constant on a set of subregions, which are obtained by adaptively partitioning the sampling region so that the variation of density values within each subregion is relatively small. The partitioning strategy is based on multiparameter optimization to estimate the maximum and minimum of the original density function in each subregion. (Author).

Download or read book Practical Importance Sampling Methods for Finite Mixture Models and Multiple Imputation written by Russell John Steele and published by . This book was released on 2002 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Multivariate Statistical Methods written by Donald F. Morrison and published by McGraw-Hill Companies. This book was released on 1976 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: Includes index, bibliography, appendix: tables and charts

Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1992 with total page 1572 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Simulation and the Monte Carlo Method written by Reuven Y. Rubinstein and published by John Wiley & Sons. This book was released on 2016-10-21 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: This accessible new edition explores the major topics in Monte Carlo simulation that have arisen over the past 30 years and presents a sound foundation for problem solving Simulation and the Monte Carlo Method, Third Edition reflects the latest developments in the field and presents a fully updated and comprehensive account of the state-of-the-art theory, methods and applications that have emerged in Monte Carlo simulation since the publication of the classic First Edition over more than a quarter of a century ago. While maintaining its accessible and intuitive approach, this revised edition features a wealth of up-to-date information that facilitates a deeper understanding of problem solving across a wide array of subject areas, such as engineering, statistics, computer science, mathematics, and the physical and life sciences. The book begins with a modernized introduction that addresses the basic concepts of probability, Markov processes, and convex optimization. Subsequent chapters discuss the dramatic changes that have occurred in the field of the Monte Carlo method, with coverage of many modern topics including: Markov Chain Monte Carlo, variance reduction techniques such as importance (re-)sampling, and the transform likelihood ratio method, the score function method for sensitivity analysis, the stochastic approximation method and the stochastic counter-part method for Monte Carlo optimization, the cross-entropy method for rare events estimation and combinatorial optimization, and application of Monte Carlo techniques for counting problems. An extensive range of exercises is provided at the end of each chapter, as well as a generous sampling of applied examples. The Third Edition features a new chapter on the highly versatile splitting method, with applications to rare-event estimation, counting, sampling, and optimization. A second new chapter introduces the stochastic enumeration method, which is a new fast sequential Monte Carlo method for tree search. In addition, the Third Edition features new material on: • Random number generation, including multiple-recursive generators and the Mersenne Twister • Simulation of Gaussian processes, Brownian motion, and diffusion processes • Multilevel Monte Carlo method • New enhancements of the cross-entropy (CE) method, including the “improved” CE method, which uses sampling from the zero-variance distribution to find the optimal importance sampling parameters • Over 100 algorithms in modern pseudo code with flow control • Over 25 new exercises Simulation and the Monte Carlo Method, Third Edition is an excellent text for upper-undergraduate and beginning graduate courses in stochastic simulation and Monte Carlo techniques. The book also serves as a valuable reference for professionals who would like to achieve a more formal understanding of the Monte Carlo method. Reuven Y. Rubinstein, DSc, was Professor Emeritus in the Faculty of Industrial Engineering and Management at Technion-Israel Institute of Technology. He served as a consultant at numerous large-scale organizations, such as IBM, Motorola, and NEC. The author of over 100 articles and six books, Dr. Rubinstein was also the inventor of the popular score-function method in simulation analysis and generic cross-entropy methods for combinatorial optimization and counting. Dirk P. Kroese, PhD, is a Professor of Mathematics and Statistics in the School of Mathematics and Physics of The University of Queensland, Australia. He has published over 100 articles and four books in a wide range of areas in applied probability and statistics, including Monte Carlo methods, cross-entropy, randomized algorithms, tele-traffic c theory, reliability, computational statistics, applied probability, and stochastic modeling.

Download or read book Aerospace System Analysis and Optimization in Uncertainty written by Loïc Brevault and published by Springer Nature. This book was released on 2020-08-26 with total page 477 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spotlighting the field of Multidisciplinary Design Optimization (MDO), this book illustrates and implements state-of-the-art methodologies within the complex process of aerospace system design under uncertainties. The book provides approaches to integrating a multitude of components and constraints with the ultimate goal of reducing design cycles. Insights on a vast assortment of problems are provided, including discipline modeling, sensitivity analysis, uncertainty propagation, reliability analysis, and global multidisciplinary optimization. The extensive range of topics covered include areas of current open research. This Work is destined to become a fundamental reference for aerospace systems engineers, researchers, as well as for practitioners and engineers working in areas of optimization and uncertainty. Part I is largely comprised of fundamentals. Part II presents methodologies for single discipline problems with a review of existing uncertainty propagation, reliability analysis, and optimization techniques. Part III is dedicated to the uncertainty-based MDO and related issues. Part IV deals with three MDO related issues: the multifidelity, the multi-objective optimization and the mixed continuous/discrete optimization and Part V is devoted to test cases for aerospace vehicle design.

Download or read book Dissertation Abstracts International written by and published by . This book was released on 2007 with total page 960 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Discrete Choice Methods with Simulation written by Kenneth Train and published by Cambridge University Press. This book was released on 2009-07-06 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes the new generation of discrete choice methods, focusing on the many advances that are made possible by simulation. Researchers use these statistical methods to examine the choices that consumers, households, firms, and other agents make. Each of the major models is covered: logit, generalized extreme value, or GEV (including nested and cross-nested logits), probit, and mixed logit, plus a variety of specifications that build on these basics. Simulation-assisted estimation procedures are investigated and compared, including maximum stimulated likelihood, method of simulated moments, and method of simulated scores. Procedures for drawing from densities are described, including variance reduction techniques such as anithetics and Halton draws. Recent advances in Bayesian procedures are explored, including the use of the Metropolis-Hastings algorithm and its variant Gibbs sampling. The second edition adds chapters on endogeneity and expectation-maximization (EM) algorithms. No other book incorporates all these fields, which have arisen in the past 25 years. The procedures are applicable in many fields, including energy, transportation, environmental studies, health, labor, and marketing.

Download or read book Survey Sampling Theory and Applications written by Raghunath Arnab and published by Academic Press. This book was released on 2017-03-08 with total page 932 pages. Available in PDF, EPUB and Kindle. Book excerpt: Survey Sampling Theory and Applications offers a comprehensive overview of survey sampling, including the basics of sampling theory and practice, as well as research-based topics and examples of emerging trends. The text is useful for basic and advanced survey sampling courses. Many other books available for graduate students do not contain material on recent developments in the area of survey sampling. The book covers a wide spectrum of topics on the subject, including repetitive sampling over two occasions with varying probabilities, ranked set sampling, Fays method for balanced repeated replications, mirror-match bootstrap, and controlled sampling procedures. Many topics discussed here are not available in other text books. In each section, theories are illustrated with numerical examples. At the end of each chapter theoretical as well as numerical exercises are given which can help graduate students. - Covers a wide spectrum of topics on survey sampling and statistics - Serves as an ideal text for graduate students and researchers in survey sampling theory and applications - Contains material on recent developments in survey sampling not covered in other books - Illustrates theories using numerical examples and exercises

Download or read book Contemporary Computational Mathematics A Celebration of the 80th Birthday of Ian Sloan written by Josef Dick and published by Springer. This book was released on 2018-05-23 with total page 1330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a tribute to Professor Ian Hugh Sloan on the occasion of his 80th birthday. It consists of nearly 60 articles written by international leaders in a diverse range of areas in contemporary computational mathematics. These papers highlight the impact and many achievements of Professor Sloan in his distinguished academic career. The book also presents state of the art knowledge in many computational fields such as quasi-Monte Carlo and Monte Carlo methods for multivariate integration, multi-level methods, finite element methods, uncertainty quantification, spherical designs and integration on the sphere, approximation and interpolation of multivariate functions, oscillatory integrals, and in general in information-based complexity and tractability, as well as in a range of other topics. The book also tells the life story of the renowned mathematician, family man, colleague and friend, who has been an inspiration to many of us. The reader may especially enjoy the story from the perspective of his family, his wife, his daughter and son, as well as grandchildren, who share their views of Ian. The clear message of the book is that Ian H. Sloan has been a role model in science and life.

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.

Download or read book Robust Monte Carlo Methods for Light Transport Simulation written by Eric Veach and published by . This book was released on 1998 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Statistical Analysis of Multivariate Failure Time Data written by Ross L. Prentice and published by CRC Press. This book was released on 2019-05-14 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Statistical Analysis of Multivariate Failure Time Data: A Marginal Modeling Approach provides an innovative look at methods for the analysis of correlated failure times. The focus is on the use of marginal single and marginal double failure hazard rate estimators for the extraction of regression information. For example, in a context of randomized trial or cohort studies, the results go beyond that obtained by analyzing each failure time outcome in a univariate fashion. The book is addressed to researchers, practitioners, and graduate students, and can be used as a reference or as a graduate course text. Much of the literature on the analysis of censored correlated failure time data uses frailty or copula models to allow for residual dependencies among failure times, given covariates. In contrast, this book provides a detailed account of recently developed methods for the simultaneous estimation of marginal single and dual outcome hazard rate regression parameters, with emphasis on multiplicative (Cox) models. Illustrations are provided of the utility of these methods using Women’s Health Initiative randomized controlled trial data of menopausal hormones and of a low-fat dietary pattern intervention. As byproducts, these methods provide flexible semiparametric estimators of pairwise bivariate survivor functions at specified covariate histories, as well as semiparametric estimators of cross ratio and concordance functions given covariates. The presentation also describes how these innovative methods may extend to handle issues of dependent censorship, missing and mismeasured covariates, and joint modeling of failure times and covariates, setting the stage for additional theoretical and applied developments. This book extends and continues the style of the classic Statistical Analysis of Failure Time Data by Kalbfleisch and Prentice. Ross L. Prentice is Professor of Biostatistics at the Fred Hutchinson Cancer Research Center and University of Washington in Seattle, Washington. He is the recipient of COPSS Presidents and Fisher awards, the AACR Epidemiology/Prevention and Team Science awards, and is a member of the National Academy of Medicine. Shanshan Zhao is a Principal Investigator at the National Institute of Environmental Health Sciences in Research Triangle Park, North Carolina.

Download or read book Proceedings of the Section on Statistical Education written by American Statistical Association. Section on Statistical Education and published by . This book was released on 1984 with total page 772 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Doing Meta Analysis with R written by Mathias Harrer and published by CRC Press. This book was released on 2021-09-15 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: Doing Meta-Analysis with R: A Hands-On Guide serves as an accessible introduction on how meta-analyses can be conducted in R. Essential steps for meta-analysis are covered, including calculation and pooling of outcome measures, forest plots, heterogeneity diagnostics, subgroup analyses, meta-regression, methods to control for publication bias, risk of bias assessments and plotting tools. Advanced but highly relevant topics such as network meta-analysis, multi-three-level meta-analyses, Bayesian meta-analysis approaches and SEM meta-analysis are also covered. A companion R package, dmetar, is introduced at the beginning of the guide. It contains data sets and several helper functions for the meta and metafor package used in the guide. The programming and statistical background covered in the book are kept at a non-expert level, making the book widely accessible. Features • Contains two introductory chapters on how to set up an R environment and do basic imports/manipulations of meta-analysis data, including exercises • Describes statistical concepts clearly and concisely before applying them in R • Includes step-by-step guidance through the coding required to perform meta-analyses, and a companion R package for the book