Download or read book Constructive and Generic Control Variates for Monte Carlo Estimation written by Tarik Borogovac and published by . This book was released on 2009 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: Estimation of quantities that can be represented as expectations of appropriately defined random variables is an important problem in diverse areas of science and engineering. Monte Carlo (MC) sampling/simulation is a very general approach for estimation, and is the method of choice in many application areas. To increase the computational efficiency of MC simulation a number of Variance Reduction Techniques (VRT), which aim to reduce the variance of the MC estimator, have been devised. The design of effective VRT's has so far relied on the existence of specific problem features, and the acuity of the user to discover and properly exploit such features. One of the most effective VRT's is the method of Control Variates (CV). This method relies on a number of auxiliary random variables, called controls, that carry information about the estimation variable and "explain" part of its variance. If the means of the controls are known, or high quality estimates of them are available, the CV technique prescribes a generic procedure for transferring the relevant information to the estimation variable, leading to a controlled estimator with smaller variance. The main difficulty with the CV technique is in discovering controls that are informative about the estimation variable. This thesis presents a generic approach to the selection controls that is applicable to a broad class of problems where the estimation variable depends on a model parameter. It is shown that, under conditions, information at a set of parameters can be used to define effective controls for estimation at neighboring parameters. A connection between sample-wise function approximation methods and the CV method is established. Motivated by this connection, controls for the estimation variable and for its sensitivity with respect to the parameter are proposed. Their effectiveness is demonstrated on simulations from the fields of finance, materials science and photon transport. The requirement of tractability of controls is replaced by generic computational procedures through which the necessary information about the controls is procured. Two alternative algorithms that perform this function are given, and the CV estimators that result are analyzed.
Download or read book Control Variate Approach for Multi user Estimation Via Monte Carlo Simulation written by Na Sun and published by . This book was released on 2013 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: Monte Carlo (MC) simulation forms a very flexible and widely used computational method employed in many areas of science and engineering. The focus of this research is on the variance reduction technique of Control Variates (CV) which is a statistical approach used to improve the efficiency of MC simulation. We consider parametric estimation problems encountered in analysing stochastic systems where the stochastic system performance or its sensitivity depends on some model or decision parameter. Furthermore, we assume that the estimation is performed by one or more users at one or several parameter values. A store and reuse setting is introduced where at a set-up stage sonic information is gathered computationally and stored. The stored information is then used at the estimation phase by users to help with their estimation problems.Three problems in this setting are addressed. (i) An analysis of the user's choices at the estimation phase is provided. The information generated at the set-up phase is stored in the form of information about a set of random variables that can be used as control variates. Users need to decide whether, and if so how, to use the stored information. A so-called cost-adjusted mean squared error is used as a measure cost of the available estimators and user's decision is formulated as a constrained minimization problem. (ii) A recent approach to defining generic control variates in parametric estimation problems is generalized in two distinct directions: the first involves considering an alternative parametrization of the original problem through a change of probability measure. This parametrization is particularly relevant to sensitivity estimation problems with respect to model and decision parameters. In the second, for problems where the quantities of interest are defined on sample paths of stochastic processes that model the underlying stochastic dynamics, systematic control variate selection based on approximate dynamics is proposed. (iii) When common random inputs are used parametric estimation variables become statistically dependent. This dependence is explicitly modelled as a random field and conditions are derived to imply the effectiveness of estimation variables as control variates. Comparisons with the metamodeling approach of Kriging and recently proposed Stochastic Kriging that use similar inputs data to predict the mean of the estimation variable are provided.
Download or read book Stochastic Simulation Optimization for Discrete Event Systems written by Chun-Hung Chen and published by World Scientific. This book was released on 2013 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discrete event systems (DES) have become pervasive in our daily lives. Examples include (but are not restricted to) manufacturing and supply chains, transportation, healthcare, call centers, and financial engineering. However, due to their complexities that often involve millions or even billions of events with many variables and constraints, modeling these stochastic simulations has long been a hard nut to crack. The advance in available computer technology, especially of cluster and cloud computing, has paved the way for the realization of a number of stochastic simulation optimization for complex discrete event systems. This book will introduce two important techniques initially proposed and developed by Professor Y C Ho and his team; namely perturbation analysis and ordinal optimization for stochastic simulation optimization, and present the state-of-the-art technology, and their future research directions.
Download or read book The use of control variates in Monte Carlo estimation of power curves written by P. Rothery and published by . This book was released on 1982 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Monte Carlo Methods written by J. Hammersley and published by Springer Science & Business Media. This book was released on 2013-03-07 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph surveys the present state of Monte Carlo methods. we have dallied with certain topics that have interested us Although personally, we hope that our coverage of the subject is reasonably complete; at least we believe that this book and the references in it come near to exhausting the present range of the subject. On the other hand, there are many loose ends; for example we mention various ideas for variance reduction that have never been seriously appli(:d in practice. This is inevitable, and typical of a subject that has remained in its infancy for twenty years or more. We are convinced Qf:ver theless that Monte Carlo methods will one day reach an impressive maturity. The main theoretical content of this book is in Chapter 5; some readers may like to begin with this chapter, referring back to Chapters 2 and 3 when necessary. Chapters 7 to 12 deal with applications of the Monte Carlo method in various fields, and can be read in any order. For the sake of completeness, we cast a very brief glance in Chapter 4 at the direct simulation used in industrial and operational research, where the very simplest Monte Carlo techniques are usually sufficient. We assume that the reader has what might roughly be described as a 'graduate' knowledge of mathematics. The actual mathematical techniques are, with few exceptions, quite elementary, but we have freely used vectors, matrices, and similar mathematical language for the sake of conciseness.
Download or read book Adaptive Control Variates in Monte Carlo Simulation written by Sujin Kim and published by . This book was released on 2006 with total page 238 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 2009-09-25 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the first simultaneous coverage of the statistical aspects of simulation and Monte Carlo methods, their commonalities and their differences for the solution of a wide spectrum of engineering and scientific problems. It contains standard material usually considered in Monte Carlo simulation as well as new material such as variance reduction techniques, regenerative simulation, and Monte Carlo optimization.
Download or read book Monte Carlo methods written by John Michael Hammersley and published by . This book was released on 1964 with total page 198 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 2016-11-07 with total page 432 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 A Multilevel Approach to Control Variates written by Adam Speight and published by . This book was released on 2016 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present a new variance reduction technique that naturally applies to price financial derivatives by Monte Carlo simulation. Inspired by multigrid methods for solving PDEs, the technique is based on control variates derived from a sequence of approximations that converge pathwise to a limiting model. It applies to a large class of problems, and is easy to implement. Theory and computational results show this method can substantially reduce computational time relative to crude Monte Carlo estimation and is competitive with other variance reduction techniques under Monte Carlo sampling.
Download or read book Monte Carlo Optimization Simulation and Sensitivity of Queueing Networks written by Reuven Y. Rubinstein and published by . This book was released on 1986-09-02 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: A theoretical treatment of Monte Carlo optimization--simulation using perturbation analysis, adaptive methods, and variance reduction techniques. Emphasizes concepts rather than mathematical completeness. Shows how to use simulation and Monte Carlo methods efficiently for estimating performance measures, sensitivities and optimization of stochastic systems.
Download or read book Regression based Monte Carlo Methods with Optimal Control Variates written by Stefan Häfner and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Control Variates for Monte Carlo Analysis of Nonlinear Statitical sic Models written by James J. Swain and published by . This book was released on 1989 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Lectures on Monte Carlo Methods written by Neal Noah Madras and published by American Mathematical Soc.. This book was released on 2002 with total page 113 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.
Download or read book Efficient Control Variates for Monte Carlo Valuation Af American Options written by Nicki Søndergaard Rasmussen and published by . This book was released on 2002 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Control Variates for Quasi Monte Carlo written by Fred J. Hickernell and published by . This book was released on 2002 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Monte Carlo and Quasi Monte Carlo Sampling written by Christiane Lemieux and published by Springer Science & Business Media. This book was released on 2009-04-03 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quasi–Monte Carlo methods have become an increasingly popular alternative to Monte Carlo methods over the last two decades. Their successful implementation on practical problems, especially in finance, has motivated the development of several new research areas within this field to which practitioners and researchers from various disciplines currently contribute. This book presents essential tools for using quasi–Monte Carlo sampling in practice. The first part of the book focuses on issues related to Monte Carlo methods—uniform and non-uniform random number generation, variance reduction techniques—but the material is presented to prepare the readers for the next step, which is to replace the random sampling inherent to Monte Carlo by quasi–random sampling. The second part of the book deals with this next step. Several aspects of quasi-Monte Carlo methods are covered, including constructions, randomizations, the use of ANOVA decompositions, and the concept of effective dimension. The third part of the book is devoted to applications in finance and more advanced statistical tools like Markov chain Monte Carlo and sequential Monte Carlo, with a discussion of their quasi–Monte Carlo counterpart. The prerequisites for reading this book are a basic knowledge of statistics and enough mathematical maturity to follow through the various techniques used throughout the book. This text is aimed at graduate students in statistics, management science, operations research, engineering, and applied mathematics. It should also be useful to practitioners who want to learn more about Monte Carlo and quasi–Monte Carlo methods and researchers interested in an up-to-date guide to these methods.
