Author: Publisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
Automatic Variance Reduction for Monte Carlo Simulations Via the Local Importance Function Transform
Author: Automatic Variance Reduction for Monte Carlo Simulations Via the Local Importance Function Transform
Author: Scott Allen TurnerA Variationally-based Variance Reduction Method for Monte Carlo Particle Transport Problems
Author: Carla Lynn BarrettMonte Carlo Methods for Particle Transport
Author: Alireza HaghighatPublisher: CRC Press
ISBN: 042958220X
Category : Mathematics
Languages : en
Pages : 214
Book Description
Fully updated with the latest developments in the eigenvalue Monte Carlo calculations and automatic variance reduction techniques and containing an entirely new chapter on fission matrix and alternative hybrid techniques. This second edition explores the uses of the Monte Carlo method for real-world applications, explaining its concepts and limitations. Featuring illustrative examples, mathematical derivations, computer algorithms, and homework problems, it is an ideal textbook and practical guide for nuclear engineers and scientists looking into the applications of the Monte Carlo method, in addition to students in physics and engineering, and those engaged in the advancement of the Monte Carlo methods. Describes general and particle-transport-specific automated variance reduction techniques Presents Monte Carlo particle transport eigenvalue issues and methodologies to address these issues Presents detailed derivation of existing and advanced formulations and algorithms with real-world examples from the author’s research activities
Student Solutions Manual to accompany Simulation and the Monte Carlo Method, Student Solutions Manual
Author: Dirk P. KroesePublisher: John Wiley & Sons
ISBN: 0470285303
Category : Mathematics
Languages : en
Pages : 204
Book Description
This accessible new edition explores the major topics in Monte Carlo simulation Simulation and the Monte Carlo Method, Second Edition reflects the latest developments in the field and presents a fully updated and comprehensive account of the major topics that have emerged in Monte Carlo simulation since the publication of the classic First Edition over twenty-five years 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 the transform likelihood ratio method and the screening 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 to rare events estimation and combinatorial optimization Application of Monte Carlo techniques for counting problems, with an emphasis on the parametric minimum cross-entropy method An extensive range of exercises is provided at the end of each chapter, with more difficult sections and exercises marked accordingly for advanced readers. A generous sampling of applied examples is positioned throughout the book, emphasizing various areas of application, and a detailed appendix presents an introduction to exponential families, a discussion of the computational complexity of stochastic programming problems, and sample MATLAB® programs. Requiring only a basic, introductory knowledge of probability and statistics, Simulation and the Monte Carlo Method, Second Edition is an excellent text for upper-undergraduate and beginning graduate courses in 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.
A Local'' Exponential Transform Method for Global Variance Reduction in Monte Carlo Transport Problems
Author: Publisher:
ISBN:
Category :
Languages : en
Pages : 7
Book Description
Numerous variance reduction techniques, such as splitting/Russian roulette, weight windows, and the exponential transform exist for improving the efficiency of Monte Carlo transport calculations. Typically, however, these methods, while reducing the variance in the problem area of interest tend to increase the variance in other, presumably less important, regions. As such, these methods tend to be not as effective in Monte Carlo calculations which require the minimization of the variance everywhere. Recently, ''Local'' Exponential Transform (LET) methods have been developed as a means of approximating the zero-variance solution. A numerical solution to the adjoint diffusion equation is used, along with an exponential representation of the adjoint flux in each cell, to determine ''local'' biasing parameters. These parameters are then used to bias the forward Monte Carlo transport calculation in a manner similar to the conventional exponential transform, but such that the transform parameters are now local in space and energy, not global. Results have shown that the Local Exponential Transform often offers a significant improvement over conventional geometry splitting/Russian roulette with weight windows. Since the biasing parameters for the Local Exponential Transform were determined from a low-order solution to the adjoint transport problem, the LET has been applied in problems where it was desirable to minimize the variance in a detector region. The purpose of this paper is to show that by basing the LET method upon a low-order solution to the forward transport problem, one can instead obtain biasing parameters which will minimize the maximum variance in a Monte Carlo transport calculation.
Approximating Integrals via Monte Carlo and Deterministic Methods
Author: Michael EvansPublisher: OUP Oxford
ISBN: 019158987X
Category : Mathematics
Languages : en
Pages : 302
Book Description
This book is designed to introduce graduate students and researchers to the primary methods useful for approximating integrals. The emphasis is on those methods that have been found to be of practical use, and although the focus is on approximating higher- dimensional integrals the lower-dimensional case is also covered. Included in the book are asymptotic techniques, multiple quadrature and quasi-random techniques as well as a complete development of Monte Carlo algorithms. For the Monte Carlo section importance sampling methods, variance reduction techniques and the primary Markov Chain Monte Carlo algorithms are covered. This book brings these various techniques together for the first time, and hence provides an accessible textbook and reference for researchers in a wide variety of disciplines.
Proceedings of the Joint International Conference on Mathematical Methods and Supercomputing for Nuclear Applications, Saratoga Springs, New York, October 5-9, 1997
Author: Transactions of the American Nuclear Society
Author: American Nuclear SocietyPublisher:
ISBN:
Category : Nuclear engineering
Languages : en
Pages : 952
Book Description
Monte Carlo Methods in Finance
Author: Je Guk KimPublisher:
ISBN:
Category : Brownian motion processes
Languages : en
Pages : 80
Book Description
Monte Carlo method has received significant consideration from the context of quantitative finance mainly due to its ease of implementation for complex problems in the field. Among topics of its application to finance, we address two topics: (1) optimal importance sampling for the Laplace transform of exponential Brownian functionals and (2) analysis on the convergence of quasi-regression method for pricing American option. In the first part of this dissertation, we present an asymptotically optimal importance sampling method for Monte Carlo simulation of the Laplace transform of exponential Brownian functionals via Large deviations principle and calculus of variations the closed form solutions of which induces an optimal measure for sampling. Some numerical tests are conducted through the Dothan bond pricing model, which shows the method achieves a significant variance reduction. Secondly, we study the convergence of a quasi-regression Monte Carlo method proposed by Glasserman and Yu (2004) that is a variant of least-squares method proposed by Longstaff and Schwartz (2001) for pricing American option. Glasserman and Yu (2004) showed that the method converges to an approximation to the true price of American option with critical relations between the number of paths simulated and the number of basis functions for two examples: Brownian motion and geometric Brownian motion. We show that the method surely converges to the true price of American option even under multiple underlying assets and prove a more promising critical relation between the number of basis functions and the number of simulations in the previous study holds. Finally, we propose a rate of convergence of the method.