Download or read book Automatic Variance Reduction for Monte Carlo Simulations Via the Local Importance Function Transform written by and published by . This book was released on 1996 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Automatic Variance Reduction for Monte Carlo Simulations Via the Local Importance Function Transform written by Scott Allen Turner and published by . This book was released on 1996 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A Variationally based Variance Reduction Method for Monte Carlo Particle Transport Problems written by Carla Lynn Barrett and published by . This book was released on 1999 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Monte Carlo Methods for Particle Transport written by Alireza Haghighat and published by CRC Press. This book was released on 2020-08-09 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Download or read book A Local Exponential Transform Method for Global Variance Reduction in Monte Carlo Transport Problems written by and published by . This book was released on 1992 with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Approximating Integrals via Monte Carlo and Deterministic Methods written by Michael Evans and published by OUP Oxford. This book was released on 2000-03-23 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Proceedings of the Joint International Conference on Mathematical Methods and Supercomputing for Nuclear Applications Saratoga Springs New York October 5 9 1997 written by and published by . This book was released on 1997 with total page 972 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Monte Carlo Methods Utilizing Mathematica written by Sujaul Chowdhury and published by Springer Nature. This book was released on 2023-02-23 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides practical demonstrations of how to carry out definite integrals with Monte Carlo methods using Mathematica. Random variates are sampled by the inverse transform method and the acceptance-rejection method using uniform, linear, Gaussian, and exponential probability distribution functions. A chapter on the application of the Variational Quantum Monte Carlo method to a simple harmonic oscillator is included. These topics are all essential for students of mathematics and physics. The author includes thorough background on each topic covered within the book in order to help readers understand the subject. The book also contains many examples to show how the methods can be applied.

Download or read book Monte Carlo Methods in Finance written by Je Guk Kim and published by . This book was released on 2015 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Transactions of the American Nuclear Society written by American Nuclear Society and published by . This book was released on 2001 with total page 952 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 AVATAR Automatic Variance Reduction in Monte Carlo Calculations written by and published by . This book was released on 1997 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: AVATAR{trademark} (Automatic Variance And Time of Analysis Reduction), accessed through the graphical user interface application, Justine{trademark}, is a superset of MCNP{trademark} that automatically invokes THREEDANT{trademark} for a three-dimensional deterministic adjoint calculation on a mesh independent of the Monte Carlo geometry, calculates weight windows, and runs MCNP. Computational efficiency increases by a factor of 2 to 5 for a three-detector oil well logging tool model. Human efficiency increases dramatically, since AVATAR eliminates the need for deep intuition and hours of tedious handwork.

Download or read book Local Exponential Transform Methods for the Monte Carlo Simulation of Multigroup Transport Problems written by Kasem Naser Abdeel and published by . This book was released on 1993 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Student Solutions Manual to accompany Simulation and the Monte Carlo Method written by Dirk P. Kroese and published by Wiley-Interscience. This book was released on 2007-12-14 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Variance Reduction by Importance Sampling and the Method of Splitting in Monte Carlo Calculations written by Burt M. Rosenbaum and published by . This book was released on 1971 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Techniques for Efficient Monte Carlo Simulation Volume III Variance Reduction written by E. J. McGrath and published by . This book was released on 1973 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many Monte Carlo simulation problems lend themselves readily to the application of variance reduction techniques. These techniques can result in great improvements in simulation efficiency. The document describes the basic concepts of variance reduction (Part 1), and a methodology for application of variance reduction techniques is presented in Part 2. Appendices include the basic analytical expressions for application of variance reduction schemes as well as an abstracted bibliography. The techniques considered here include importance sampling, Russian roulette and splitting, systematic sampling, stratified sampling, expected values, statistical estimation, correlated sampling, history reanalysis, control variates, antithetic variates, regression, sequantial sampling, adjoint formulation, transformations, orthonormal and conditional Monte Carlo. Emphasis has been placed on presentation of the material for application by the general user. This has been accomplished by presenting a step by step procedure for selection and application of the appropriate technique(s) for a given problem. (Author).

Download or read book Variance Reduction for Multi variable Monte Carlo Simulation written by 陳淑秋 and published by . This book was released on 2005 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: