Approximating Integrals Via Monte Carlo And Deterministic Methods

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Approximating Integrals Via Monte Carlo and Deterministic Methods

Michael John Evans,T. Swartz,Associate Professor Department of Mathematics and Statistics Tim Swartz
Approximating Integrals Via Monte Carlo and Deterministic Methods Book PDF

Author : Michael John Evans,T. Swartz,Associate Professor Department of Mathematics and Statistics Tim Swartz
Publisher : Oxford University Press on Demand
Page : 288 pages
File Size : 53,8 Mb
Release : 2000
Category : Business & Economics
ISBN : 0198502788

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Approximating Integrals Via Monte Carlo and Deterministic Methods by Michael John Evans,T. Swartz,Associate Professor Department of Mathematics and Statistics Tim Swartz Pdf

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 thelower-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 primaryMarkov 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.

Approximating Integrals via Monte Carlo and Deterministic Methods

Michael Evans,Timothy Swartz
Approximating Integrals via Monte Carlo and Deterministic Methods Book PDF

Author : Michael Evans,Timothy Swartz
Publisher : OUP Oxford
Page : 302 pages
File Size : 44,7 Mb
Release : 2000-03-23
Category : Mathematics
ISBN : 9780191589874

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Approximating Integrals via Monte Carlo and Deterministic Methods by Michael Evans,Timothy Swartz Pdf

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.

Monte Carlo and Quasi-Monte Carlo Methods 2000

Kai-Tai Fang,Fred J. Hickernell,Harald Niederreiter
Monte Carlo and Quasi Monte Carlo Methods 2000 Book PDF

Author : Kai-Tai Fang,Fred J. Hickernell,Harald Niederreiter
Publisher : Springer Science & Business Media
Page : 570 pages
File Size : 48,9 Mb
Release : 2011-06-28
Category : Mathematics
ISBN : 9783642560460

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Monte Carlo and Quasi-Monte Carlo Methods 2000 by Kai-Tai Fang,Fred J. Hickernell,Harald Niederreiter Pdf

This book represents the refereed proceedings of the Fourth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing which was held at Hong Kong Baptist University in 2000. An important feature are invited surveys of the state-of-the-art in key areas such as multidimensional numerical integration, low-discrepancy point sets, random number generation, and applications of Monte Carlo and quasi-Monte Carlo methods. These proceedings include also carefully selected contributed papers on all aspects of Monte Carlo and quasi-Monte Carlo methods. The reader will be informed about current research in this very active field.

Stochastic Analysis 2010

Dan Crisan
Stochastic Analysis 2010 Book PDF

Author : Dan Crisan
Publisher : Springer Science & Business Media
Page : 303 pages
File Size : 43,5 Mb
Release : 2010-11-26
Category : Mathematics
ISBN : 9783642153587

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Stochastic Analysis 2010 by Dan Crisan Pdf

Stochastic Analysis aims to provide mathematical tools to describe and model high dimensional random systems. Such tools arise in the study of Stochastic Differential Equations and Stochastic Partial Differential Equations, Infinite Dimensional Stochastic Geometry, Random Media and Interacting Particle Systems, Super-processes, Stochastic Filtering, Mathematical Finance, etc. Stochastic Analysis has emerged as a core area of late 20th century Mathematics and is currently undergoing a rapid scientific development. The special volume “Stochastic Analysis 2010” provides a sample of the current research in the different branches of the subject. It includes the collected works of the participants at the Stochastic Analysis section of the 7th ISAAC Congress organized at Imperial College London in July 2009.

Introducing Monte Carlo Methods with R

Christian Robert,George Casella
Introducing Monte Carlo Methods with R Book PDF

Author : Christian Robert,George Casella
Publisher : Springer Science & Business Media
Page : 297 pages
File Size : 47,5 Mb
Release : 2010
Category : Computers
ISBN : 9781441915757

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Introducing Monte Carlo Methods with R by Christian Robert,George Casella Pdf

This book covers the main tools used in statistical simulation from a programmer’s point of view, explaining the R implementation of each simulation technique and providing the output for better understanding and comparison.

Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan

Josef Dick,Frances Y. Kuo,Henryk Woźniakowski
Contemporary Computational Mathematics A Celebration of the 80th Birthday of Ian Sloan Book PDF

Author : Josef Dick,Frances Y. Kuo,Henryk Woźniakowski
Publisher : Springer
Page : 1309 pages
File Size : 45,5 Mb
Release : 2018-05-23
Category : Mathematics
ISBN : 9783319724560

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Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan by Josef Dick,Frances Y. Kuo,Henryk Woźniakowski Pdf

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.

Random Number Generation and Monte Carlo Methods

James E. Gentle
Random Number Generation and Monte Carlo Methods Book PDF

Author : James E. Gentle
Publisher : Springer Science & Business Media
Page : 387 pages
File Size : 42,8 Mb
Release : 2006-04-18
Category : Computers
ISBN : 9780387216102

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Random Number Generation and Monte Carlo Methods by James E. Gentle Pdf

Monte Carlo simulation has become one of the most important tools in all fields of science. Simulation methodology relies on a good source of numbers that appear to be random. These "pseudorandom" numbers must pass statistical tests just as random samples would. Methods for producing pseudorandom numbers and transforming those numbers to simulate samples from various distributions are among the most important topics in statistical computing. This book surveys techniques of random number generation and the use of random numbers in Monte Carlo simulation. The book covers basic principles, as well as newer methods such as parallel random number generation, nonlinear congruential generators, quasi Monte Carlo methods, and Markov chain Monte Carlo. The best methods for generating random variates from the standard distributions are presented, but also general techniques useful in more complicated models and in novel settings are described. The emphasis throughout the book is on practical methods that work well in current computing environments. The book includes exercises and can be used as a test or supplementary text for various courses in modern statistics. It could serve as the primary test for a specialized course in statistical computing, or as a supplementary text for a course in computational statistics and other areas of modern statistics that rely on simulation. The book, which covers recent developments in the field, could also serve as a useful reference for practitioners. Although some familiarity with probability and statistics is assumed, the book is accessible to a broad audience. The second edition is approximately 50% longer than the first edition. It includes advances in methods for parallel random number generation, universal methods for generation of nonuniform variates, perfect sampling, and software for random number generation.

Uncertainty Quantification in Computational Science

Sunetra Sarkar,Jeroen A S Witteveen
Uncertainty Quantification in Computational Science Book PDF

Author : Sunetra Sarkar,Jeroen A S Witteveen
Publisher : World Scientific
Page : 196 pages
File Size : 55,8 Mb
Release : 2016-08-19
Category : Electronic
ISBN : 9789814730594

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Uncertainty Quantification in Computational Science by Sunetra Sarkar,Jeroen A S Witteveen Pdf

During the last decade, research in Uncertainty Quantification (UC) has received a tremendous boost, in fluid engineering and coupled structural-fluids systems. New algorithms and adaptive variants have also emerged. This timely compendium overviews in detail the current state of the art of the field, including advances in structural engineering, along with the recent focus on fluids and coupled systems. Such a strong compilation of these vibrant research areas will certainly be an inspirational reference material for the scientific community.

Monte Carlo Methods for Applied Scientists

Ivan Dimov
Monte Carlo Methods for Applied Scientists Book PDF

Author : Ivan Dimov
Publisher : World Scientific
Page : 308 pages
File Size : 41,8 Mb
Release : 2008
Category : Mathematics
ISBN : 9789812779892

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Monte Carlo Methods for Applied Scientists by Ivan Dimov Pdf

The Monte Carlo method is inherently parallel and the extensive and rapid development in parallel computers, computational clusters and grids has resulted in renewed and increasing interest in this method. At the same time there has been an expansion in the application areas and the method is now widely used in many important areas of science including nuclear and semiconductor physics, statistical mechanics and heat and mass transfer. This book attempts to bridge the gap between theory and practice concentrating on modern algorithmic implementation on parallel architecture machines. Although a suitable text for final year postgraduate mathematicians and computational scientists it is principally aimed at the applied scientists: only a small amount of mathematical knowledge is assumed and theorem proving is kept to a minimum, with the main focus being on parallel algorithms development often to applied industrial problems. A selection of algorithms developed both for serial and parallel machines are provided. Sample Chapter(s). Chapter 1: Introduction (231 KB). Contents: Basic Results of Monte Carlo Integration; Optimal Monte Carlo Method for Multidimensional Integrals of Smooth Functions; Iterative Monte Carlo Methods for Linear Equations; Markov Chain Monte Carlo Methods for Eigenvalue Problems; Monte Carlo Methods for Boundary-Value Problems (BVP); Superconvergent Monte Carlo for Density Function Simulation by B-Splines; Solving Non-Linear Equations; Algorithmic Effciency for Different Computer Models; Applications for Transport Modeling in Semiconductors and Nanowires. Readership: Applied scientists and mathematicians.

Data Analysis from Statistical Foundations

Donald Alexander Stuart Fraser,A. K. Md. Ehsanes Saleh
Data Analysis from Statistical Foundations Book PDF

Author : Donald Alexander Stuart Fraser,A. K. Md. Ehsanes Saleh
Publisher : Nova Publishers
Page : 442 pages
File Size : 41,7 Mb
Release : 2001
Category : Mathematics
ISBN : 1560729686

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Data Analysis from Statistical Foundations by Donald Alexander Stuart Fraser,A. K. Md. Ehsanes Saleh Pdf

Data Analysis from Statistical Foundations

Computation of Multivariate Normal and t Probabilities

Alan Genz,Frank Bretz
Computation of Multivariate Normal and t Probabilities Book PDF

Author : Alan Genz,Frank Bretz
Publisher : Springer Science & Business Media
Page : 130 pages
File Size : 53,8 Mb
Release : 2009-07-09
Category : Computers
ISBN : 9783642016899

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Computation of Multivariate Normal and t Probabilities by Alan Genz,Frank Bretz Pdf

Multivariate normal and t probabilities are needed for statistical inference in many applications. Modern statistical computation packages provide functions for the computation of these probabilities for problems with one or two variables. This book describes recently developed methods for accurate and efficient computation of the required probability values for problems with two or more variables. The book discusses methods for specialized problems as well as methods for general problems. The book includes examples that illustrate the probability computations for a variety of applications.

Numerical Methods for Nonlinear Estimating Equations

Christopher G. Small,Jinfang Wang
Numerical Methods for Nonlinear Estimating Equations Book PDF

Author : Christopher G. Small,Jinfang Wang
Publisher : Oxford University Press
Page : 330 pages
File Size : 46,7 Mb
Release : 2003
Category : Mathematics
ISBN : 0198506880

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Numerical Methods for Nonlinear Estimating Equations by Christopher G. Small,Jinfang Wang Pdf

Non linearity arises in statistical inference in various ways, with varying degrees of severity, as an obstacle to statistical analysis. More entrenched forms of nonlinearity often require intensive numerical methods to construct estimators, and the use of root search algorithms, or one-step estimators, is a standard method of solution. This book provides a comprehensive study of nonlinear estimating equations and artificial likelihood's for statistical inference. It provides extensive coverage and comparison of hill climbing algorithms, which when started at points of nonconcavity often have very poor convergence properties, and for additional flexibility proposes a number of modification to the standard methods for solving these algorithms. The book also extends beyond simple root search algorithms to include a discussion of the testing of roots for consistency, and the modification of available estimating functions to provide greater stability in inference. A variety of examples from practical applications are included to illustrate the problems and possibilities thus making this text ideal for the research statistician and graduate student.

Surrogate Model-Based Engineering Design and Optimization

Ping Jiang,Qi Zhou,Xinyu Shao
Surrogate Model Based Engineering Design and Optimization Book PDF

Author : Ping Jiang,Qi Zhou,Xinyu Shao
Publisher : Springer Nature
Page : 240 pages
File Size : 40,8 Mb
Release : 2019-11-01
Category : Technology & Engineering
ISBN : 9789811507311

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Surrogate Model-Based Engineering Design and Optimization by Ping Jiang,Qi Zhou,Xinyu Shao Pdf

This book covers some of the most popular methods in design space sampling, ensembling surrogate models, multi-fidelity surrogate model construction, surrogate model selection and validation, surrogate-based robust design optimization, and surrogate-based evolutionary optimization. Surrogate or metamodels are now frequently used in complex engineering product design to replace expensive simulations or physical experiments. They are constructed from available input parameter values and the corresponding output performance or quantities of interest (QOIs) to provide predictions based on the fitted or interpolated mathematical relationships. The book highlights a range of methods for ensembling surrogate and multi-fidelity models, which offer a good balance between surrogate modeling accuracy and building cost. A number of real-world engineering design problems, such as three-dimensional aircraft design, are also provided to illustrate the ability of surrogates for supporting complex engineering design. Lastly, illustrative examples are included throughout to help explain the approaches in a more “hands-on” manner.

Computational Approaches for Aerospace Design

Andy Keane,Prasanth Nair
Computational Approaches for Aerospace Design Book PDF

Author : Andy Keane,Prasanth Nair
Publisher : John Wiley & Sons
Page : 602 pages
File Size : 44,7 Mb
Release : 2005-08-05
Category : Technology & Engineering
ISBN : 9780470855478

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Computational Approaches for Aerospace Design by Andy Keane,Prasanth Nair Pdf

Over the last fifty years, the ability to carry out analysis as a precursor to decision making in engineering design has increased dramatically. In particular, the advent of modern computing systems and the development of advanced numerical methods have made computational modelling a vital tool for producing optimized designs. This text explores how computer-aided analysis has revolutionized aerospace engineering, providing a comprehensive coverage of the latest technologies underpinning advanced computational design. Worked case studies and over 500 references to the primary research literature allow the reader to gain a full understanding of the technology, giving a valuable insight into the world’s most complex engineering systems. Key Features: Includes background information on the history of aerospace design and established optimization, geometrical and mathematical modelling techniques, setting recent engineering developments in a relevant context. Examines the latest methods such as evolutionary and response surface based optimization, adjoint and numerically differentiated sensitivity codes, uncertainty analysis, and concurrent systems integration schemes using grid-based computing. Methods are illustrated with real-world applications of structural statics, dynamics and fluid mechanics to satellite, aircraft and aero-engine design problems. Senior undergraduate and postgraduate engineering students taking courses in aerospace, vehicle and engine design will find this a valuable resource. It will also be useful for practising engineers and researchers working on computational approaches to design.

Integrated Tracking, Classification, and Sensor Management

Mahendra Mallick,Vikram Krishnamurthy,Ba-Ngu Vo
Integrated Tracking Classification and Sensor Management Book PDF

Author : Mahendra Mallick,Vikram Krishnamurthy,Ba-Ngu Vo
Publisher : John Wiley & Sons
Page : 738 pages
File Size : 42,9 Mb
Release : 2012-12-03
Category : Technology & Engineering
ISBN : 9780470639054

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Integrated Tracking, Classification, and Sensor Management by Mahendra Mallick,Vikram Krishnamurthy,Ba-Ngu Vo Pdf

A unique guide to the state of the art of tracking, classification, and sensor management This book addresses the tremendous progress made over the last few decades in algorithm development and mathematical analysis for filtering, multi-target multi-sensor tracking, sensor management and control, and target classification. It provides for the first time an integrated treatment of these advanced topics, complete with careful mathematical formulation, clear description of the theory, and real-world applications. Written by experts in the field, Integrated Tracking, Classification, and Sensor Management provides readers with easy access to key Bayesian modeling and filtering methods, multi-target tracking approaches, target classification procedures, and large scale sensor management problem-solving techniques. Features include: An accessible coverage of random finite set based multi-target filtering algorithms such as the Probability Hypothesis Density filters and multi-Bernoulli filters with focus on problem solving A succinct overview of the track-oriented MHT that comprehensively collates all significant developments in filtering and tracking A state-of-the-art algorithm for hybrid Bayesian network (BN) inference that is efficient and scalable for complex classification models New structural results in stochastic sensor scheduling and algorithms for dynamic sensor scheduling and management Coverage of the posterior Cramer-Rao lower bound (PCRLB) for target tracking and sensor management Insight into cutting-edge military and civilian applications, including intelligence, surveillance, and reconnaissance (ISR) With its emphasis on the latest research results, Integrated Tracking, Classification, and Sensor Management is an invaluable guide for researchers and practitioners in statistical signal processing, radar systems, operations research, and control theory.