Lectures on Monte Carlo Methods

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Author :
Publisher : American Mathematical Soc.
ISBN 13 : 0821829785
Total Pages : 113 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Lectures on Monte Carlo Methods by : Neal Noah Madras

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.

Monte Carlo Methods

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Author :
Publisher : American Mathematical Soc.
ISBN 13 : 9780821871324
Total Pages : 246 pages
Book Rating : 4.8/5 (713 download)

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Book Synopsis Monte Carlo Methods by : Neal Noah Madras

Download or read book Monte Carlo Methods written by Neal Noah Madras and published by American Mathematical Soc.. This book was released on 2000-01-01 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Workshop on Monte Carlo Methods held at The Fields Institute for Research in Mathematical Sciences (Toronto, 1998). The workshop brought together researchers in physics, statistics, and probability. The papers in this volume - of the invited speakers and contributors to the poster session - represent the interdisciplinary emphasis of the conference. Monte Carlo methods have been used intensively in many branches of scientific inquiry. Markov chain methods have been at the forefront of much of this work, serving as the basis of many numerical studies in statistical physics and related areas since the Metropolis algorithm was introduced in 1953. Statisticians and theoretical computer scientists have used these methods in recent years, working on different fundamental research questions, yet using similar Monte Carlo methodology. This volume focuses on Monte Carlo methods that appear to have wide applicability and emphasizes new methods, practical applications and theoretical analysis. It will be of interest to researchers and graduate students who study and/or use Monte Carlo methods in areas of probability, statistics, theoretical physics, or computer science.

Monte Carlo Methods

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Author :
Publisher : American Mathematical Soc.
ISBN 13 : 0821819925
Total Pages : 238 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Monte Carlo Methods by : Neal Noah Madras

Download or read book Monte Carlo Methods written by Neal Noah Madras and published by American Mathematical Soc.. This book was released on 2000 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Workshop on Monte Carlo Methods held at The Fields Institute for Research in Mathematical Sciences (Toronto, 1998). The workshop brought together researchers in physics, statistics, and probability. The papers in this volume - of the invited speakers and contributors to the poster session - represent the interdisciplinary emphasis of the conference. Monte Carlo methods have been used intensively in many branches of scientific inquiry. Markov chain methods have been at the forefront of much of this work, serving as the basis of many numerical studies in statistical physics and related areas since the Metropolis algorithm was introduced in 1953. Statisticians and theoretical computer scientists have used these methods in recent years, working on different fundamental research questions, yet using similar Monte Carlo methodology. This volume focuses on Monte Carlo methods that appear to have wide applicability and emphasizes new methods, practical applications and theoretical analysis. It will be of interest to researchers and graduate students who study and/or use Monte Carlo methods in areas of probability, statistics, theoretical physics, or computer science.

Sequential Monte Carlo Methods for Nonlinear Discrete-Time Filtering

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Author :
Publisher : Springer Nature
ISBN 13 : 3031025350
Total Pages : 87 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Sequential Monte Carlo Methods for Nonlinear Discrete-Time Filtering by : Marcelo G.

Download or read book Sequential Monte Carlo Methods for Nonlinear Discrete-Time Filtering written by Marcelo G. and published by Springer Nature. This book was released on 2022-06-01 with total page 87 pages. Available in PDF, EPUB and Kindle. Book excerpt: In these notes, we introduce particle filtering as a recursive importance sampling method that approximates the minimum-mean-square-error (MMSE) estimate of a sequence of hidden state vectors in scenarios where the joint probability distribution of the states and the observations is non-Gaussian and, therefore, closed-form analytical expressions for the MMSE estimate are generally unavailable. We begin the notes with a review of Bayesian approaches to static (i.e., time-invariant) parameter estimation. In the sequel, we describe the solution to the problem of sequential state estimation in linear, Gaussian dynamic models, which corresponds to the well-known Kalman (or Kalman-Bucy) filter. Finally, we move to the general nonlinear, non-Gaussian stochastic filtering problem and present particle filtering as a sequential Monte Carlo approach to solve that problem in a statistically optimal way. We review several techniques to improve the performance of particle filters, including importance function optimization, particle resampling, Markov Chain Monte Carlo move steps, auxiliary particle filtering, and regularized particle filtering. We also discuss Rao-Blackwellized particle filtering as a technique that is particularly well-suited for many relevant applications such as fault detection and inertial navigation. Finally, we conclude the notes with a discussion on the emerging topic of distributed particle filtering using multiple processors located at remote nodes in a sensor network. Throughout the notes, we often assume a more general framework than in most introductory textbooks by allowing either the observation model or the hidden state dynamic model to include unknown parameters. In a fully Bayesian fashion, we treat those unknown parameters also as random variables. Using suitable dynamic conjugate priors, that approach can be applied then to perform joint state and parameter estimation. Table of Contents: Introduction / Bayesian Estimation of Static Vectors / The Stochastic Filtering Problem / Sequential Monte Carlo Methods / Sampling/Importance Resampling (SIR) Filter / Importance Function Selection / Markov Chain Monte Carlo Move Step / Rao-Blackwellized Particle Filters / Auxiliary Particle Filter / Regularized Particle Filters / Cooperative Filtering with Multiple Observers / Application Examples / Summary

Handbook of Monte Carlo Methods

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Publisher : John Wiley & Sons
ISBN 13 : 1118014952
Total Pages : 627 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis Handbook of Monte Carlo Methods by : Dirk P. Kroese

Download or read book Handbook of Monte Carlo Methods written by Dirk P. Kroese and published by John Wiley & Sons. This book was released on 2013-06-06 with total page 627 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive overview of Monte Carlo simulation that explores the latest topics, techniques, and real-world applications More and more of today’s numerical problems found in engineering and finance are solved through Monte Carlo methods. The heightened popularity of these methods and their continuing development makes it important for researchers to have a comprehensive understanding of the Monte Carlo approach. Handbook of Monte Carlo Methods provides the theory, algorithms, and applications that helps provide a thorough understanding of the emerging dynamics of this rapidly-growing field. The authors begin with a discussion of fundamentals such as how to generate random numbers on a computer. Subsequent chapters discuss key Monte Carlo topics and methods, including: Random variable and stochastic process generation Markov chain Monte Carlo, featuring key algorithms such as the Metropolis-Hastings method, the Gibbs sampler, and hit-and-run Discrete-event simulation Techniques for the statistical analysis of simulation data including the delta method, steady-state estimation, and kernel density estimation Variance reduction, including importance sampling, latin hypercube sampling, and conditional Monte Carlo Estimation of derivatives and sensitivity analysis Advanced topics including cross-entropy, rare events, kernel density estimation, quasi Monte Carlo, particle systems, and randomized optimization The presented theoretical concepts are illustrated with worked examples that use MATLAB®, a related Web site houses the MATLAB® code, allowing readers to work hands-on with the material and also features the author's own lecture notes on Monte Carlo methods. Detailed appendices provide background material on probability theory, stochastic processes, and mathematical statistics as well as the key optimization concepts and techniques that are relevant to Monte Carlo simulation. Handbook of Monte Carlo Methods is an excellent reference for applied statisticians and practitioners working in the fields of engineering and finance who use or would like to learn how to use Monte Carlo in their research. It is also a suitable supplement for courses on Monte Carlo methods and computational statistics at the upper-undergraduate and graduate levels.

Advanced Lectures on Machine Learning

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Publisher : Springer
ISBN 13 : 3540286500
Total Pages : 246 pages
Book Rating : 4.5/5 (42 download)

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Book Synopsis Advanced Lectures on Machine Learning by : Olivier Bousquet

Download or read book Advanced Lectures on Machine Learning written by Olivier Bousquet and published by Springer. This book was released on 2011-03-22 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: Machine Learning has become a key enabling technology for many engineering applications, investigating scientific questions and theoretical problems alike. To stimulate discussions and to disseminate new results, a summer school series was started in February 2002, the documentation of which is published as LNAI 2600. This book presents revised lectures of two subsequent summer schools held in 2003 in Canberra, Australia, and in Tübingen, Germany. The tutorial lectures included are devoted to statistical learning theory, unsupervised learning, Bayesian inference, and applications in pattern recognition; they provide in-depth overviews of exciting new developments and contain a large number of references. Graduate students, lecturers, researchers and professionals alike will find this book a useful resource in learning and teaching machine learning.

Monte Carlo Methods in Ab Initio Quantum Chemistry

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Publisher : World Scientific
ISBN 13 : 9814506753
Total Pages : 320 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Monte Carlo Methods in Ab Initio Quantum Chemistry by : B L Hammond

Download or read book Monte Carlo Methods in Ab Initio Quantum Chemistry written by B L Hammond and published by World Scientific. This book was released on 1994-03-29 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the basic theory and application of the Monte Carlo method to the electronic structure of atoms and molecules. It assumes no previous knowledge of the subject, only a knowledge of molecular quantum mechanics at the first-year graduate level. A working knowledge of traditional ab initio quantum chemistry is helpful, but not essential. Some distinguishing features of this book are: Clear exposition of the basic theory at a level to facilitate independent study.Discussion of the various versions of the theory: diffusion Monte Carlo, Green's function Monte Carlo, and release node Monte Carlo.Commentary on the important features that distinguish this stochastic approach from ab initio methods. Contents:Introduction to Monte Carlo MethodsVariational MethodsGreen's Function MethodsTreating FermionsVariational Trial FunctionsExcited StatesElectronic PropertiesDerivatives and Finite DifferencesHeavy AtomsAtomic UnitsEvaluating the Trial FunctionSample Diffusion Monte Carlo Program Readership: Chemists and physicists.

Monte Carlo Simulation in Statistical Physics

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Publisher : Springer Science & Business Media
ISBN 13 : 366230273X
Total Pages : 132 pages
Book Rating : 4.6/5 (623 download)

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Book Synopsis Monte Carlo Simulation in Statistical Physics by : Kurt Binder

Download or read book Monte Carlo Simulation in Statistical Physics written by Kurt Binder and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: When learning very formal material one comes to a stage where one thinks one has understood the material. Confronted with a "realiife" problem, the passivity of this understanding sometimes becomes painfully elear. To be able to solve the problem, ideas, methods, etc. need to be ready at hand. They must be mastered (become active knowledge) in order to employ them successfully. Starting from this idea, the leitmotif, or aim, of this book has been to elose this gap as much as possible. How can this be done? The material presented here was born out of a series of lectures at the Summer School held at Figueira da Foz (Portugal) in 1987. The series of lectures was split into two concurrent parts. In one part the "formal material" was presented. Since the background of those attending varied widely, the presentation of the formal material was kept as pedagogic as possible. In the formal part the general ideas behind the Monte Carlo method were developed. The Monte Carlo method has now found widespread appli cation in many branches of science such as physics, chemistry, and biology. Because of this, the scope of the lectures had to be narrowed down. We could not give a complete account and restricted the treatment to the ap plication of the Monte Carlo method to the physics of phase transitions. Here particular emphasis is placed on finite-size effects.

Quantum Monte Carlo Methods in Physics and Chemistry

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Publisher : Springer Science & Business Media
ISBN 13 : 9780792355519
Total Pages : 488 pages
Book Rating : 4.3/5 (555 download)

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Book Synopsis Quantum Monte Carlo Methods in Physics and Chemistry by : M.P. Nightingale

Download or read book Quantum Monte Carlo Methods in Physics and Chemistry written by M.P. Nightingale and published by Springer Science & Business Media. This book was released on 1998-12-31 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years there has been a considerable growth in interest in Monte Carlo methods, and quantum Monte Carlo methods in particlular. Clearly, the ever-increasing computational power available to researchers, has stimulated the development of improved algorithms, and almost all fields in computational physics and chemistry are affected by their applications. Here we just mention some fields that are covered in the lecture notes contained in this volume, viz. electronic structure studies of atoms, molecules and solids, nuclear structure, and low- or zero-temperature studies of strongly-correlated quantum systems, both of the continuum and lattice variety, and cooperative phenomena in classical systems. Although each area of application may have its own peculiarities, requiring specialized solutions, all share the same basic methodology. It was with the intention of bringing together researchers and students from these various areas that the NATO Advanced Study Institute on Quantum Monte Carlo Methods in Physics and Chemistry was held at Cornell University from 12 to 24 July, 1998. This book contains material presented at the Institute in a series of mini courses in quantum Monte Carlo methods. The program consisted of lectures predominantly of a pedagogical nature, and of more specialized seminars. The levels varied from introductory to advanced, and from basic methods to applications; the program was intended for an audience working towards the Ph.D. level and above. Despite the essentially pedagogic nature of the Institute, several of the lectures and seminars contained in this volume present recent developments not previously published.

The Monte Carlo Method

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Publisher :
ISBN 13 : 9780226767499
Total Pages : 63 pages
Book Rating : 4.7/5 (674 download)

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Book Synopsis The Monte Carlo Method by : Ilʹi͡a Meerovich Sobolʹ

Download or read book The Monte Carlo Method written by Ilʹi͡a Meerovich Sobolʹ and published by . This book was released on 1974 with total page 63 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Simulation and the Monte Carlo Method

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Publisher : John Wiley & Sons
ISBN 13 : 1118632389
Total Pages : 432 pages
Book Rating : 4.1/5 (186 download)

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Book Synopsis Simulation and the Monte Carlo Method by : Reuven Y. Rubinstein

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 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.

Monte Carlo Methods

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Publisher : Springer Nature
ISBN 13 : 9811329710
Total Pages : 433 pages
Book Rating : 4.8/5 (113 download)

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Book Synopsis Monte Carlo Methods by : Adrian Barbu

Download or read book Monte Carlo Methods written by Adrian Barbu and published by Springer Nature. This book was released on 2020-02-24 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book seeks to bridge the gap between statistics and computer science. It provides an overview of Monte Carlo methods, including Sequential Monte Carlo, Markov Chain Monte Carlo, Metropolis-Hastings, Gibbs Sampler, Cluster Sampling, Data Driven MCMC, Stochastic Gradient descent, Langevin Monte Carlo, Hamiltonian Monte Carlo, and energy landscape mapping. Due to its comprehensive nature, the book is suitable for developing and teaching graduate courses on Monte Carlo methods. To facilitate learning, each chapter includes several representative application examples from various fields. The book pursues two main goals: (1) It introduces researchers to applying Monte Carlo methods to broader problems in areas such as Computer Vision, Computer Graphics, Machine Learning, Robotics, Artificial Intelligence, etc.; and (2) it makes it easier for scientists and engineers working in these areas to employ Monte Carlo methods to enhance their research.

Sequential Monte Carlo Methods in Practice

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Publisher : Springer Science & Business Media
ISBN 13 : 1475734379
Total Pages : 590 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Sequential Monte Carlo Methods in Practice by : Arnaud Doucet

Download or read book Sequential Monte Carlo Methods in Practice written by Arnaud Doucet and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: Monte Carlo methods are revolutionizing the on-line analysis of data in many fileds. They have made it possible to solve numerically many complex, non-standard problems that were previously intractable. This book presents the first comprehensive treatment of these techniques.

Functional Integration

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Publisher : Springer Science & Business Media
ISBN 13 : 1489903194
Total Pages : 436 pages
Book Rating : 4.4/5 (899 download)

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Book Synopsis Functional Integration by : Cécile Dewitt-Morette

Download or read book Functional Integration written by Cécile Dewitt-Morette and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: The program of the Institute covered several aspects of functional integration -from a robust mathematical foundation to many applications, heuristic and rigorous, in mathematics, physics, and chemistry. It included analytic and numerical computational techniques. One of the goals was to encourage cross-fertilization between these various aspects and disciplines. The first week was focused on quantum and classical systems with a finite number of degrees of freedom; the second week on field theories. During the first week the basic course, given by P. Cartier, was a presentation of a recent rigorous approach to functional integration which does not resort to discretization, nor to analytic continuation. It provides a definition of functional integrals simpler and more powerful than the original ones. Could this approach accommodate the works presented by the other lecturers? Although much remains to be done before answering "Yes," there seems to be no major obstacle along the road. The other courses taught during the first week presented: a) a solid introduction to functional numerical techniques (A. Sokal) and their applications to functional integrals encountered in chemistry (N. Makri). b) integrals based on Poisson processes and their applications to wave propagation (S. K. Foong), in particular a wave-restorer or wave-designer algorithm yielding the initial wave profile when one can only observe its distortion through a dissipative medium. c) the formulation of a quantum equivalence principle (H. Kleinert) which. given the flat space theory, yields a well-defined quantum theory in spaces with curvature and torsion.

Markov Chain Monte Carlo

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Publisher : World Scientific
ISBN 13 : 9812564276
Total Pages : 239 pages
Book Rating : 4.8/5 (125 download)

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Book Synopsis Markov Chain Monte Carlo by : W. S. Kendall

Download or read book Markov Chain Monte Carlo written by W. S. Kendall and published by World Scientific. This book was released on 2005 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: Markov Chain Monte Carlo (MCMC) originated in statistical physics, but has spilled over into various application areas, leading to a corresponding variety of techniques and methods. That variety stimulates new ideas and developments from many different places, and there is much to be gained from cross-fertilization. This book presents five expository essays by leaders in the field, drawing from perspectives in physics, statistics and genetics, and showing how different aspects of MCMC come to the fore in different contexts. The essays derive from tutorial lectures at an interdisciplinary program at the Institute for Mathematical Sciences, Singapore, which exploited the exciting ways in which MCMC spreads across different disciplines.

Monte Carlo and Quasi-Monte Carlo Methods

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Publisher : Springer
ISBN 13 : 3319914367
Total Pages : 479 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Monte Carlo and Quasi-Monte Carlo Methods by : Art B. Owen

Download or read book Monte Carlo and Quasi-Monte Carlo Methods written by Art B. Owen and published by Springer. This book was released on 2018-07-03 with total page 479 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the refereed proceedings of the Twelfth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing that was held at Stanford University (California) in August 2016. These biennial conferences are major events for Monte Carlo and quasi-Monte Carlo researchers. The proceedings include articles based on invited lectures as well as carefully selected contributed papers on all theoretical aspects and applications of Monte Carlo and quasi-Monte Carlo methods. Offering information on the latest developments in these very active areas, this book is an excellent reference resource for theoreticians and practitioners interested in solving high-dimensional computational problems, arising in particular, in finance, statistics, computer graphics and the solution of PDEs.

Monte Carlo Methods

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Publisher :
ISBN 13 :
Total Pages : 194 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Monte Carlo Methods by : John Michael Hammersley

Download or read book Monte Carlo Methods written by John Michael Hammersley and published by . This book was released on 1965 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: