# Exploring Monte Carlo Methods

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## Exploring Monte Carlo Methods

Author : William L. Dunn,J. Kenneth Shultis
Publisher : Elsevier
Release : 2011-05-24
ISBN : 9780080930619
Language : En, Es, Fr & De

Book Description :

Exploring Monte Carlo Methods is a basic text that describes the numerical methods that have come to be known as "Monte Carlo." The book treats the subject generically through the first eight chapters and, thus, should be of use to anyone who wants to learn to use Monte Carlo. The next two chapters focus on applications in nuclear engineering, which are illustrative of uses in other fields. Five appendices are included, which provide useful information on probability distributions, general-purpose Monte Carlo codes for radiation transport, and other matters. The famous "Buffon’s needle problem" provides a unifying theme as it is repeatedly used to illustrate many features of Monte Carlo methods. This book provides the basic detail necessary to learn how to apply Monte Carlo methods and thus should be useful as a text book for undergraduate or graduate courses in numerical methods. It is written so that interested readers with only an understanding of calculus and differential equations can learn Monte Carlo on their own. Coverage of topics such as variance reduction, pseudo-random number generation, Markov chain Monte Carlo, inverse Monte Carlo, and linear operator equations will make the book useful even to experienced Monte Carlo practitioners. Provides a concise treatment of generic Monte Carlo methods Proofs for each chapter Appendixes include Certain mathematical functions; Bose Einstein functions, Fermi Dirac functions, Watson functions

## Exploring Monte Carlo Methods

Author : William L. Dunn,J. Kenneth Shultis
Publisher : Elsevier
Release : 2022-07-25
ISBN : 0128197455
Language : En, Es, Fr & De

Book Description :

Exploring Monte Carlo Methods, Second Edition provides a valuable introduction to the numerical methods that have come to be known as "Monte Carlo." This unique and trusted resource for course use, as well as researcher reference, offers accessible coverage, clear explanations and helpful examples throughout. Building from the basics, the text also includes applications in a variety of fields, such as physics, nuclear engineering, finance and investment, medical modeling and prediction, archaeology, geology and transportation planning. Provides a comprehensive yet concise treatment of Monte Carlo methods Uses the famous "Buffon’s needle problem" as a unifying theme to illustrate the many aspects of Monte Carlo methods Includes numerous exercises and useful appendices on: Certain mathematical functions, Bose Einstein functions, Fermi Dirac functions and Watson functions

## Handbook of Monte Carlo Methods

Author : Dirk P. Kroese,Thomas Taimre,Zdravko I. Botev
Publisher : John Wiley & Sons
Release : 2013-06-06
ISBN : 9781118014950
Language : En, Es, Fr & De

Book Description :

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.

## Explorations in Monte Carlo Methods

Author : Ronald W. Shonkwiler,Franklin Mendivil
Publisher : Springer Science & Business Media
Release : 2009-08-11
ISBN : 0387878378
Language : En, Es, Fr & De

Book Description :

Monte Carlo methods are among the most used and useful computational tools available today, providing efficient and practical algorithims to solve a wide range of scientific and engineering problems. Applications covered in this book include optimization, finance, statistical mechanics, birth and death processes, and gambling systems. Explorations in Monte Carlo Methods provides a hands-on approach to learning this subject. Each new idea is carefully motivated by a realistic problem, thus leading from questions to theory via examples and numerical simulations. Programming exercises are integrated throughout the text as the primary vehicle for learning the material. Each chapter ends with a large collection of problems illustrating and directing the material. This book is suitable as a textbook for students of engineering and the sciences, as well as mathematics.

## Forecasting in Mathematics

Author : Abdo Abou Jaoude
Publisher : BoD – Books on Demand
Release : 2021-01-27
ISBN : 1838808256
Language : En, Es, Fr & De

Book Description :

Mathematical probability and statistics are an attractive, thriving, and respectable part of mathematics. Some mathematicians and philosophers of science say they are the gateway to mathematics’ deepest mysteries. Moreover, mathematical statistics denotes an accumulation of mathematical discussions connected with efforts to most efficiently collect and use numerical data subject to random or deterministic variations. Currently, the concept of probability and mathematical statistics has become one of the fundamental notions of modern science and the philosophy of nature. This book is an illustration of the use of mathematics to solve specific problems in engineering, statistics, and science in general.

## Reinforcement Learning second edition

Author : Richard S. Sutton,Andrew G. Barto
Publisher : MIT Press
Release : 2018-11-13
ISBN : 0262352702
Language : En, Es, Fr & De

Book Description :

The significantly expanded and updated new edition of a widely used text on reinforcement learning, one of the most active research areas in artificial intelligence. Reinforcement learning, one of the most active research areas in artificial intelligence, is a computational approach to learning whereby an agent tries to maximize the total amount of reward it receives while interacting with a complex, uncertain environment. In Reinforcement Learning, Richard Sutton and Andrew Barto provide a clear and simple account of the field's key ideas and algorithms. This second edition has been significantly expanded and updated, presenting new topics and updating coverage of other topics. Like the first edition, this second edition focuses on core online learning algorithms, with the more mathematical material set off in shaded boxes. Part I covers as much of reinforcement learning as possible without going beyond the tabular case for which exact solutions can be found. Many algorithms presented in this part are new to the second edition, including UCB, Expected Sarsa, and Double Learning. Part II extends these ideas to function approximation, with new sections on such topics as artificial neural networks and the Fourier basis, and offers expanded treatment of off-policy learning and policy-gradient methods. Part III has new chapters on reinforcement learning's relationships to psychology and neuroscience, as well as an updated case-studies chapter including AlphaGo and AlphaGo Zero, Atari game playing, and IBM Watson's wagering strategy. The final chapter discusses the future societal impacts of reinforcement learning.

## Monte Carlo Methods for Particle Transport

Author : Alireza Haghighat
Publisher : CRC Press
Release : 2020-08-09
ISBN : 0429584105
Language : En, Es, Fr & De

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

## Introducing Monte Carlo Methods with R

Author : Christian Robert,George Casella
Publisher : Springer Science & Business Media
Release : 2010
ISBN : 1441915753
Language : En, Es, Fr & De

Book Description :

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.

## Theory Application and Implementation of Monte Carlo Method in Science and Technology

Author : Pooneh Saidi Bidokhti
Publisher : BoD – Books on Demand
Release : 2019-12-18
ISBN : 1789855454
Language : En, Es, Fr & De

Book Description :

The Monte Carlo method is a numerical technique to model the probability of all possible outcomes in a process that cannot easily be predicted due to the interference of random variables. It is a technique used to understand the impact of risk, uncertainty, and ambiguity in forecasting models. However, this technique is complicated by the amount of computer time required to achieve sufficient precision in the simulations and evaluate their accuracy. This book discusses the general principles of the Monte Carlo method with an emphasis on techniques to decrease simulation time and increase accuracy.

## Intelligent IoT Systems in Personalized Health Care

Author : Arun Kumar Sangaiah,Subhas Chandra Mukhopadhyay
Release : 2020-12-01
ISBN : 0128232048
Language : En, Es, Fr & De

Book Description :

Intelligent IoT Systems in Personalized Health Care delivers a significant forum for the technical advancement of IoMT learning in parallel computing environments across biomedical engineering diversified domains and its applications. Pursuing an interdisciplinary approach, the book focuses on methods used to identify and acquire valid, potentially useful knowledge sources. The book presents novel, in-depth, fundamental research contributions from a methodological/application perspective to help readers understand the fusion of AI with IoT and its capabilities in solving a diverse range of problems for biomedical engineering and its real-world personalized health care applications. The book is well suited for researchers exploring the significance of IoT based architecture to perform predictive analytics of user activities in sustainable health. Presents novel, in-depth, fundamental research contributions from a methodological/application perspective to help readers understand the fusion of AI with IoT Illustrates state-of-the-art developments in new theories and applications of IoMT techniques as applied to parallel computing environments in biomedical engineering systems Presents concepts and technologies successfully used in the implementation of today's intelligent data-centric IoT systems and Edge-Cloud-Big data

## Monte Carlo Simulation and Resampling Methods for Social Science

Author : Thomas M. Carsey,Jeffrey J. Harden
Publisher : SAGE Publications
Release : 2013-08-05
ISBN : 1483324923
Language : En, Es, Fr & De

Book Description :

Taking the topics of a quantitative methodology course and illustrating them through Monte Carlo simulation, Monte Carlo Simulation and Resampling Methods for Social Science, by Thomas M. Carsey and Jeffrey J. Harden, examines abstract principles, such as bias, efficiency, and measures of uncertainty in an intuitive, visual way. Instead of thinking in the abstract about what would happen to a particular estimator "in repeated samples," the book uses simulation to actually create those repeated samples and summarize the results. The book includes basic examples appropriate for readers learning the material for the first time, as well as more advanced examples that a researcher might use to evaluate an estimator he or she was using in an actual research project. The book also covers a wide range of topics related to Monte Carlo simulation, such as resampling methods, simulations of substantive theory, simulation of quantities of interest (QI) from model results, and cross-validation. Complete R code from all examples is provided so readers can replicate every analysis presented using R.

## Monte Carlo Methods

Author : Malvin H. Kalos,Paula A. Whitlock
Publisher : John Wiley & Sons
Release : 2008-09-26
ISBN : 352761740X
Language : En, Es, Fr & De

Book Description :

This introduction to Monte Carlo Methods seeks to identify and study the unifying elements that underlie their effective application. It focuses on two basic themes. The first is the importance of random walks as they occur both in natural stochastic systems and in their relationship to integral and differential equations. The second theme is that of variance reduction in general and importance sampling in particular as a technique for efficient use of the methods. Random walks are introduced with an elementary example in which the modelling of radiation transport arises directly from a schematic probabilistic description of the interaction of radiation with matter. Building on that example, the relationship between random walks and integral equations is outlined. The applicability of these ideas to other problems is shown by a clear and elementary introduction to the solution of the Schrodinger equation by random walks. The detailed discussion of variance reduction includes Monte Carlo evaluation of finite-dimensional integrals. Special attention is given to importance sampling, partly because of its intrinsic interest in quadrature, partly because of its general usefulness in the solution of integral equations. One significant feature is that Monte Carlo Methods treats the "Metropolis algorithm" in the context of sampling methods, clearly distinguishing it from importance sampling. Physicists, chemists, statisticians, mathematicians, and computer scientists will find Monte Carlo Methods a complete and stimulating introduction.

## Hands On Simulation Modeling with Python

Author : Giuseppe Ciaburro
Publisher : Packt Publishing Ltd
Release : 2020-07-17
ISBN : 1838988653
Language : En, Es, Fr & De

Book Description :

Enhance your simulation modeling skills by creating and analyzing digital prototypes of a physical model using Python programming with this comprehensive guide Key FeaturesLearn to create a digital prototype of a real model using hands-on examplesEvaluate the performance and output of your prototype using simulation modeling techniquesUnderstand various statistical and physical simulations to improve systems using PythonBook Description Simulation modeling helps you to create digital prototypes of physical models to analyze how they work and predict their performance in the real world. With this comprehensive guide, you'll understand various computational statistical simulations using Python. Starting with the fundamentals of simulation modeling, you'll understand concepts such as randomness and explore data generating processes, resampling methods, and bootstrapping techniques. You'll then cover key algorithms such as Monte Carlo simulations and Markov decision processes, which are used to develop numerical simulation models, and discover how they can be used to solve real-world problems. As you advance, you'll develop simulation models to help you get accurate results and enhance decision-making processes. Using optimization techniques, you'll learn to modify the performance of a model to improve results and make optimal use of resources. The book will guide you in creating a digital prototype using practical use cases for financial engineering, prototyping project management to improve planning, and simulating physical phenomena using neural networks. By the end of this book, you'll have learned how to construct and deploy simulation models of your own to overcome real-world challenges. What you will learnGain an overview of the different types of simulation modelsGet to grips with the concepts of randomness and data generation processUnderstand how to work with discrete and continuous distributionsWork with Monte Carlo simulations to calculate a definite integralFind out how to simulate random walks using Markov chainsObtain robust estimates of confidence intervals and standard errors of population parametersDiscover how to use optimization methods in real-life applicationsRun efficient simulations to analyze real-world systemsWho this book is for Hands-On Simulation Modeling with Python is for simulation developers and engineers, model designers, and anyone already familiar with the basic computational methods that are used to study the behavior of systems. This book will help you explore advanced simulation techniques such as Monte Carlo methods, statistical simulations, and much more using Python. Working knowledge of Python programming language is required.

## Computational Statistics in Data Science

Author : Richard A. Levine,Walter W. Piegorsch,Hao Helen Zhang,Thomas C. M. Lee
Publisher : John Wiley & Sons
Release : 2022-03-23
ISBN : 1119561086
Language : En, Es, Fr & De

Book Description :

Ein unverzichtbarer Leitfaden bei der Anwendung computergestützter Statistik in der modernen Datenwissenschaft In Computational Statistics in Data Science präsentiert ein Team aus bekannten Mathematikern und Statistikern eine fundierte Zusammenstellung von Konzepten, Theorien, Techniken und Praktiken der computergestützten Statistik für ein Publikum, das auf der Suche nach einem einzigen, umfassenden Referenzwerk für Statistik in der modernen Datenwissenschaft ist. Das Buch enthält etliche Kapitel zu den wesentlichen konkreten Bereichen der computergestützten Statistik, in denen modernste Techniken zeitgemäß und verständlich dargestellt werden. Darüber hinaus bietet Computational Statistics in Data Science einen kostenlosen Zugang zu den fertigen Einträgen im Online-Nachschlagewerk Wiley StatsRef: Statistics Reference Online. Außerdem erhalten die Leserinnen und Leser: * Eine gründliche Einführung in die computergestützte Statistik mit relevanten und verständlichen Informationen für Anwender und Forscher in verschiedenen datenintensiven Bereichen * Umfassende Erläuterungen zu aktuellen Themen in der Statistik, darunter Big Data, Datenstromverarbeitung, quantitative Visualisierung und Deep Learning Das Werk eignet sich perfekt für Forscher und Wissenschaftler sämtlicher Fachbereiche, die Techniken der computergestützten Statistik auf einem gehobenen oder fortgeschrittenen Niveau anwenden müssen. Zudem gehört Computational Statistics in Data Science in das Bücherregal von Wissenschaftlern, die sich mit der Erforschung und Entwicklung von Techniken der computergestützten Statistik und statistischen Grafiken beschäftigen.

## Illustrating Statistical Procedures Finding Meaning in Quantitative Data

Author : Ray W. Cooksey
Publisher : Springer Nature
Release : 2020-05-14
ISBN : 9811525374
Language : En, Es, Fr & De

Book Description :

This book occupies a unique position in the field of statistical analysis in the behavioural and social sciences in that it targets learners who would benefit from learning more conceptually and less computationally about statistical procedures and the software packages that can be used to implement them. This book provides a comprehensive overview of this important research skill domain with an emphasis on visual support for learning and better understanding. The primary focus is on fundamental concepts, procedures and interpretations of statistical analyses within a single broad illustrative research context. The book covers a wide range of descriptive, correlational and inferential statistical procedures as well as more advanced procedures not typically covered in introductory and intermediate statistical texts. It is an ideal reference for postgraduate students as well as for researchers seeking to broaden their conceptual exposure to what is possible in statistical analysis.

## Nuclear Engineering

Author : Zafar Ullah Koreshi
Release : 2022-03-23
ISBN : 0323908314
Language : En, Es, Fr & De

Book Description :

Nuclear Engineering Mathematical Modeling and Simulation presents the mathematical modeling of neutron diffusion and transport. Aimed at students and early career engineers, this highly practical and visual resource guides the reader through computer simulations using the Monte Carlo Method which can be applied to a variety of applications, including power generation, criticality assemblies, nuclear detection systems, and nuclear medicine to name a few. The book covers optimization in both the traditional deterministic framework of variational methods and the stochastic framework of Monte Carlo methods. Specific sections cover the fundamentals of nuclear physics, computer codes used for neutron and photon radiation transport simulations, applications of analyses and simulations, optimization techniques for both fixed-source and multiplying systems, and various simulations in the medical area where radioisotopes are used in cancer treatment. Provides a highly visual and practical reference that includes mathematical modeling, formulations, models and methods throughout Includes all current major computer codes, such as ANISN, MCNP and MATLAB for user coding and analysis Guides the reader through simulations for the design optimization of both present-day and future nuclear systems

## Monte Carlo Simulation and Finance

Author : Don L. McLeish
Publisher : John Wiley & Sons
Release : 2011-09-13
ISBN : 1118160940
Language : En, Es, Fr & De

Book Description :

Monte Carlo methods have been used for decades in physics, engineering, statistics, and other fields. Monte Carlo Simulation and Finance explains the nuts and bolts of this essential technique used to value derivatives and other securities. Author and educator Don McLeish examines this fundamental process, and discusses important issues, including specialized problems in finance that Monte Carlo and Quasi-Monte Carlo methods can help solve and the different ways Monte Carlo methods can be improved upon. This state-of-the-art book on Monte Carlo simulation methods is ideal for finance professionals and students. Order your copy today.

## Forensic Metrology

Author : Ted Vosk,Ashley F. Emery
Publisher : CRC Press
Release : 2014-09-26
ISBN : 143982620X
Language : En, Es, Fr & De

Book Description :

Forensic metrology is the application of scientific measurement to the investigation and prosecution of crime. Forensic measurements are relied upon to determine breath and blood alcohol and drug concentrations, weigh seized drugs, perform accident reconstruction, and for many other applications. Forensic metrology provides a basic framework for th

Author : Victor Sapritsky,Alexander Prokhorov
Publisher : Springer Nature
Release : 2020-10-19
ISBN : 3030577899
Language : En, Es, Fr & De

Book Description :

This book, the first of a two-volume set, focuses on the basic physical principles of blackbody radiometry and describes artificial sources of blackbody radiation, widely used as sources of optical radiation, whose energy characteristics can be calculated on the base of fundamental physical laws. Following a review of radiometric quantities, radiation laws, and radiative heat transfer, it introduces the basic principles of blackbody radiators design, details of their practical implementation, and methods of measuring their defining characteristics, as well as metrological aspects of blackbody-based measurements. Chapters are dedicated to the effective emissivity concept, methods of increasing effective emissivities, their measurement and modeling using the Monte Carlo method, techniques of blackbody radiators heating, cooling, isothermalization, and measuring their temperature. An extensive and comprehensive reference source, this book is of considerable value to students, researchers, and engineers involved in any aspect of blackbody radiometry.

## Physics and Finance

Author : Volker Ziemann
Publisher : Springer Nature
Release : 2021-01-18
ISBN : 3030636437
Language : En, Es, Fr & De

Book Description :

This book introduces physics students to concepts and methods of finance. Despite being perceived as quite distant from physics, finance shares a number of common methods and ideas, usually related to noise and uncertainties. Juxtaposing the key methods to applications in both physics and finance articulates both differences and common features, this gives students a deeper understanding of the underlying ideas. Moreover, they acquire a number of useful mathematical and computational tools, such as stochastic differential equations, path integrals, Monte-Carlo methods, and basic cryptology. Each chapter ends with a set of carefully designed exercises enabling readers to test their comprehension.