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| introducing monte carlo methods with r: Introducing Monte Carlo Methods with R Christian Robert, George Casella, 2010 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. |
| introducing monte carlo methods with r: Monte Carlo Statistical Methods Christian Robert, George Casella, 2013-03-14 Monte Carlo statistical methods, particularly those based on Markov chains, are now an essential component of the standard set of techniques used by statisticians. This new edition has been revised towards a coherent and flowing coverage of these simulation techniques, with incorporation of the most recent developments in the field. In particular, the introductory coverage of random variable generation has been totally revised, with many concepts being unified through a fundamental theorem of simulation There are five completely new chapters that cover Monte Carlo control, reversible jump, slice sampling, sequential Monte Carlo, and perfect sampling. There is a more in-depth coverage of Gibbs sampling, which is now contained in three consecutive chapters. The development of Gibbs sampling starts with slice sampling and its connection with the fundamental theorem of simulation, and builds up to two-stage Gibbs sampling and its theoretical properties. A third chapter covers the multi-stage Gibbs sampler and its variety of applications. Lastly, chapters from the previous edition have been revised towards easier access, with the examples getting more detailed coverage. This textbook is intended for a second year graduate course, but will also be useful to someone who either wants to apply simulation techniques for the resolution of practical problems or wishes to grasp the fundamental principles behind those methods. The authors do not assume familiarity with Monte Carlo techniques (such as random variable generation), with computer programming, or with any Markov chain theory (the necessary concepts are developed in Chapter 6). A solutions manual, which covers approximately 40% of the problems, is available for instructors who require the book for a course. Christian P. Robert is Professor of Statistics in the Applied Mathematics Department at Université Paris Dauphine, France. He is also Head of the Statistics Laboratoryat the Center for Research in Economics and Statistics (CREST) of the National Institute for Statistics and Economic Studies (INSEE) in Paris, and Adjunct Professor at Ecole Polytechnique. He has written three other books and won the 2004 DeGroot Prize for The Bayesian Choice, Second Edition, Springer 2001. He also edited Discretization and MCMC Convergence Assessment, Springer 1998. He has served as associate editor for the Annals of Statistics, Statistical Science and the Journal of the American Statistical Association. He is a fellow of the Institute of Mathematical Statistics, and a winner of the Young Statistician Award of the Société de Statistique de Paris in 1995. George Casella is Distinguished Professor and Chair, Department of Statistics, University of Florida. He has served as the Theory and Methods Editor of the Journal of the American Statistical Association and Executive Editor of Statistical Science. He has authored three other textbooks: Statistical Inference, Second Edition, 2001, with Roger L. Berger; Theory of Point Estimation, 1998, with Erich Lehmann; and Variance Components, 1992, with Shayle R. Searle and Charles E. McCulloch. He is a fellow of the Institute of Mathematical Statistics and the American Statistical Association, and an elected fellow of the International Statistical Institute. |
| introducing monte carlo methods with r: Handbook of Markov Chain Monte Carlo Steve Brooks, Andrew Gelman, Galin Jones, Xiao-Li Meng, 2011-05-10 Since their popularization in the 1990s, Markov chain Monte Carlo (MCMC) methods have revolutionized statistical computing and have had an especially profound impact on the practice of Bayesian statistics. Furthermore, MCMC methods have enabled the development and use of intricate models in an astonishing array of disciplines as diverse as fisherie |
| introducing monte carlo methods with r: Simulation and the Monte Carlo Method Reuven Y. Rubinstein, Dirk P. Kroese, 2016-10-21 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. |
| introducing monte carlo methods with r: Bayesian Computation with R Jim Albert, 2009-04-20 There has been dramatic growth in the development and application of Bayesian inference in statistics. Berger (2000) documents the increase in Bayesian activity by the number of published research articles, the number of books,andtheextensivenumberofapplicationsofBayesianarticlesinapplied disciplines such as science and engineering. One reason for the dramatic growth in Bayesian modeling is the availab- ity of computational algorithms to compute the range of integrals that are necessary in a Bayesian posterior analysis. Due to the speed of modern c- puters, it is now possible to use the Bayesian paradigm to ?t very complex models that cannot be ?t by alternative frequentist methods. To ?t Bayesian models, one needs a statistical computing environment. This environment should be such that one can: write short scripts to de?ne a Bayesian model use or write functions to summarize a posterior distribution use functions to simulate from the posterior distribution construct graphs to illustrate the posterior inference An environment that meets these requirements is the R system. R provides a wide range of functions for data manipulation, calculation, and graphical d- plays. Moreover, it includes a well-developed, simple programming language that users can extend by adding new functions. Many such extensions of the language in the form of packages are easily downloadable from the Comp- hensive R Archive Network (CRAN). |
| introducing monte carlo methods with r: Introduction to Probability Simulation and Gibbs Sampling with R Eric A. Suess, Bruce E. Trumbo, 2010-06-15 The first seven chapters use R for probability simulation and computation, including random number generation, numerical and Monte Carlo integration, and finding limiting distributions of Markov Chains with both discrete and continuous states. Applications include coverage probabilities of binomial confidence intervals, estimation of disease prevalence from screening tests, parallel redundancy for improved reliability of systems, and various kinds of genetic modeling. These initial chapters can be used for a non-Bayesian course in the simulation of applied probability models and Markov Chains. Chapters 8 through 10 give a brief introduction to Bayesian estimation and illustrate the use of Gibbs samplers to find posterior distributions and interval estimates, including some examples in which traditional methods do not give satisfactory results. WinBUGS software is introduced with a detailed explanation of its interface and examples of its use for Gibbs sampling for Bayesian estimation. No previous experience using R is required. An appendix introduces R, and complete R code is included for almost all computational examples and problems (along with comments and explanations). Noteworthy features of the book are its intuitive approach, presenting ideas with examples from biostatistics, reliability, and other fields; its large number of figures; and its extraordinarily large number of problems (about a third of the pages), ranging from simple drill to presentation of additional topics. Hints and answers are provided for many of the problems. These features make the book ideal for students of statistics at the senior undergraduate and at the beginning graduate levels. |
| introducing monte carlo methods with r: Statistical Computing with R Maria L. Rizzo, 2007-11-15 Computational statistics and statistical computing are two areas that employ computational, graphical, and numerical approaches to solve statistical problems, making the versatile R language an ideal computing environment for these fields. One of the first books on these topics to feature R, Statistical Computing with R covers the traditiona |
| introducing monte carlo methods with r: Markov Chain Monte Carlo Dani Gamerman, 1997-10-01 Bridging the gap between research and application, Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference provides a concise, and integrated account of Markov chain Monte Carlo (MCMC) for performing Bayesian inference. This volume, which was developed from a short course taught by the author at a meeting of Brazilian statisticians and probabilists, retains the didactic character of the original course text. The self-contained text units make MCMC accessible to scientists in other disciplines as well as statisticians. It describes each component of the theory in detail and outlines related software, which is of particular benefit to applied scientists. |
| introducing monte carlo methods with r: Bayesian Essentials with R Jean-Michel Marin, Christian P. Robert, 2013-10-28 This Bayesian modeling book provides a self-contained entry to computational Bayesian statistics. Focusing on the most standard statistical models and backed up by real datasets and an all-inclusive R (CRAN) package called bayess, the book provides an operational methodology for conducting Bayesian inference, rather than focusing on its theoretical and philosophical justifications. Readers are empowered to participate in the real-life data analysis situations depicted here from the beginning. Special attention is paid to the derivation of prior distributions in each case and specific reference solutions are given for each of the models. Similarly, computational details are worked out to lead the reader towards an effective programming of the methods given in the book. In particular, all R codes are discussed with enough detail to make them readily understandable and expandable. Bayesian Essentials with R can be used as a textbook at both undergraduate and graduate levels. It is particularly useful with students in professional degree programs and scientists to analyze data the Bayesian way. The text will also enhance introductory courses on Bayesian statistics. Prerequisites for the book are an undergraduate background in probability and statistics, if not in Bayesian statistics. |
| introducing monte carlo methods with r: Principles and Practice of Clinical Trials Steven Piantadosi, Curtis L. Meinert, 2022-07-19 This is a comprehensive major reference work for our SpringerReference program covering clinical trials. Although the core of the Work will focus on the design, analysis, and interpretation of scientific data from clinical trials, a broad spectrum of clinical trial application areas will be covered in detail. This is an important time to develop such a Work, as drug safety and efficacy emphasizes the Clinical Trials process. Because of an immense and growing international disease burden, pharmaceutical and biotechnology companies continue to develop new drugs. Clinical trials have also become extremely globalized in the past 15 years, with over 225,000 international trials ongoing at this point in time. Principles in Practice of Clinical Trials is truly an interdisciplinary that will be divided into the following areas: 1) Clinical Trials Basic Perspectives 2) Regulation and Oversight 3) Basic Trial Designs 4) Advanced Trial Designs 5) Analysis 6) Trial Publication 7) Topics Related Specific Populations and Legal Aspects of Clinical Trials The Work is designed to be comprised of 175 chapters and approximately 2500 pages. The Work will be oriented like many of our SpringerReference Handbooks, presenting detailed and comprehensive expository chapters on broad subjects. The Editors are major figures in the field of clinical trials, and both have written textbooks on the topic. There will also be a slate of 7-8 renowned associate editors that will edit individual sections of the Reference. |
| introducing monte carlo methods with r: Bayesian Core: A Practical Approach to Computational Bayesian Statistics Jean-Michel Marin, Christian Robert, 2007-05-26 This Bayesian modeling book is intended for practitioners and applied statisticians looking for a self-contained entry to computational Bayesian statistics. Focusing on standard statistical models and backed up by discussed real datasets available from the book website, it provides an operational methodology for conducting Bayesian inference, rather than focusing on its theoretical justifications. Special attention is paid to the derivation of prior distributions in each case and specific reference solutions are given for each of the models. Similarly, computational details are worked out to lead the reader towards an effective programming of the methods given in the book. |
| introducing monte carlo methods with r: Accelerating Monte Carlo methods for Bayesian inference in dynamical models Johan Dahlin, 2016-03-22 Making decisions and predictions from noisy observations are two important and challenging problems in many areas of society. Some examples of applications are recommendation systems for online shopping and streaming services, connecting genes with certain diseases and modelling climate change. In this thesis, we make use of Bayesian statistics to construct probabilistic models given prior information and historical data, which can be used for decision support and predictions. The main obstacle with this approach is that it often results in mathematical problems lacking analytical solutions. To cope with this, we make use of statistical simulation algorithms known as Monte Carlo methods to approximate the intractable solution. These methods enjoy well-understood statistical properties but are often computational prohibitive to employ. The main contribution of this thesis is the exploration of different strategies for accelerating inference methods based on sequential Monte Carlo (SMC) and Markov chain Monte Carlo (MCMC). That is, strategies for reducing the computational effort while keeping or improving the accuracy. A major part of the thesis is devoted to proposing such strategies for the MCMC method known as the particle Metropolis-Hastings (PMH) algorithm. We investigate two strategies: (i) introducing estimates of the gradient and Hessian of the target to better tailor the algorithm to the problem and (ii) introducing a positive correlation between the point-wise estimates of the target. Furthermore, we propose an algorithm based on the combination of SMC and Gaussian process optimisation, which can provide reasonable estimates of the posterior but with a significant decrease in computational effort compared with PMH. Moreover, we explore the use of sparseness priors for approximate inference in over-parametrised mixed effects models and autoregressive processes. This can potentially be a practical strategy for inference in the big data era. Finally, we propose a general method for increasing the accuracy of the parameter estimates in non-linear state space models by applying a designed input signal. Borde Riksbanken höja eller sänka reporäntan vid sitt nästa möte för att nå inflationsmålet? Vilka gener är förknippade med en viss sjukdom? Hur kan Netflix och Spotify veta vilka filmer och vilken musik som jag vill lyssna på härnäst? Dessa tre problem är exempel på frågor där statistiska modeller kan vara användbara för att ge hjälp och underlag för beslut. Statistiska modeller kombinerar teoretisk kunskap om exempelvis det svenska ekonomiska systemet med historisk data för att ge prognoser av framtida skeenden. Dessa prognoser kan sedan användas för att utvärdera exempelvis vad som skulle hända med inflationen i Sverige om arbetslösheten sjunker eller hur värdet på mitt pensionssparande förändras när Stockholmsbörsen rasar. Tillämpningar som dessa och många andra gör statistiska modeller viktiga för många delar av samhället. Ett sätt att ta fram statistiska modeller bygger på att kontinuerligt uppdatera en modell allteftersom mer information samlas in. Detta angreppssätt kallas för Bayesiansk statistik och är särskilt användbart när man sedan tidigare har bra insikter i modellen eller tillgång till endast lite historisk data för att bygga modellen. En nackdel med Bayesiansk statistik är att de beräkningar som krävs för att uppdatera modellen med den nya informationen ofta är mycket komplicerade. I sådana situationer kan man istället simulera utfallet från miljontals varianter av modellen och sedan jämföra dessa mot de historiska observationerna som finns till hands. Man kan sedan medelvärdesbilda över de varianter som gav bäst resultat för att på så sätt ta fram en slutlig modell. Det kan därför ibland ta dagar eller veckor för att ta fram en modell. Problemet blir särskilt stort när man använder mer avancerade modeller som skulle kunna ge bättre prognoser men som tar för lång tid för att bygga. I denna avhandling använder vi ett antal olika strategier för att underlätta eller förbättra dessa simuleringar. Vi föreslår exempelvis att ta hänsyn till fler insikter om systemet och därmed minska antalet varianter av modellen som behöver undersökas. Vi kan således redan utesluta vissa modeller eftersom vi har en bra uppfattning om ungefär hur en bra modell ska se ut. Vi kan också förändra simuleringen så att den enklare rör sig mellan olika typer av modeller. På detta sätt utforskas rymden av alla möjliga modeller på ett mer effektivt sätt. Vi föreslår ett antal olika kombinationer och förändringar av befintliga metoder för att snabba upp anpassningen av modellen till observationerna. Vi visar att beräkningstiden i vissa fall kan minska ifrån några dagar till någon timme. Förhoppningsvis kommer detta i framtiden leda till att man i praktiken kan använda mer avancerade modeller som i sin tur resulterar i bättre prognoser och beslut. |
| introducing monte carlo methods with r: Monte Carlo Simulation for the Pharmaceutical Industry Mark Chang, 2010-09-29 Helping you become a creative, logical thinker and skillful simulator, Monte Carlo Simulation for the Pharmaceutical Industry: Concepts, Algorithms, and Case Studies provides broad coverage of the entire drug development process, from drug discovery to preclinical and clinical trial aspects to commercialization. It presents the theories and metho |
| introducing monte carlo methods with r: Randomization, Bootstrap and Monte Carlo Methods in Biology Bryan F.J. Manly, 2018-10-03 Modern computer-intensive statistical methods play a key role in solving many problems across a wide range of scientific disciplines. This new edition of the bestselling Randomization, Bootstrap and Monte Carlo Methods in Biology illustrates the value of a number of these methods with an emphasis on biological applications. This textbook focuses on three related areas in computational statistics: randomization, bootstrapping, and Monte Carlo methods of inference. The author emphasizes the sampling approach within randomization testing and confidence intervals. Similar to randomization, the book shows how bootstrapping, or resampling, can be used for confidence intervals and tests of significance. It also explores how to use Monte Carlo methods to test hypotheses and construct confidence intervals. New to the Third Edition Updated information on regression and time series analysis, multivariate methods, survival and growth data as well as software for computational statistics References that reflect recent developments in methodology and computing techniques Additional references on new applications of computer-intensive methods in biology Providing comprehensive coverage of computer-intensive applications while also offering data sets online, Randomization, Bootstrap and Monte Carlo Methods in Biology, Third Edition supplies a solid foundation for the ever-expanding field of statistics and quantitative analysis in biology. |
| introducing monte carlo methods with r: Monte Carlo Methods in Finance Peter Jäckel, 2002-04-03 Dieses Buch ist ein handlicher und praktischer Leitfaden zur Monte Carlo Simulation (MCS). Er gibt eine Einführung in Standardmethoden und fortgeschrittene Verfahren, um die zunehmende Komplexität derivativer Portfolios besser zu erfassen. Das hier behandelte Spektrum von MCS-Anwendungen reicht von der Preisbestimmung komplexerer Derivate, z.B. von amerikanischen und asiatischen Optionen, bis hin zur Messung des Value at Risk und zur Modellierung komplexer Marktdynamik. Anhand einer Vielzahl praktischer Beispiele wird erläutert, wie man Monte Carlo Methoden einsetzt. Dabei gehen die Autoren zunächst auf die Grundlagen und danach auf fortgeschrittene Techniken ein. Darüber hinaus geben sie nützliche Tipps und Hinweise für das Entwickeln und Arbeiten mit MCS-Methoden. Die Autoren sind Experten auf dem Gebiet der Monte Carlo Simulation und verfügen über langjährige Erfahrung im Umgang mit MCS-Methoden. Die Begleit-CD enthält Excel Muster Spreadsheets sowie VBA und C++ Code Snippets, die der Leser installieren und so mit den im Buch beschriebenen Beispiele frei experimentieren kann. Monte Carlo Methods in Finance - ein unverzichtbares Nachschlagewerk für quantitative Analysten, die bei der Bewertung von Optionspreisen und Riskmanagement auf Modelle zurückgreifen müssen. |
| introducing monte carlo methods with r: Uncertainty in Engineering Louis J. M. Aslett, Frank P. A. Coolen, Jasper De Bock, 2021-12-09 This open access book provides an introduction to uncertainty quantification in engineering. Starting with preliminaries on Bayesian statistics and Monte Carlo methods, followed by material on imprecise probabilities, it then focuses on reliability theory and simulation methods for complex systems. The final two chapters discuss various aspects of aerospace engineering, considering stochastic model updating from an imprecise Bayesian perspective, and uncertainty quantification for aerospace flight modelling. Written by experts in the subject, and based on lectures given at the Second Training School of the European Research and Training Network UTOPIAE (Uncertainty Treatment and Optimization in Aerospace Engineering), which took place at Durham University (United Kingdom) from 2 to 6 July 2018, the book offers an essential resource for students as well as scientists and practitioners. |
| introducing monte carlo methods with r: Advanced R Hadley Wickham, 2015-09-15 An Essential Reference for Intermediate and Advanced R Programmers Advanced R presents useful tools and techniques for attacking many types of R programming problems, helping you avoid mistakes and dead ends. With more than ten years of experience programming in R, the author illustrates the elegance, beauty, and flexibility at the heart of R. The book develops the necessary skills to produce quality code that can be used in a variety of circumstances. You will learn: The fundamentals of R, including standard data types and functions Functional programming as a useful framework for solving wide classes of problems The positives and negatives of metaprogramming How to write fast, memory-efficient code This book not only helps current R users become R programmers but also shows existing programmers what’s special about R. Intermediate R programmers can dive deeper into R and learn new strategies for solving diverse problems while programmers from other languages can learn the details of R and understand why R works the way it does. |
| introducing monte carlo methods with r: Forecasting in Mathematics Abdo Abou Jaoude, 2021 |
| introducing monte carlo methods with r: Sequential Monte Carlo Methods in Practice Arnaud Doucet, Nando de Freitas, Neil Gordon, 2013-03-09 Monte Carlo methods are revolutionising the on-line analysis of data in fields as diverse as financial modelling, target tracking and computer vision. These methods, appearing under the names of bootstrap filters, condensation, optimal Monte Carlo filters, particle filters and survial of the fittest, have made it possible to solve numerically many complex, non-standarard problems that were previously intractable. This book presents the first comprehensive treatment of these techniques, including convergence results and applications to tracking, guidance, automated target recognition, aircraft navigation, robot navigation, econometrics, financial modelling, neural networks,optimal control, optimal filtering, communications, reinforcement learning, signal enhancement, model averaging and selection, computer vision, semiconductor design, population biology, dynamic Bayesian networks, and time series analysis. This will be of great value to students, researchers and practicioners, who have some basic knowledge of probability. Arnaud Doucet received the Ph. D. degree from the University of Paris- XI Orsay in 1997. From 1998 to 2000, he conducted research at the Signal Processing Group of Cambridge University, UK. He is currently an assistant professor at the Department of Electrical Engineering of Melbourne University, Australia. His research interests include Bayesian statistics, dynamic models and Monte Carlo methods. Nando de Freitas obtained a Ph.D. degree in information engineering from Cambridge University in 1999. He is presently a research associate with the artificial intelligence group of the University of California at Berkeley. His main research interests are in Bayesian statistics and the application of on-line and batch Monte Carlo methods to machine learning. |
| introducing monte carlo methods with r: The Art of R Programming Norman Matloff, 2011-10-11 R is the world's most popular language for developing statistical software: Archaeologists use it to track the spread of ancient civilizations, drug companies use it to discover which medications are safe and effective, and actuaries use it to assess financial risks and keep economies running smoothly. The Art of R Programming takes you on a guided tour of software development with R, from basic types and data structures to advanced topics like closures, recursion, and anonymous functions. No statistical knowledge is required, and your programming skills can range from hobbyist to pro. Along the way, you'll learn about functional and object-oriented programming, running mathematical simulations, and rearranging complex data into simpler, more useful formats. You'll also learn to: –Create artful graphs to visualize complex data sets and functions –Write more efficient code using parallel R and vectorization –Interface R with C/C++ and Python for increased speed or functionality –Find new R packages for text analysis, image manipulation, and more –Squash annoying bugs with advanced debugging techniques Whether you're designing aircraft, forecasting the weather, or you just need to tame your data, The Art of R Programming is your guide to harnessing the power of statistical computing. |
| introducing monte carlo methods with r: Introducing Monte Carlo Methods with R Christian P. Robert, George Casella, 2010-04-17 |
| introducing monte carlo methods with r: Essentials of Monte Carlo Simulation Nick T. Thomopoulos, 2015-01-28 Essentials of Monte Carlo Simulation focuses on the fundamentals of Monte Carlo methods using basic computer simulation techniques. The theories presented in this text deal with systems that are too complex to solve analytically. As a result, readers are given a system of interest and constructs using computer code, as well as algorithmic models to emulate how the system works internally. After the models are run several times, in a random sample way, the data for each output variable(s) of interest is analyzed by ordinary statistical methods. This book features 11 comprehensive chapters, and discusses such key topics as random number generators, multivariate random variates, and continuous random variates. Over 100 numerical examples are presented as part of the appendix to illustrate useful real world applications. The text also contains an easy to read presentation with minimal use of difficult mathematical concepts. Very little has been published in the area of computer Monte Carlo simulation methods, and this book will appeal to students and researchers in the fields of Mathematics and Statistics. |
| introducing monte carlo methods with r: Monte Carlo Methods for Particle Transport Alireza Haghighat, 2020-08-09 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: Computational Materials Science Kaoru Ohno, Keivan Esfarjani, Yoshiyuki Kawazoe, 2012-12-06 There has been much progress in the computational approaches in the field of materials science during the past two decades. In particular, computer simula tion has become a very important tool in this field since it is a bridge between theory, which is often limited by its oversimplified models, and experiment, which is limited by the physical parameters. Computer simulation, on the other hand, can partially fulfill both of these paradigms, since it is based on theories and is in fact performing experiment but under any arbitrary, even unphysical, conditions. This progress is indebted to advances in computational physics and chem istry. Ab initio methods are being used widely and frequently in order to determine the electronic and/or atomic structures of different materials. The ultimate goal is to be able to predict various properties of a material just from its atomic coordinates, and also, in some cases, to even predict the sta ble atomic positions of a given material. However, at present, the applications of ab initio methods are severely limited with respect to the number of par ticles and the time scale of dynamical simulation. This is one extreme of the methodology based on very accurate electronic-level calculations. |
| introducing monte carlo methods with r: Monte Carlo and Quasi-Monte Carlo Sampling Christiane Lemieux, 2009-04-03 Quasi–Monte Carlo methods have become an increasingly popular alternative to Monte Carlo methods over the last two decades. Their successful implementation on practical problems, especially in finance, has motivated the development of several new research areas within this field to which practitioners and researchers from various disciplines currently contribute. This book presents essential tools for using quasi–Monte Carlo sampling in practice. The first part of the book focuses on issues related to Monte Carlo methods—uniform and non-uniform random number generation, variance reduction techniques—but the material is presented to prepare the readers for the next step, which is to replace the random sampling inherent to Monte Carlo by quasi–random sampling. The second part of the book deals with this next step. Several aspects of quasi-Monte Carlo methods are covered, including constructions, randomizations, the use of ANOVA decompositions, and the concept of effective dimension. The third part of the book is devoted to applications in finance and more advanced statistical tools like Markov chain Monte Carlo and sequential Monte Carlo, with a discussion of their quasi–Monte Carlo counterpart. The prerequisites for reading this book are a basic knowledge of statistics and enough mathematical maturity to follow through the various techniques used throughout the book. This text is aimed at graduate students in statistics, management science, operations research, engineering, and applied mathematics. It should also be useful to practitioners who want to learn more about Monte Carlo and quasi–Monte Carlo methods and researchers interested in an up-to-date guide to these methods. |
| introducing monte carlo methods with r: Political Analysis Using R James E. Monogan III, 2015-12-14 This book provides a narrative of how R can be useful in the analysis of public administration, public policy, and political science data specifically, in addition to the social sciences more broadly. It can serve as a textbook and reference manual for students and independent researchers who wish to use R for the first time or broaden their skill set with the program. While the book uses data drawn from political science, public administration, and policy analyses, it is written so that students and researchers in other fields should find it accessible and useful as well. By the end of the first seven chapters, an entry-level user should be well acquainted with how to use R as a traditional econometric software program. The remaining four chapters will begin to introduce the user to advanced techniques that R offers but many other programs do not make available such as how to use contributed libraries or write programs in R. The book details how to perform nearly every task routinely associated with statistical modeling: descriptive statistics, basic inferences, estimating common models, and conducting regression diagnostics. For the intermediate or advanced reader, the book aims to open up the wide array of sophisticated methods options that R makes freely available. It illustrates how user-created libraries can be installed and used in real data analysis, focusing on a handful of libraries that have been particularly prominent in political science. The last two chapters illustrate how the user can conduct linear algebra in R and create simple programs. A key point in these chapters will be that such actions are substantially easier in R than in many other programs, so advanced techniques are more accessible in R, which will appeal to scholars and policy researchers who already conduct extensive data analysis. Additionally, the book should draw the attention of students and teachers of quantitative methods in the political disciplines. |
| introducing monte carlo methods with r: Markov Chain Monte Carlo in Practice W.R. Gilks, S. Richardson, David Spiegelhalter, 1995-12-01 In a family study of breast cancer, epidemiologists in Southern California increase the power for detecting a gene-environment interaction. In Gambia, a study helps a vaccination program reduce the incidence of Hepatitis B carriage. Archaeologists in Austria place a Bronze Age site in its true temporal location on the calendar scale. And in France, researchers map a rare disease with relatively little variation. Each of these studies applied Markov chain Monte Carlo methods to produce more accurate and inclusive results. General state-space Markov chain theory has seen several developments that have made it both more accessible and more powerful to the general statistician. Markov Chain Monte Carlo in Practice introduces MCMC methods and their applications, providing some theoretical background as well. The authors are researchers who have made key contributions in the recent development of MCMC methodology and its application. Considering the broad audience, the editors emphasize practice rather than theory, keeping the technical content to a minimum. The examples range from the simplest application, Gibbs sampling, to more complex applications. The first chapter contains enough information to allow the reader to start applying MCMC in a basic way. The following chapters cover main issues, important concepts and results, techniques for implementing MCMC, improving its performance, assessing model adequacy, choosing between models, and applications and their domains. Markov Chain Monte Carlo in Practice is a thorough, clear introduction to the methodology and applications of this simple idea with enormous potential. It shows the importance of MCMC in real applications, such as archaeology, astronomy, biostatistics, genetics, epidemiology, and image analysis, and provides an excellent base for MCMC to be applied to other fields as well. |
| introducing monte carlo methods with r: Robust Monte Carlo Methods for Light Transport Simulation Eric Veach, 1998 |
| introducing monte carlo methods with r: A Guide to Monte Carlo Simulations in Statistical Physics David P. Landau, Kurt Binder, 2000-08-17 This book describes all aspects of Monte Carlo simulation of complex physical systems encountered in condensed-matter physics and statistical mechanics, as well as in related fields, such as polymer science and lattice gauge theory. The authors give a succinct overview of simple sampling methods and develop the importance sampling method. In addition they introduce quantum Monte Carlo methods, aspects of simulations of growth phenomena and other systems far from equilibrium, and the Monte Carlo Renormalization Group approach to critical phenomena. The book includes many applications, examples, and current references, and exercises to help the reader. |
| introducing monte carlo methods with r: Handbook in Monte Carlo Simulation Paolo Brandimarte, 2014-06-20 An accessible treatment of Monte Carlo methods, techniques, and applications in the field of finance and economics Providing readers with an in-depth and comprehensive guide, the Handbook in Monte Carlo Simulation: Applications in Financial Engineering, Risk Management, and Economics presents a timely account of the applicationsof Monte Carlo methods in financial engineering and economics. Written by an international leading expert in thefield, the handbook illustrates the challenges confronting present-day financial practitioners and provides various applicationsof Monte Carlo techniques to answer these issues. The book is organized into five parts: introduction andmotivation; input analysis, modeling, and estimation; random variate and sample path generation; output analysisand variance reduction; and applications ranging from option pricing and risk management to optimization. The Handbook in Monte Carlo Simulation features: An introductory section for basic material on stochastic modeling and estimation aimed at readers who may need a summary or review of the essentials Carefully crafted examples in order to spot potential pitfalls and drawbacks of each approach An accessible treatment of advanced topics such as low-discrepancy sequences, stochastic optimization, dynamic programming, risk measures, and Markov chain Monte Carlo methods Numerous pieces of R code used to illustrate fundamental ideas in concrete terms and encourage experimentation The Handbook in Monte Carlo Simulation: Applications in Financial Engineering, Risk Management, and Economics is a complete reference for practitioners in the fields of finance, business, applied statistics, econometrics, and engineering, as well as a supplement for MBA and graduate-level courses on Monte Carlo methods and simulation. |
| introducing monte carlo methods with r: Statistical Design George Casella, 2008-04-03 Statistical design is one of the fundamentals of our subject, being at the core of the growth of statistics during the previous century. In this book the basic theoretical underpinnings are covered. It describes the principles that drive good designs and good statistics. Design played a key role in agricultural statistics and set down principles of good practice, principles that still apply today. Statistical design is all about understanding where the variance comes from, and making sure that is where the replication is. Indeed, it is probably correct to say that these principles are even more important today. |
| introducing monte carlo methods with r: Explorations in Monte Carlo Methods Ronald W. Shonkwiler, Franklin Mendivil, 2009-08-11 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. 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. The problem-oriented approach makes it ideal for an applied course in basic probability and for a more specialized course in Monte Carlo methods. Topics include probability distributions, counting combinatorial objects, simulated annealing, genetic algorithms, option pricing, gamblers ruin, statistical mechanics, sampling, and random number generation. |
| introducing monte carlo methods with r: Mathematical Problems in Data Science Li M. Chen, Zhixun Su, Bo Jiang, 2015-12-15 This book describes current problems in data science and Big Data. Key topics are data classification, Graph Cut, the Laplacian Matrix, Google Page Rank, efficient algorithms, hardness of problems, different types of big data, geometric data structures, topological data processing, and various learning methods. For unsolved problems such as incomplete data relation and reconstruction, the book includes possible solutions and both statistical and computational methods for data analysis. Initial chapters focus on exploring the properties of incomplete data sets and partial-connectedness among data points or data sets. Discussions also cover the completion problem of Netflix matrix; machine learning method on massive data sets; image segmentation and video search. This book introduces software tools for data science and Big Data such MapReduce, Hadoop, and Spark. This book contains three parts. The first part explores the fundamental tools of data science. It includes basic graph theoretical methods, statistical and AI methods for massive data sets. In second part, chapters focus on the procedural treatment of data science problems including machine learning methods, mathematical image and video processing, topological data analysis, and statistical methods. The final section provides case studies on special topics in variational learning, manifold learning, business and financial data rec overy, geometric search, and computing models. Mathematical Problems in Data Science is a valuable resource for researchers and professionals working in data science, information systems and networks. Advanced-level students studying computer science, electrical engineering and mathematics will also find the content helpful. |
| introducing monte carlo methods with r: Digital Dice Paul Nahin, 2013-03-24 Some probability problems are so difficult that they stump the smartest mathematicians. But even the hardest of these problems can often be solved with a computer and a Monte Carlo simulation, in which a random-number generator simulates a physical process, such as a million rolls of a pair of dice. This is what Digital Dice is all about: how to get numerical answers to difficult probability problems without having to solve complicated mathematical equations. Popular-math writer Paul Nahin challenges readers to solve twenty-one difficult but fun problems, from determining the odds of coin-flipping games to figuring out the behavior of elevators. Problems build from relatively easy (deciding whether a dishwasher who breaks most of the dishes at a restaurant during a given week is clumsy or just the victim of randomness) to the very difficult (tackling branching processes of the kind that had to be solved by Manhattan Project mathematician Stanislaw Ulam). In his characteristic style, Nahin brings the problems to life with interesting and odd historical anecdotes. Readers learn, for example, not just how to determine the optimal stopping point in any selection process but that astronomer Johannes Kepler selected his second wife by interviewing eleven women. The book shows readers how to write elementary computer codes using any common programming language, and provides solutions and line-by-line walk-throughs of a MATLAB code for each problem. Digital Dice will appeal to anyone who enjoys popular math or computer science. In a new preface, Nahin wittily addresses some of the responses he received to the first edition. |
| introducing monte carlo methods with r: Monte Carlo Simulation and Finance Don L. McLeish, 2011-09-13 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. |
| introducing monte carlo methods with r: Theory of Point Estimation Erich L. Lehmann, George Casella, 2006-05-02 Since the publication in 1983 of Theory of Point Estimation, much new work has made it desirable to bring out a second edition. The inclusion of the new material has increased the length of the book from 500 to 600 pages; of the approximately 1000 references about 25% have appeared since 1983. The greatest change has been the addition to the sparse treatment of Bayesian inference in the first edition. This includes the addition of new sections on Equivariant, Hierarchical, and Empirical Bayes, and on their comparisons. Other major additions deal with new developments concerning the information in equality and simultaneous and shrinkage estimation. The Notes at the end of each chapter now provide not only bibliographic and historical material but also introductions to recent development in point estimation and other related topics which, for space reasons, it was not possible to include in the main text. The problem sections also have been greatly expanded. On the other hand, to save space most of the discussion in the first edition on robust estimation (in particu lar L, M, and R estimators) has been deleted. This topic is the subject of two excellent books by Hampel et al (1986) and Staudte and Sheather (1990). Other than subject matter changes, there have been some minor modifications in the presentation. |
| introducing monte carlo methods with r: Discretization and MCMC Convergence Assessment Christian P. Robert, 2012-12-06 The exponential increase in the use of MCMC methods and the corre sponding applications in domains of even higher complexity have caused a growing concern about the available convergence assessment methods and the realization that some of these methods were not reliable enough for all-purpose analyses. Some researchers have mainly focussed on the con vergence to stationarity and the estimation of rates of convergence, in rela tion with the eigenvalues of the transition kernel. This monograph adopts a different perspective by developing (supposedly) practical devices to assess the mixing behaviour of the chain under study and, more particularly, it proposes methods based on finite (state space) Markov chains which are obtained either through a discretization of the original Markov chain or through a duality principle relating a continuous state space Markov chain to another finite Markov chain, as in missing data or latent variable models. The motivation for the choice of finite state spaces is that, although the resulting control is cruder, in the sense that it can often monitor con vergence for the discretized version alone, it is also much stricter than alternative methods, since the tools available for finite Markov chains are universal and the resulting transition matrix can be estimated more accu rately. Moreover, while some setups impose a fixed finite state space, other allow for possible refinements in the discretization level and for consecutive improvements in the convergence monitoring. |
| introducing monte carlo methods with r: The BUGS Book David Lunn, Chris Jackson, Nicky Best, Andrew Thomas, David Spiegelhalter, 2012-10-02 Bayesian statistical methods have become widely used for data analysis and modelling in recent years, and the BUGS software has become the most popular software for Bayesian analysis worldwide. Authored by the team that originally developed this software, The BUGS Book provides a practical introduction to this program and its use. The text presents |
| introducing monte carlo methods with r: Stochastic Simulation and Monte Carlo Methods Carl Graham, Denis Talay, 2013-07-16 In various scientific and industrial fields, stochastic simulations are taking on a new importance. This is due to the increasing power of computers and practitioners’ aim to simulate more and more complex systems, and thus use random parameters as well as random noises to model the parametric uncertainties and the lack of knowledge on the physics of these systems. The error analysis of these computations is a highly complex mathematical undertaking. Approaching these issues, the authors present stochastic numerical methods and prove accurate convergence rate estimates in terms of their numerical parameters (number of simulations, time discretization steps). As a result, the book is a self-contained and rigorous study of the numerical methods within a theoretical framework. After briefly reviewing the basics, the authors first introduce fundamental notions in stochastic calculus and continuous-time martingale theory, then develop the analysis of pure-jump Markov processes, Poisson processes, and stochastic differential equations. In particular, they review the essential properties of Itô integrals and prove fundamental results on the probabilistic analysis of parabolic partial differential equations. These results in turn provide the basis for developing stochastic numerical methods, both from an algorithmic and theoretical point of view. The book combines advanced mathematical tools, theoretical analysis of stochastic numerical methods, and practical issues at a high level, so as to provide optimal results on the accuracy of Monte Carlo simulations of stochastic processes. It is intended for master and Ph.D. students in the field of stochastic processes and their numerical applications, as well as for physicists, biologists, economists and other professionals working with stochastic simulations, who will benefit from the ability to reliably estimate and control the accuracy of their simulations. |
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Mar 27, 2025 · Hey, congratulations on launching a roadmap - I'm a huge fan of having that information available and following developments on software and games like this, probably very …
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Edit your display name in Teams meetings
Mar 6, 2025 · Hi, Microsoft 365 Insiders! We’re excited to let you know that you can now change your display name in Teams meetings.
Introducing the Windows roadmap - Windows IT Pro Blog
Mar 27, 2025 · Hey, congratulations on launching a roadmap - I'm a huge fan of having that information available and following developments on software and games like this, probably …
Introducing new agents in Microsoft 365
Nov 19, 2024 · Today, we’re introducing new agents in SharePoint, where employees can use and create scoped agents grounded in their SharePoint data, instantly getting real-time …
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Feb 24, 2025 · Going forward, we’re introducing new tenant-level outbound email limits (also known as the Tenant External Recipient Rate Limit or TERRL) that are calculated based on …
Introducing flexible sections in SharePoint Pages and News
Feb 13, 2025 · Thank you for the introduction of the flexible section! I'm testing but having many issues. When logged in as a test user (using the same computer and browser as the main …
Introducing Windows 11 checkpoint cumulative updates
Jul 15, 2024 · With Windows 11, version 24H2, we’re introducing a new concept of checkpoint cumulative updates. This will allow you to get features and security enhancements via the …
Introducing Themes by Copilot in Outlook | Microsoft Community …
Nov 7, 2024 · Copilot in Outlook now helps anyone with a Copilot enabled subscription or commercial license create unique and personal themes powered by AI.
Introducing the GPT-4o-Audio-Preview: A New Era of Audio …
Jan 22, 2025 · Good one for the gpt 40 model to have different flavours. Considering there are still few things that are very brittle for the realtime model to not be stable in protection - Voice …
Introducing MAI-DS-R1 | Microsoft Community Hub
Apr 17, 2025 · Phase 3: Introducing the Crisis . Scammer’s Story: Sudden emergency (e.g., medical issue, stranded abroad, or a failed business deal). “I hate to ask, but I need $2,000 for …
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