Dirk P. Kroese - Böcker

Praise for the first edition:“In nine succinct but information-packed chapters, the authors provide a logically structured and robust introduction to the mathematical and statistical methods underpinning the still-evolving field of AI and data science.”- Joacim Rocklöv and Albert A. Gayle, International Journal of Epidemiology, Volume 49, Issue 6“This book organizes the algorithms clearly and cleverly. The way the Python code was written follows the algorithm closely—very useful for readers who wish to understand the rationale and flow of the background knowledge.”- Yin-Ju Lai and Chuhsing Kate Hsiao, Biometrics, Volume 77, Issue 4The purpose of Data Science and Machine Learning: Mathematical and Statistical Methods is to provide an accessible, yet comprehensive textbook intended for students interested in gaining a better understanding of the mathematics and statistics that underpin the rich variety of ideas and machine learning algorithms in data science.New in the Second EditionThis expanded edition provides updates across key areas of statistical learning:Monte Carlo Methods: A new section introducing regenerative rejection sampling - a simpler alternative to MCMC.Unsupervised Learning: Inclusion of two multidimensional diffusion kernel density estimators, as well as the bandwidth perturbation matching method for the optimal data-driven bandwidth selection.Regression: New automatic bandwidth selection for local linear regression.Feature Selection and Shrinkage: A new chapter introducing the klimax method for model selection in high-dimensions.Reinforcement Learning: A new chapter on contemporary topics such as policy iteration, temporal difference learning, and policy gradient methods, all complete with Python code.Appendices: Expanded treatment of linear algebra, functional analysis, and optimization that includes the coordinate-descent method and the novel Majorization–Minimization method for constrained optimization.Key Features:Focuses on mathematical understanding.Presentation is self-contained, accessible, and comprehensive.Extensive list of exercises and worked-out examples.Many concrete algorithms with Python code.Full color throughout and extensive indexing.A single-counter consecutive numbering of all theorems, definitions, equations, etc., for easier text searches.

This book is a comprehensive and accessible introduction to the cross-entropy (CE) method. The CE method started life around 1997 when the first author proposed an adaptive algorithm for rare-event simulation using a cross-entropy minimization technique. It was soon realized that the underlying ideas had a much wider range of application than just in rare-event simulation; they could be readily adapted to tackle quite general combinatorial and multi-extremal optimization problems, including many problems associated with the field of learning algorithms and neural computation. The book is based on an advanced undergraduate course on the CE method, given at the Israel Institute of Technology (Technion) for the last three years. It is aimed at a broad audience of engineers, computer scientists, mathematicians, statisticians and in general anyone, theorist or practitioner, who is interested in smart simulation, fast optimization, learning algorithms, image processing, etc. Our aim was to write a book on the CE method which was accessible to advanced undergraduate students and engineers who simply want to apply the CE method in their work, while at the same time accentu­ ating the unifying and novel mathematical ideas behind the CE method, so as to stimulate further research at a postgraduate level.

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 generationMarkov chain Monte Carlo, featuring key algorithms such as the Metropolis-Hastings method, the Gibbs sampler, and hit-and-runDiscrete-event simulationTechniques for the statistical analysis of simulation data including the delta method, steady-state estimation, and kernel density estimationVariance reduction, including importance sampling, latin hypercube sampling, and conditional Monte CarloEstimation of derivatives and sensitivity analysisAdvanced topics including cross-entropy, rare events, kernel density estimation, quasi Monte Carlo, particle systems, and randomized optimizationThe 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.

This accessible new edition explores the major topics in Monte Carlo simulation Simulation and the Monte Carlo Method, Second Edition reflects the latest developments in the field and presents a fully updated and comprehensive account of the major topics that have emerged in Monte Carlo simulation since the publication of the classic First Edition over twenty-five years ago. While maintaining its accessible and intuitive approach, this revised edition features a wealth of up-to-date information that facilitates a deeper understanding of problem solving across a wide array of subject areas, such as engineering, statistics, computer science, mathematics, and the physical and life sciences.The book begins with a modernized introduction that addresses the basic concepts of probability, Markov processes, and convex optimization. Subsequent chapters discuss the dramatic changes that have occurred in the field of the Monte Carlo method, with coverage of many modern topics including:Markov Chain Monte CarloVariance reduction techniques such as the transform likelihood ratio method and the screening methodThe score function method for sensitivity analysisThe stochastic approximation method and the stochastic counter-part method for Monte Carlo optimizationThe cross-entropy method to rare events estimation and combinatorial optimizationApplication of Monte Carlo techniques for counting problems, with an emphasis on the parametric minimum cross-entropy methodAn extensive range of exercises is provided at the end of each chapter, with more difficult sections and exercises marked accordingly for advanced readers. A generous sampling of applied examples is positioned throughout the book, emphasizing various areas of application, and a detailed appendix presents an introduction to exponential families, a discussion of the computational complexity of stochastic programming problems, and sample MATLAB® programs.Requiring only a basic, introductory knowledge of probability and statistics, Simulation and the Monte Carlo Method, Second Edition is an excellent text for upper-undergraduate and beginning graduate courses in simulation and Monte Carlo techniques. The book also serves as a valuable reference for professionals who would like to achieve a more formal understanding of the Monte Carlo method.

An Advanced Course in Probability and Stochastic Processes provides a modern and rigorous treatment of probability theory and stochastic processes at an upper undergraduate and graduate level. Starting with the foundations of measure theory, this book introduces the key concepts of probability theory in an accessible way, providing full proofs and extensive examples and illustrations. Fundamental stochastic processes such as Gaussian processes, Poisson random measures, Lévy processes, Markov processes, and Itô processes are presented and explored in considerable depth, showcasing their many interconnections. Special attention is paid to martingales and the Wiener process and their central role in the treatment of stochastic integrals and stochastic calculus. This book includes many exercises, designed to test and challenge the reader and expand their skillset. An Advanced Course in Probability and Stochastic Processes is meant for students and researchers who have a solid mathematical background and who have had prior exposure to elementary probability and stochastic processes.Key Features:Focus on mathematical understandingRigorous and self-contained Accessible and comprehensiveHigh-quality illustrationsIncludes essential simulation algorithmsExtensive list of exercises and worked-out examplesElegant and consistent notation

It also offers an integrated treatment of mathematical statistics and modern statistical computation, emphasizing statistical modeling, computational techniques, and applications.The 2nd edition changes the programming language used in the text from MATLAB to Julia.

This book, Statistical Modeling and Computation, provides a unique introduction to modern statistics from both classical and Bayesian perspectives. It also offers an integrated treatment of mathematical statistics and modern statistical computation, emphasizing statistical modeling, computational techniques, and applications.The 2nd edition changes the programming language used in the text from MATLAB to Julia. For all examples with computing components, the authors provide data sets and their own Julia codes. The new edition features numerous full color graphics to illustrate the concepts discussed in the text, and adds three entirely new chapters on a variety of popular topics, including:Regularization and the Lasso regressionBayesian shrinkage methodsNonparametric statistical testsSplines and the Gaussian process regressionJoshua C. C. Chan is Professor of Economics, and holds the endowed Olson Chair at Purdue University. He is an elected fellow at the International Association for Applied Econometrics and served as Chair for the Economics, Finance and Business Section of the International Society for Bayesian Analysis from 2020-2022. His research focuses on building new high-dimensional time-series models and developing efficient estimation methods for these models. He has published over 50 papers in peer-reviewed journals, including some top-field journals such as Journal of Econometrics, Journal of the American Statistical Association and Journal of Business and Economic Statistics.Dirk Kroese is Professor of Mathematics and Statistics at the University of Queensland. He is known for his significant contributions to the fields of applied probability, mathematical statistics, machine learning, and Monte Carlo methods. He has published over 140 articles and 7 books. He is a pioneer of the well-known Cross-Entropy (CE) method, which is being used around the world to help solve difficult estimation and optimization problems in science, engineering, and finance.  In addition to his scholarly contributions, Dirk Kroese is recognized for his role as an educator and mentor, having supervised and inspired numerous students and researchers.

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 exercisesSimulation 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.

This book is a comprehensive and accessible introduction to the cross-entropy (CE) method. The CE method started life around 1997 when the first author proposed an adaptive algorithm for rare-event simulation using a cross-entropy minimization technique. It was soon realized that the underlying ideas had a much wider range of application than just in rare-event simulation; they could be readily adapted to tackle quite general combinatorial and multi-extremal optimization problems, including many problems associated with the field of learning algorithms and neural computation. The book is based on an advanced undergraduate course on the CE method, given at the Israel Institute of Technology (Technion) for the last three years. It is aimed at a broad audience of engineers, computer scientists, mathematicians, statisticians and in general anyone, theorist or practitioner, who is interested in smart simulation, fast optimization, learning algorithms, image processing, etc. Our aim was to write a book on the CE method which was accessible to advanced undergraduate students and engineers who simply want to apply the CE method in their work, while at the same time accentu­ ating the unifying and novel mathematical ideas behind the CE method, so as to stimulate further research at a postgraduate level.