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Thls text ls about one small fteld on the crossroads of statlstlcs, operatlons research and computer sclence. Statistleians need random number generators to test and compare estlmators before uslng them ln real l fe. In operatlons research, random numbers are a key component ln arge scale slmulatlons. Computer sclen tlsts need randomness ln program testlng, game playlng and comparlsons of algo rlthms. The appl catlons are wlde and varled. Yet all depend upon the same com puter generated random numbers. Usually, the randomness demanded by an appl catlon has some bullt-ln structure: typlcally, one needs more than just a sequence of Independent random blts or Independent uniform 0,1] random vari ables. Some users need random variables wlth unusual densltles, or random com blnatorlal objects wlth speclftc propertles, or random geometrlc objects, or ran dom processes wlth weil deftned dependence structures. Thls ls preclsely the sub ject area of the book, the study of non-uniform random varlates. The plot evolves around the expected complexlty of random varlate genera tlon algorlthms. We set up an ldeal zed computatlonal model (wlthout overdolng lt), we lntroduce the notlon of unlformly bounded expected complexlty, and we study upper and lower bounds for computatlonal complexlty. In short, a touch of computer sclence ls added to the fteld. To keep everythlng abstract, no tlmlngs or computer programs are lncluded. Thls was a Iabor of Iove. George Marsagl a created CS690, a course on ran dom number generat on at the School of Computer Sclence of McG ll Unlverslty."
Non-uniform random variate generation is an established research area in the intersection of mathematics, statistics and computer science. Although random variate generation with popular standard distributions have become part of every course on discrete event simulation and on Monte Carlo methods, the recent concept of universal (also called automatic or black-box) random variate generation can only be found dispersed in literature. This new concept has great practical advantages that are little known to most simulation practitioners. Being unique in its overall organization the book covers not only the mathematical and statistical theory, but also deals with the implementation of such methods. All algorithms introduced in the book are designed for practical use in simulation and have been coded and made available by the authors. Examples of possible applications of the presented algorithms (including option pricing, VaR and Bayesian statistics) are presented at the end of the book.
An up-to-date account of the theory and practice of generating random variates from probability distributions is presented in this accessible text. After a brief introduction to simulation, the author discusses the general principles for generating and testing uniform and non-uniform variates. These techniques are applied to univariate and multivariate distributions, Markov processes, and order statistics. Dr. Dagpunar has included Fortran 77 programs for generating the more familiar distributions and a set of graphical aids for the manual generation of variates. Competing methods are also compared and their advantages and disadvantages discussed. In addition, algorithms throughout the book enable readers to generate variates from selected distributions, making this an invaluable guide for statisticians, operational researchers, computer scientists, and postgraduates engaged in computer simulation.
The recent concept of universal (also called automatic or black-box) random variate generation can only be found dispersed in the literature. Being unique in its overall organization, the book covers not only the mathematical and statistical theory but also deals with the implementation of such methods. All algorithms introduced in the book are designed for practical use in simulation and have been coded and made available by the authors. Examples of possible applications of the presented algorithms (including option pricing, VaR and Bayesian statistics) are presented at the end of the book.
Simulation means driving a model of a system with suitable inputs and observing the corresponding outputs. It is widely applied in engineering, in business, and in the physical and social sciences. Simulation method ology araws on computer. science, statistics, and operations research and is now sufficiently developed and coherent to be called a discipline in its own right. A course in simulation is an essential part of any operations re search or computer science program. A large fraction of applied work in these fields involves simulation; the techniques of simulation, as tools, are as fundamental as those of linear programming or compiler construction, for example. Simulation sometimes appears deceptively easy, but perusal of this book will reveal unexpected depths. Many simulation studies are statistically defective and many simulation programs are inefficient. We hope that our book will help to remedy this situation. It is intended to teach how to simulate effectively. A simulation project has three crucial components, each of which must always be tackled: (1) data gathering, model building, and validation; (2) statistical design and estimation; (3) programming and implementation. Generation of random numbers (Chapters 5 and 6) pervades simulation, but unlike the three components above, random number generators need not be constructed from scratch for each project. Usually random number packages are available. That is one reason why the chapters on random numbers, which contain mainly reference material, follow the ch!lPters deal ing with experimental design and output analysis.
This book contains 30 selected, refereed papers from an in- ternational conference on bootstrapping and related techni- ques held in Trier 1990. Thepurpose of the book is to in- form about recent research in the area of bootstrap, jack- knife and Monte Carlo Tests. Addressing the novice and the expert it covers as well theoretical as practical aspects of these statistical techniques. Potential users in different disciplines as biometry, epidemiology, computer science, economics and sociology but also theoretical researchers s- hould consult the book to be informed on the state of the art in this area.
Data simulation is a fundamental technique in statistical programming and research. Rick Wicklin's Simulating Data with SAS brings together the most useful algorithms and the best programming techniques for efficient data simulation in an accessible how-to book for practicing statisticians and statistical programmers. This book discusses in detail how to simulate data from common univariate and multivariate distributions, and how to use simulation to evaluate statistical techniques. It also covers simulating correlated data, data for regression models, spatial data, and data with given moments. It provides tips and techniques for beginning programmers, and offers libraries of functions for advanced practitioners. As the first book devoted to simulating data across a range of statistical applications, Simulating Data with SAS is an essential tool for programmers, analysts, researchers, and students who use SAS software. This book is part of the SAS Press program.
As with the bestselling first edition, Computational Statistics Handbook with MATLAB, Second Edition covers some of the most commonly used contemporary techniques in computational statistics. With a strong, practical focus on implementing the methods, the authors include algorithmic descriptions of the procedures as well as
This book provides an introduction to the mathematical and algorithmic foundations of data science, including machine learning, high-dimensional geometry, and analysis of large networks. Topics include the counterintuitive nature of data in high dimensions, important linear algebraic techniques such as singular value decomposition, the theory of random walks and Markov chains, the fundamentals of and important algorithms for machine learning, algorithms and analysis for clustering, probabilistic models for large networks, representation learning including topic modelling and non-negative matrix factorization, wavelets and compressed sensing. Important probabilistic techniques are developed including the law of large numbers, tail inequalities, analysis of random projections, generalization guarantees in machine learning, and moment methods for analysis of phase transitions in large random graphs. Additionally, important structural and complexity measures are discussed such as matrix norms and VC-dimension. This book is suitable for both undergraduate and graduate courses in the design and analysis of algorithms for data.