An Introduction to Statistical Computing

A Simulation-based Approach
Author: Jochen Voss
Publisher: John Wiley & Sons
ISBN: 1118728025
Category: Mathematics
Page: 400
View: 1505

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A comprehensive introduction to sampling-based methods in statistical computing The use of computers in mathematics and statistics has opened up a wide range of techniques for studying otherwise intractable problems. Sampling-based simulation techniques are now an invaluable tool for exploring statistical models. This book gives a comprehensive introduction to the exciting area of sampling-based methods. An Introduction to Statistical Computing introduces the classical topics of random number generation and Monte Carlo methods. It also includes some advanced methods such as the reversible jump Markov chain Monte Carlo algorithm and modern methods such as approximate Bayesian computation and multilevel Monte Carlo techniques An Introduction to Statistical Computing: Fully covers the traditional topics of statistical computing. Discusses both practical aspects and the theoretical background. Includes a chapter about continuous-time models. Illustrates all methods using examples and exercises. Provides answers to the exercises (using the statistical computing environment R); the corresponding source code is available online. Includes an introduction to programming in R. This book is mostly self-contained; the only prerequisites are basic knowledge of probability up to the law of large numbers. Careful presentation and examples make this book accessible to a wide range of students and suitable for self-study or as the basis of a taught course

Bilinear Regression Analysis

An Introduction
Author: Dietrich von Rosen
Publisher: Springer
ISBN: 3319787845
Category: Mathematics
Page: 468
View: 5510

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This book expands on the classical statistical multivariate analysis theory by focusing on bilinear regression models, a class of models comprising the classical growth curve model and its extensions. In order to analyze the bilinear regression models in an interpretable way, concepts from linear models are extended and applied to tensor spaces. Further, the book considers decompositions of tensor products into natural subspaces, and addresses maximum likelihood estimation, residual analysis, influential observation analysis and testing hypotheses, where properties of estimators such as moments, asymptotic distributions or approximations of distributions are also studied. Throughout the text, examples and several analyzed data sets illustrate the different approaches, and fresh insights into classical multivariate analysis are provided. This monograph is of interest to researchers and Ph.D. students in mathematical statistics, signal processing and other fields where statistical multivariate analysis is utilized. It can also be used as a text for second graduate-level courses on multivariate analysis.

Elements of Computational Statistics


Author: James E. Gentle
Publisher: Springer Science & Business Media
ISBN: 0387216111
Category: Computers
Page: 420
View: 5158

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Will provide a more elementary introduction to these topics than other books available; Gentle is the author of two other Springer books

Statistical Pattern Recognition


Author: Andrew R. Webb
Publisher: John Wiley & Sons
ISBN: 0470854782
Category: Mathematics
Page: 514
View: 7745

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Statistical pattern recognition is a very active area of study and research, which has seen many advances in recent years. New and emerging applications - such as data mining, web searching, multimedia data retrieval, face recognition, and cursive handwriting recognition - require robust and efficient pattern recognition techniques. Statistical decision making and estimation are regarded as fundamental to the study of pattern recognition. Statistical Pattern Recognition, Second Edition has been fully updated with new methods, applications and references. It provides a comprehensive introduction to this vibrant area - with material drawn from engineering, statistics, computer science and the social sciences - and covers many application areas, such as database design, artificial neural networks, and decision support systems. * Provides a self-contained introduction to statistical pattern recognition. * Each technique described is illustrated by real examples. * Covers Bayesian methods, neural networks, support vector machines, and unsupervised classification. * Each section concludes with a description of the applications that have been addressed and with further developments of the theory. * Includes background material on dissimilarity, parameter estimation, data, linear algebra and probability. * Features a variety of exercises, from 'open-book' questions to more lengthy projects. The book is aimed primarily at senior undergraduate and graduate students studying statistical pattern recognition, pattern processing, neural networks, and data mining, in both statistics and engineering departments. It is also an excellent source of reference for technical professionals working in advanced information development environments. For further information on the techniques and applications discussed in this book please visit www.statistical-pattern-recognition.net

Random Graphs for Statistical Pattern Recognition


Author: David J. Marchette
Publisher: John Wiley & Sons
ISBN: 9780471722083
Category: Mathematics
Page: 264
View: 5955

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A timely convergence of two widely used disciplines Random Graphs for Statistical Pattern Recognition is the firstbook to address the topic of random graphs as it applies tostatistical pattern recognition. Both topics are of vital interestto researchers in various mathematical and statistical fields andhave never before been treated together in one book. The use ofdata random graphs in pattern recognition in clustering andclassification is discussed, and the applications for bothdisciplines are enhanced with new tools for the statistical patternrecognition community. New and interesting applications for randomgraph users are also introduced. This important addition to statistical literaturefeatures: Information that previously has been available only throughscattered journal articles Practical tools and techniques for a wide range of real-worldapplications New perspectives on the relationship between patternrecognition and computational geometry Numerous experimental problems to encourage practicalapplications With its comprehensive coverage of two timely fields, enhancedwith many references and real-world examples, Random Graphs forStatistical Pattern Recognition is a valuable resource forindustry professionals and students alike.

Weibull Models


Author: D. N. Prabhakar Murthy,Min Xie,Renyan Jiang
Publisher: John Wiley & Sons
ISBN: 9780471473275
Category: Mathematics
Page: 408
View: 1978

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A comprehensive perspective on Weibull models The literature on Weibull models is vast, disjointed, andscattered across many different journals. Weibull Models is acomprehensive guide that integrates all the different facets ofWeibull models in a single volume. This book will be of great help to practitioners in reliabilityand other disciplines in the context of modeling data sets usingWeibull models. For researchers interested in these modelingtechniques, exercises at the end of each chapter define potentialtopics for future research. Organized into seven distinct parts, Weibull Models: Covers model analysis, parameter estimation, model validation,and application Serves as both a handbook and a research monograph. As ahandbook, it classifies the different models and presents theirproperties. As a research monograph, it unifies the literature andpresents the results in an integrated manner Intertwines theory and application Focuses on model identification prior to model parameterestimation Discusses the usefulness of the Weibull Probability plot (WPP)in the model selection to model a given data set Highlights the use of Weibull models in reliability theory Filled with in-depth analysis, Weibull Models pulls together themost relevant information on this topic to give everyone fromreliability engineers to applied statisticians involved withreliability and survival analysis a clear look at what Weibullmodels can offer.

Statistical Computing in C++ and R


Author: Randall L. Eubank,Ana Kupresanin
Publisher: CRC Press
ISBN: 1466515376
Category: Mathematics
Page: 556
View: 3080

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With the advancement of statistical methodology inextricably linked to the use of computers, new methodological ideas must be translated into usable code and then numerically evaluated relative to competing procedures. In response to this, Statistical Computing in C++ and R concentrates on the writing of code rather than the development and study of numerical algorithms per se. The book discusses code development in C++ and R and the use of these symbiotic languages in unison. It emphasizes that each offers distinct features that, when used in tandem, can take code writing beyond what can be obtained from either language alone. The text begins with some basics of object-oriented languages, followed by a "boot-camp" on the use of C++ and R. The authors then discuss code development for the solution of specific computational problems that are relevant to statistics including optimization, numerical linear algebra, and random number generation. Later chapters introduce abstract data structures (ADTs) and parallel computing concepts. The appendices cover R and UNIX Shell programming. Features Includes numerous student exercises ranging from elementary to challenging Integrates both C++ and R for the solution of statistical computing problems Uses C++ code in R and R functions in C++ programs Provides downloadable programs, available from the authors’ website The translation of a mathematical problem into its computational analog (or analogs) is a skill that must be learned, like any other, by actively solving relevant problems. The text reveals the basic principles of algorithmic thinking essential to the modern statistician as well as the fundamental skill of communicating with a computer through the use of the computer languages C++ and R. The book lays the foundation for original code development in a research environment.

Einführung in Statistik und Messwertanalyse für Physiker

Monographie
Author: G. Bohm,G. Zech
Publisher: N.A
ISBN: 9783540257592
Category:
Page: 400
View: 5698

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Die Einf]hrung in die Statistik und Messwertanalyse f]r Physiker richtet sich weniger an mathematischen \berlegungen aus, sondern stellt die praktische Anwendung in den Vordergrund und schdrft die Intuition experimentelle Ergebnisse richtig einzuschdtzen. Zahlreiche ausf]hrlich betrachtete Beispiele dienen dazu, hdufig bei der Datenanalyse gemachte Fehler zu vermeiden (unsinnige Anwendung des Chi-Quadrattests, Funktionenanpassung bei falscher Parametrisierung, Entfaltung mit willk]rlicher Regularisierung). Ein besonderes Augenmerk wird auf den Vergleich von Daten mit Monte-Carlo-Simulationen gelenkt. Moderne Experimente kommen nicht ohne Simulation aus. Deshalb ist es wichtig zu wissen, wie Parameteranpassungen und Entfaltungen in diesem Fall durchgef]rt werden. Au_erdem werden den Studierenden moderne Entwicklungen der Statistik nahegebracht, die in dlteren Lehrb]chern nicht behandelt werden.

Biostatistics

A Methodology For the Health Sciences
Author: Gerald van Belle
Publisher: Wiley-Interscience
ISBN: N.A
Category: Mathematics
Page: 871
View: 3345

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THOMAS S. LUMLEY and GERALD VAN BELLE * Data sets, tables, additional examples, and solutions to selected problems will be housed on the web * Instructors will have the opportunity to submit their own problems and solutions to be added to the website (with proper citations) * Authors will comprehensively update all the material in the book, focusing on current techniques and applications * An additional appendix will mention current software packages, web sites, and important data sets that are available to students and practitioners.

Statistical and Machine Learning Approaches for Network Analysis


Author: Matthias Dehmer,Subhash C. Basak
Publisher: John Wiley & Sons
ISBN: 111834698X
Category: Mathematics
Page: 344
View: 1770

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Explore the multidisciplinary nature of complex networks through machine learning techniques Statistical and Machine Learning Approaches for Network Analysis provides an accessible framework for structurally analyzing graphs by bringing together known and novel approaches on graph classes and graph measures for classification. By providing different approaches based on experimental data, the book uniquely sets itself apart from the current literature by exploring the application of machine learning techniques to various types of complex networks. Comprised of chapters written by internationally renowned researchers in the field of interdisciplinary network theory, the book presents current and classical methods to analyze networks statistically. Methods from machine learning, data mining, and information theory are strongly emphasized throughout. Real data sets are used to showcase the discussed methods and topics, which include: A survey of computational approaches to reconstruct and partition biological networks An introduction to complex networks—measures, statistical properties, and models Modeling for evolving biological networks The structure of an evolving random bipartite graph Density-based enumeration in structured data Hyponym extraction employing a weighted graph kernel Statistical and Machine Learning Approaches for Network Analysis is an excellent supplemental text for graduate-level, cross-disciplinary courses in applied discrete mathematics, bioinformatics, pattern recognition, and computer science. The book is also a valuable reference for researchers and practitioners in the fields of applied discrete mathematics, machine learning, data mining, and biostatistics.

Understanding Computational Bayesian Statistics


Author: William M. Bolstad
Publisher: John Wiley & Sons
ISBN: 1118209923
Category: Mathematics
Page: 336
View: 3226

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A hands-on introduction to computational statistics from a Bayesian point of view Providing a solid grounding in statistics while uniquely covering the topics from a Bayesian perspective, Understanding Computational Bayesian Statistics successfully guides readers through this new, cutting-edge approach. With its hands-on treatment of the topic, the book shows how samples can be drawn from the posterior distribution when the formula giving its shape is all that is known, and how Bayesian inferences can be based on these samples from the posterior. These ideas are illustrated on common statistical models, including the multiple linear regression model, the hierarchical mean model, the logistic regression model, and the proportional hazards model. The book begins with an outline of the similarities and differences between Bayesian and the likelihood approaches to statistics. Subsequent chapters present key techniques for using computer software to draw Monte Carlo samples from the incompletely known posterior distribution and performing the Bayesian inference calculated from these samples. Topics of coverage include: Direct ways to draw a random sample from the posterior by reshaping a random sample drawn from an easily sampled starting distribution The distributions from the one-dimensional exponential family Markov chains and their long-run behavior The Metropolis-Hastings algorithm Gibbs sampling algorithm and methods for speeding up convergence Markov chain Monte Carlo sampling Using numerous graphs and diagrams, the author emphasizes a step-by-step approach to computational Bayesian statistics. At each step, important aspects of application are detailed, such as how to choose a prior for logistic regression model, the Poisson regression model, and the proportional hazards model. A related Web site houses R functions and Minitab macros for Bayesian analysis and Monte Carlo simulations, and detailed appendices in the book guide readers through the use of these software packages. Understanding Computational Bayesian Statistics is an excellent book for courses on computational statistics at the upper-level undergraduate and graduate levels. It is also a valuable reference for researchers and practitioners who use computer programs to conduct statistical analyses of data and solve problems in their everyday work.

Applied Statistics

Analysis of Variance and Regression
Author: Ruth M. Mickey,Olive Jean Dunn,Virginia A. Clark
Publisher: John Wiley & Sons Incorporated
ISBN: N.A
Category: Mathematics
Page: 448
View: 6506

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The Wiley Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists. ". . . overall this is an excellent book . . . I recommend this book to everyone . . ." --Statistical Methods in Medical Research ". . . it contains a wealth of useful up-to-date information and examples from the health sciences." --Technometrics Applied Statistics: Analysis of Variance and Regression, Third Edition has been thoroughly revised to provide a comprehensive and up-to-date combination of sound statistical methodology, practical advice on the application of this methodology, and interpretation of output from statistical programs. Special features include comprehensive treatment of each topic, from summarization of data to presentation of results; a greater emphasis on regression, data screening, and confidence intervals; in-depth discussion of design-related topics such as mixed models and random effects; and overviews of more advanced topics. This valuable, self-contained textbook is eminently suitable for upper-undergraduate/graduate students and applied researchers with an interest in ANOVA techniques.

Econometric inference using simulation techniques


Author: Herman K. van Dijk,Alain Monfort
Publisher: John Wiley & Sons
ISBN: 9780471956235
Category: Business & Economics
Page: 265
View: 8860

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Noted international researchers present the very latest knowledge in the field. This essential work covers the three main areas of econometric inference where the use of simulation methods has been successful--Bayesian inference, classical inference, the solution and stochastic simulation of dynamic econometric models, especially general equilibrium models.

Large-Scale Inverse Problems and Quantification of Uncertainty


Author: Lorenz Biegler,George Biros,Omar Ghattas,Matthias Heinkenschloss,David Keyes,Bani Mallick,Luis Tenorio,Bart van Bloemen Waanders,Karen Willcox,Youssef Marzouk
Publisher: John Wiley & Sons
ISBN: 1119957583
Category: Mathematics
Page: 388
View: 1109

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This book focuses on computational methods for large-scale statistical inverse problems and provides an introduction to statistical Bayesian and frequentist methodologies. Recent research advances for approximation methods are discussed, along with Kalman filtering methods and optimization-based approaches to solving inverse problems. The aim is to cross-fertilize the perspectives of researchers in the areas of data assimilation, statistics, large-scale optimization, applied and computational mathematics, high performance computing, and cutting-edge applications. The solution to large-scale inverse problems critically depends on methods to reduce computational cost. Recent research approaches tackle this challenge in a variety of different ways. Many of the computational frameworks highlighted in this book build upon state-of-the-art methods for simulation of the forward problem, such as, fast Partial Differential Equation (PDE) solvers, reduced-order models and emulators of the forward problem, stochastic spectral approximations, and ensemble-based approximations, as well as exploiting the machinery for large-scale deterministic optimization through adjoint and other sensitivity analysis methods. Key Features: Brings together the perspectives of researchers in areas of inverse problems and data assimilation. Assesses the current state-of-the-art and identify needs and opportunities for future research. Focuses on the computational methods used to analyze and simulate inverse problems. Written by leading experts of inverse problems and uncertainty quantification. Graduate students and researchers working in statistics, mathematics and engineering will benefit from this book.