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A self-contained introduction to the methods and techniques of symmetry analysis used to solve ODEs and PDEs Symmetry Analysis of Differential Equations: An Introduction presents an accessible approach to the uses of symmetry methods in solving both ordinary differential equations (ODEs) and partial differential equations (PDEs). Providing comprehensive coverage, the book fills a gap in the literature by discussing elementary symmetry concepts and invariance, including methods for reducing the complexity of ODEs and PDEs in an effort to solve the associated problems. Thoroughly class-tested, the author presents classical methods in a systematic, logical, and well-balanced manner. As the book progresses, the chapters graduate from elementary symmetries and the invariance of algebraic equations, to ODEs and PDEs, followed by coverage of the nonclassical method and compatibility. Symmetry Analysis of Differential Equations: An Introduction also features: Detailed, step-by-step examples to guide readers through the methods of symmetry analysis End-of-chapter exercises, varying from elementary to advanced, with select solutions to aid in the calculation of the presented algorithmic methods Symmetry Analysis of Differential Equations: An Introduction is an ideal textbook for upper-undergraduate and graduate-level courses in symmetry methods and applied mathematics. The book is also a useful reference for professionals in science, physics, and engineering, as well as anyone wishing to learn about the use of symmetry methods in solving differential equations.

Several points of disagreement exist between different modelling traditions as to whether complex models are always better than simpler models, as to how to combine results from different models and how to propagate model uncertainty into forecasts. This book represents the result of collaboration between scientists from many disciplines to show how these conflicts can be resolved. Key Features: Introduces important concepts in modelling, outlining different traditions in the use of simple and complex modelling in statistics. Provides numerous case studies on complex modelling, such as climate change, flood risk and new drug development. Concentrates on varying models, including flood risk analysis models, the petrol industry forecasts and summarizes the evolution of water distribution systems. Written by experienced statisticians and engineers in order to facilitate communication between modellers in different disciplines. Provides a glossary giving terms commonly used in different modelling traditions. This book provides a much-needed reference guide to approaching statistical modelling. Scientists involved with modelling complex systems in areas such as climate change, flood prediction and prevention, financial market modelling and systems engineering will benefit from this book. It will also be a useful source of modelling case histories.

Praise for the Fourth Edition «As with previous editions, the authors have produced a leading textbook on regression.» —Journal of the American Statistical Association A comprehensive and up-to-date introduction to the fundamentals of regression analysis Introduction to Linear Regression Analysis, Fifth Edition continues to present both the conventional and less common uses of linear regression in today’s cutting-edge scientific research. The authors blend both theory and application to equip readers with an understanding of the basic principles needed to apply regression model-building techniques in various fields of study, including engineering, management, and the health sciences. Following a general introduction to regression modeling, including typical applications, a host of technical tools are outlined such as basic inference procedures, introductory aspects of model adequacy checking, and polynomial regression models and their variations. The book then discusses how transformations and weighted least squares can be used to resolve problems of model inadequacy and also how to deal with influential observations. The Fifth Edition features numerous newly added topics, including: A chapter on regression analysis of time series data that presents the Durbin-Watson test and other techniques for detecting autocorrelation as well as parameter estimation in time series regression models Regression models with random effects in addition to a discussion on subsampling and the importance of the mixed model Tests on individual regression coefficients and subsets of coefficients Examples of current uses of simple linear regression models and the use of multiple regression models for understanding patient satisfaction data. In addition to Minitab, SAS, and S-PLUS, the authors have incorporated JMP and the freely available R software to illustrate the discussed techniques and procedures in this new edition. Numerous exercises have been added throughout, allowing readers to test their understanding of the material. Introduction to Linear Regression Analysis, Fifth Edition is an excellent book for statistics and engineering courses on regression at the upper-undergraduate and graduate levels. The book also serves as a valuable, robust resource for professionals in the fields of engineering, life and biological sciences, and the social sciences.

"This book should have a place on the bookshelf of every forensic scientist who cares about the science of evidence interpretation" Dr. Ian Evett, Principal Forensic Services Ltd, London, UK Continuing developments in science and technology mean that the amounts of information forensic scientists are able to provide for criminal investigations is ever increasing. The commensurate increase in complexity creates difficulties for scientists and lawyers with regard to evaluation and interpretation, notably with respect to issues of inference and decision. Probability theory, implemented through graphical methods, and specifically Bayesian networks, provides powerful methods to deal with this complexity. Extensions of these methods to elements of decision theory provide further support and assistance to the judicial system. Bayesian Networks for Probabilistic Inference and Decision Analysis in Forensic Science provides a unique and comprehensive introduction to the use of Bayesian decision networks for the evaluation and interpretation of scientific findings in forensic science, and for the support of decision-makers in their scientific and legal tasks. • Includes self-contained introductions to probability and decision theory. • Develops the characteristics of Bayesian networks, object-oriented Bayesian networks and their extension to decision models. • Features implementation of the methodology with reference to commercial and academically available software. • Presents standard networks and their extensions that can be easily implemented and that can assist in the reader’s own analysis of real cases. • Provides a technique for structuring problems and organizing data based on methods and principles of scientific reasoning. • Contains a method for the construction of coherent and defensible arguments for the analysis and evaluation of scientific findings and for decisions based on them. • Is written in a lucid style, suitable for forensic scientists and lawyers with minimal mathematical background. • Includes a foreword by Ian Evett. The clear and accessible style of this second edition makes this book ideal for all forensic scientists, applied statisticians and graduate students wishing to evaluate forensic findings from the perspective of probability and decision analysis. It will also appeal to lawyers and other scientists and professionals interested in the evaluation and interpretation of forensic findings, including decision making based on scientific information.

Практическое пособие предназначено для учащихся 2—3 классов начальной школы для самостоятельного изучения таблицы умножения. Основные принципы, взятые при создании рабочей тетради, – это понимание взаимосвязи умножения и сложения, умножения и деления, а также разнообразие упражнений, которые способствуют запоминанию.

Statistical Methods for Spatial and Spatio-Temporal Data Analysis provides a complete range of spatio-temporal covariance functions and discusses ways of constructing them. This book is a unified approach to modeling spatial and spatio-temporal data together with significant developments in statistical methodology with applications in R. This book includes: Methods for selecting valid covariance functions from the empirical counterparts that overcome the existing limitations of the traditional methods. The most innovative developments in the different steps of the kriging process. An up-to-date account of strategies for dealing with data evolving in space and time. An accompanying website featuring R code and examples

Praise for the Second Edition “This book should be an essential part of the personal library of every practicing statistician.”—Technometrics Thoroughly revised and updated, the new edition of Nonparametric Statistical Methods includes additional modern topics and procedures, more practical data sets, and new problems from real-life situations. The book continues to emphasize the importance of nonparametric methods as a significant branch of modern statistics and equips readers with the conceptual and technical skills necessary to select and apply the appropriate procedures for any given situation. Written by leading statisticians, Nonparametric Statistical Methods, Third Edition provides readers with crucial nonparametric techniques in a variety of settings, emphasizing the assumptions underlying the methods. The book provides an extensive array of examples that clearly illustrate how to use nonparametric approaches for handling one- or two-sample location and dispersion problems, dichotomous data, and one-way and two-way layout problems. In addition, the Third Edition features: The use of the freely available R software to aid in computation and simulation, including many new R programs written explicitly for this new edition New chapters that address density estimation, wavelets, smoothing, ranked set sampling, and Bayesian nonparametrics Problems that illustrate examples from agricultural science, astronomy, biology, criminology, education, engineering, environmental science, geology, home economics, medicine, oceanography, physics, psychology, sociology, and space science Nonparametric Statistical Methods, Third Edition is an excellent reference for applied statisticians and practitioners who seek a review of nonparametric methods and their relevant applications. The book is also an ideal textbook for upper-undergraduate and first-year graduate courses in applied nonparametric statistics.

AN INTERDISCIPLINARY PERSPECTIVE TO THE EVOLUTION OF THEORY AND METHODOLOGY WITHIN COGNITIVE INTERVIEW PROCESSES Providing a comprehensive approach to cognitive interviewing in the field of survey methodology, Cognitive Interviewing Methodology delivers a clear guide that draws upon modern, cutting-edge research from a variety of fields. Each chapter begins by summarizing the prevailing paradigms that currently dominate the field of cognitive interviewing. Then underlying theoretical foundations are presented, which supplies readers with the necessary background to understand newly-evolving techniques in the field. The theories lead into developed and practiced methods by leading practitioners, researchers, and/or academics. Finally, the edited guide lays out the limitations of cognitive interviewing studies and explores the benefits of cognitive interviewing with other methodological approaches. With a primary focus on question evaluation, Cognitive Interviewing Methodology also includes: Step-by-step procedures for conducting cognitive interviewing studies, which includes the various aspects of data collection, questionnaire design, and data interpretation Newly developed tools to benefit cognitive interviewing studies as well as the field of question evaluation, such as Q-Notes, a data entry and analysis software application, and Q-Bank, an online resource that houses question evaluation studies A unique method for questionnaire designers, survey managers, and data users to analyze, present, and document survey data results from a cognitive interviewing study An excellent reference for survey researchers and practitioners in the social sciences who utilize cognitive interviewing techniques in their everyday work, Cognitive Interviewing Methodology is also a useful supplement for courses on survey methods at the upper-undergraduate and graduate-level.

This book aims to help engineers, Masters students and young researchers to understand and gain a general knowledge of logistic systems optimization problems and techniques, such as system design, layout, stock management, quality management, lot-sizing or scheduling. It summarizes the evaluation and optimization methods used to solve the most frequent problems. In particular, the authors also emphasize some recent and interesting scientific developments, as well as presenting some industrial applications and some solved instances from real-life cases. Performance evaluation tools (Petri nets, the Markov process, discrete event simulation, etc.) and optimization techniques (branch-and-bound, dynamic programming, genetic algorithms, ant colony optimization, etc.) are presented first. Then, new optimization methods are presented to solve systems design problems, layout problems and buffer-sizing optimization. Forecasting methods, inventory optimization, packing problems, lot-sizing quality management and scheduling are presented with examples in the final chapters.

A new edition of the definitive guide to logistic regression modeling for health science and other applications This thoroughly expanded Third Edition provides an easily accessible introduction to the logistic regression (LR) model and highlights the power of this model by examining the relationship between a dichotomous outcome and a set of covariables. Applied Logistic Regression, Third Edition emphasizes applications in the health sciences and handpicks topics that best suit the use of modern statistical software. The book provides readers with state-of-the-art techniques for building, interpreting, and assessing the performance of LR models. New and updated features include: A chapter on the analysis of correlated outcome data A wealth of additional material for topics ranging from Bayesian methods to assessing model fit Rich data sets from real-world studies that demonstrate each method under discussion Detailed examples and interpretation of the presented results as well as exercises throughout Applied Logistic Regression, Third Edition is a must-have guide for professionals and researchers who need to model nominal or ordinal scaled outcome variables in public health, medicine, and the social sciences as well as a wide range of other fields and disciplines.

A reference to answer all your statistical confidentiality questions. This handbook provides technical guidance on statistical disclosure control and on how to approach the problem of balancing the need to provide users with statistical outputs and the need to protect the confidentiality of respondents. Statistical disclosure control is combined with other tools such as administrative, legal and IT in order to define a proper data dissemination strategy based on a risk management approach. The key concepts of statistical disclosure control are presented, along with the methodology and software that can be used to apply various methods of statistical disclosure control. Numerous examples and guidelines are also featured to illustrate the topics covered. Statistical Disclosure Control: Presents a combination of both theoretical and practical solutions Introduces all the key concepts and definitions involved with statistical disclosure control. Provides a high level overview of how to approach problems associated with confidentiality. Provides a broad-ranging review of the methods available to control disclosure. Explains the subtleties of group disclosure control. Features examples throughout the book along with case studies demonstrating how particular methods are used. Discusses microdata, magnitude and frequency tabular data, and remote access issues. Written by experts within leading National Statistical Institutes. Official statisticians, academics and market researchers who need to be informed and make decisions on disclosure limitation will benefit from this book.

In recent years, the theory has become widely accepted and has been further developed, but a detailed introduction is needed in order to make the material available and accessible to a wide audience. This will be the first book providing such an introduction, covering core theory and recent developments which can be applied to many application areas. All authors of individual chapters are leading researchers on the specific topics, assuring high quality and up-to-date contents. An Introduction to Imprecise Probabilities provides a comprehensive introduction to imprecise probabilities, including theory and applications reflecting the current state if the art. Each chapter is written by experts on the respective topics, including: Sets of desirable gambles; Coherent lower (conditional) previsions; Special cases and links to literature; Decision making; Graphical models; Classification; Reliability and risk assessment; Statistical inference; Structural judgments; Aspects of implementation (including elicitation and computation); Models in finance; Game-theoretic probability; Stochastic processes (including Markov chains); Engineering applications. Essential reading for researchers in academia, research institutes and other organizations, as well as practitioners engaged in areas such as risk analysis and engineering.