A novel exposition of the analysis of variance and regression. The key feature here is that these tools are viewed in their natural mathematical setting - the geometry of finite dimensions. This is because geometry clarifies the basic statistics and unifies the many aspects of analysing variance and regression.

Probability is an area of mathematics of tremendous contemporary importance across all aspects of human endeavour. This book is a compact account of the basic features of probability and random processes at the level of first and second year mathematics undergraduates and Masters' students in cognate fields. It is suitable for a first course in probability, plus a follow-up course in random processes including Markov chains. A special feature is the authors' attention to rigorous mathematics: not everything is rigorous, but the need for rigour is explained at difficult junctures. The text is enriched by simple exercises, together with problems (with very brief hints) many of which are taken from final examinations at Cambridge and Oxford. The first eight chapters form a course in basic probability, being an account of events, random variables, and distributions - discrete and continuous random variables are treated separately - together with simple versions of the law of large numbers and the central limit theorem. There is an account of moment generating functions and their applications. The following three chapters are about branching processes, random walks, and continuous-time random processes such as the Poisson process. The final chapter is a fairly extensive account of Markov chains in discrete time. This second edition develops the success of the first edition through an updated presentation, the extensive new chapter on Markov chains, and a number of new sections to ensure comprehensive coverage of the syllabi at major universities.

This book primarily aims to discuss emerging topics in statistical methods and to booster research, education, and training to advance statistical modeling on interval-censored survival data. Commonly collected from public health and biomedical research, among other sources, interval-censored survival data can easily be mistaken for typical right-censored survival data, which can result in erroneous statistical inference due to the complexity of this type of data. The book invites a group of internationally leading researchers to systematically discuss and explore the historical development of the associated methods and their computational implementations, as well as emerging topics related to interval-censored data. It covers a variety of topics, including univariate interval-censored data, multivariate interval-censored data, clustered interval-censored data, competing risk interval-censored data, data with interval-censored covariates, interval-censored data from electric medical records, and misclassified interval-censored data. Researchers, students, and practitioners can directly make use of the state-of-the-art methods covered in the book to tackle their problems in research, education, training and consultation.

This book analyses the models for major risks related to flight safety in the aviation sector and presents risk estimation methods through examples of several known aviation enterprises. The book provides a comprehensive content for professionals engaged in the development of flight safety regulatory framework as well as in the design and operation of ground-based or on-board flight support radio electronic systems. The book is also useful for senior students and postgraduates in aviation specialties, especially those related to air traffic management.

Geometric tolerances are changing the way we design and manufacture industrial products. Geometric Tolerances covers their impact on the world of design and production, highlighting new perspectives, possibilities, current issues and future challenges. The topics covered are designed to be relevant to readers from a variety of backgrounds, ranging from product designers and manufacturers to quality inspection engineers and quality engineers involved in statistical process monitoring. Areas included are: * selection of appropriate geometric tolerances and how they stack up in assembled products; * inspection of parts subjected to geometric tolerancing from the macro to the micro and sub-micro scales; and * enhancement of efficiency and efficacy of quality monitoring. Geometric Tolerances provides the reader with the most recent scientific research in the field, as well as with a significant amount of real-life industrial case studies, delivering a multidisciplinary, synoptic view of one of the hottest and most strategic topics in industrial production.

This book showcases state-of-the-art advances in service science and related fields of research, education, and practice. It presents emerging technologies and applications in contexts ranging from healthcare, energy, finance, and information technology to transportation, sports, logistics, and public services. Regardless of its size and service, every service organization is a service system. Due to the socio-technical nature of service systems, a systems approach must be adopted in order to design, develop and deliver services aimed at meeting end users' utilitarian and socio-psychological needs alike. Understanding services and service systems often requires combining multiple methods to consider how interactions between people, technologies, organizations and information create value under various conditions. The papers in this volume highlight a host of ways to approach these challenges in service science and are based on submissions to the 2021 INFORMS Conference on Service Science.

This book delves into the concept of data as a critical enterprise asset needed for informed decision making, compliance, regulatory reporting and insights into trends, behaviors, performance and patterns. With good data being key to staying ahead in a competitive market, enterprises capture and store exponential volumes of data. Considering the business impact of data, there needs to be adequate management around it to derive the best value. Data governance is one of the core data management related functions. However, it is often overlooked, misunderstood or confused with other terminologies and data management functions. Given the pervasiveness of data and the importance of data, this book provides comprehensive understanding of the business drivers for data governance and benefits of data governance, the interactions of data governance function with other data management functions and various components and aspects of data governance that can be facilitated by technology and tools, the distinction between data management tools and data governance tools, the readiness checks to perform before exploring the market to purchase a data governance tool, the different aspects that must be considered when comparing and selecting the appropriate data governance technologies and tools from large number of options available in the marketplace and the different market players that provide tools for supporting data governance. This book combines the data and data governance knowledge that the author has gained over years of working in different industrial and research programs and projects associated with data, processes and technologies with unique perspectives gained through interviews with thought leaders and data experts. This book is highly beneficial for IT students, academicians, information management and business professionals and researchers to enhance their knowledge and get guidance on implementing data governance in their own data initiatives.

This book describes concepts and tools needed for water resources management, including methods for modeling, simulation, optimization, big data analysis, data mining, remote sensing, geographical information system, game theory, conflict resolution, System dynamics, agent-based models, multiobjective, multicriteria, and multiattribute decision making and risk and uncertainty analysis, for better and sustainable management of water resources and consumption, thus mitigating the present and future global water shortage crisis. It presents the applications of these tools through case studies which demonstrate its benefits of proper management of water resources systems. This book acts as a reference for students, professors, industrial practitioners, and stakeholders in the field of water resources and hydrology.

A Course in Mathematical and Statistical Ecology

The volume represents presentations given at the 86th annual meeting of the Psychometric Society, held virtually on July 19-23, 2021. About 500 individuals contributed paper presentations, symposiums, poster presentations, pre-conference workshops, keynote presentations, and invited presentations. Since the 77th meeting, Springer has published the conference proceedings volume from this annual meeting to allow presenters to share their work and ideas with the wider research community, while still undergoing a thorough review process. This proceedings covers a diverse set of psychometric topics, including item response theory, Bayesian models, reliability, longitudinal measures, and cognitive diagnostic models.

During the last two decades, structural equation modeling (SEM) has emerged as a powerful multivariate data analysis tool in social science research settings, especially in the fields of sociology, psychology, and education. Although its roots can be traced back to the first half of this century, when Spearman (1904) developed factor analysis and Wright (1934) introduced path analysis, it was not until the 1970s that the works by Karl Joreskog and his associates (e. g., Joreskog, 1977; Joreskog and Van Thillo, 1973) began to make general SEM techniques accessible to the social and behavioral science research communities. Today, with the development and increasing avail ability of SEM computer programs, SEM has become a well-established and respected data analysis method, incorporating many of the traditional analysis techniques as special cases. State-of-the-art SEM software packages such as LISREL (Joreskog and Sorbom, 1993a, b) and EQS (Bentler, 1993; Bentler and Wu, 1993) handle a variety of ordinary least squares regression designs as well as complex structural equation models involving variables with arbitrary distributions. Unfortunately, many students and researchers hesitate to use SEM methods, perhaps due to the somewhat complex underlying statistical repre sentation and theory. In my opinion, social science students and researchers can benefit greatly from acquiring knowledge and skills in SEM since the methods-applied appropriately-can provide a bridge between the theo retical and empirical aspects of behavioral research."

Focussing on applications, this book covers a very broad range, including simple and complex univariate and multivariate density estimation, nonparametric regression estimation, categorical data smoothing, and applications of smoothing to other areas of statistics. It will thus be of particular interest to data analysts, as arguments generally proceed from actual data rather than statistical theory, while the "Background Material" sections will interest statisticians studying the field. Over 750 references allow researchers to find the original sources for more details, and the "Computational Issues" sections provide sources for statistical software that use the methods discussed. Each chapter includes exercises with a heavily computational focus based upon the data sets used in the book, making it equally suitable as a textbook for a course in smoothing.

First Published in 1967. Routledge is an imprint of Taylor & Francis, an informa company.

This monograph addresses two quite different topics, in the belief that each can shed light on the other. Firstly, it lays the foundation for a particular view of the bootstrap. Secondly, it gives an account of Edgeworth expansion. Chapter 1 is about the bootstrap, witih almost no mention of Edgeworth expansion; Chapter 2 is about Edgeworth expansion, with scarcely a word about the bootstrap; and Chapters 3 and 4 bring these two themes together, using Edgeworth expansion to explore and develop the properites of the bootstrap. The book is aimed a a graduate level audience who has some exposure to the methods of theoretical statistics. However, technical details are delayed until the last chapter (entitled "Details of Mathematical Rogour"), and so a mathematically able reader without knowledge of the rigorous theory of probability will have no trouble understanding the first four-fifths of the book. The book simultaneously fills two gaps in the literature; it provides a very readable graduate level account of the theory of Edgeworth expansion, and it gives a detailed introduction to the theory of bootstrap methods.

This volume contains the papers presented at the meeting "Distributions with given marginals and statistical modelling", held in Barcelona (Spain), July 17- 20, 2000. This is the fourth meeting on given marginals, showing that this topic has aremarkable interest. BRIEF HISTORY The construction of distributions with given marginals started with the seminal papers by Hoeffding (1940) and Fn!chet (1951). Since then, many others have contributed on this topic: Dall' Aglio, Farlie, Gumbel, Johnson, Kellerer, Kotz, Morgenstern, Marshali, Olkin, Strassen, Vitale, Whitt, etc., as weIl as Arnold, Cambanis, Deheuvels, Genest, Frank, Joe, Kirneldorf, Nelsen, Ruschendorf, Sampson, Scarsini, Tiit, etc. In 1957 Sklar and Schweizer introduced probabilistic metric spaces. In 1975 Kirneldorf and Sampson studied the uniform representation of a bivariate dis- tribution and proposed the desirable conditions that should be satisfied by any bivariate family. In 1991 Darsow, Nguyen and Olsen defined a natural operation between cop- ulas, with applications in stochastic processes. In 1993, AIsina, Nelsen and Schweizer introduced the notion of quasi-copula.

Spaces of homogeneous type were introduced as a generalization to the Euclidean space and serve as a suffi cient setting in which one can generalize the classical isotropic Harmonic analysis and function space theory. This setting is sometimes too general, and the theory is limited. Here, we present a set of fl exible ellipsoid covers of n that replace the Euclidean balls and support a generalization of the theory with fewer limitations.

An accessible introduction to probability, stochastic processes, and statistics for computer science and engineering applications

This updated and revised edition of the popular classic relates fundamental concepts in probability and statistics to the computer sciences and engineering. The author uses Markov chains and other statistical tools to illustrate processes in reliability of computer systems and networks, fault tolerance, and performance.

This edition features an entirely new section on stochastic Petri nets–as well as new sections on system availability modeling, wireless system modeling, numerical solution techniques for Markov chains, and software reliability modeling, among other subjects. Extensive revisions take new developments in solution techniques and applications into account and bring this work totally up to date. It includes more than 200 worked examples and self-study exercises for each section.

Probability and Statistics with Reliability, Queuing and Computer Science Applications, Second Edition offers a comprehensive introduction to probability, stochastic processes, and statistics for students of computer science, electrical and computer engineering, and applied mathematics. Its wealth of practical examples and up-to-date information makes it an excellent resource for practitioners as well.

Matrix-analytic and related methods have become recognized as an important and fundamental approach for the mathematical analysis of general classes of complex stochastic models. Research in the area of matrix-analytic and related methods seeks to discover underlying probabilistic structures intrinsic in such stochastic models, develop numerical algorithms for computing functionals (e.g., performance measures) of the underlying stochastic processes, and apply these probabilistic structures and/or computational algorithms within a wide variety of fields. This volume presents recent research results on: the theory, algorithms and methodologies concerning matrix-analytic and related methods in stochastic models; and the application of matrix-analytic and related methods in various fields, which includes but is not limited to computer science and engineering, communication networks and telephony, electrical and industrial engineering, operations research, management science, financial and risk analysis, and bio-statistics. These research studies provide deep insights and understanding of the stochastic models of interest from a mathematics and/or applications perspective, as well as identify directions for future research.

An effective technique for data analysis in the social sciences

The recent explosion in longitudinal data in the social sciences highlights the need for this timely publication. Latent Curve Models: A Structural Equation Perspective provides an effective technique to analyze latent curve models (LCMs). This type of data features random intercepts and slopes that permit each case in a sample to have a different trajectory over time. Furthermore, researchers can include variables to predict the parameters governing these trajectories.

The authors synthesize a vast amount of research and findings and, at the same time, provide original results. The book analyzes LCMs from the perspective of structural equation models (SEMs) with latent variables. While the authors discuss simple regression-based procedures that are useful in the early stages of LCMs, most of the presentation uses SEMs as a driving tool. This cutting-edge work includes some of the authors' recent work on the autoregressive latent trajectory model, suggests new models for method factors in multiple indicators, discusses repeated latent variable models, and establishes the identification of a variety of LCMs.

This text has been thoroughly class-tested and makes extensive use of pedagogical tools to aid readers in mastering and applying LCMs quickly and easily to their own data sets. Key features include: Chapter introductions and summaries that provide a quick overview of highlights Empirical examples provided throughout that allow readers to test their newly found knowledge and discover practical applications Conclusions at the end of each chapter that stress the essential points that readers need to understand foradvancement to more sophisticated topics Extensive footnoting that points the way to the primary literature for more information on particular topics

With its emphasis on modeling and the use of numerous examples, this is an excellent book for graduate courses in latent trajectory models as well as a supplemental text for courses in structural modeling. This book is an excellent aid and reference for researchers in quantitative social and behavioral sciences who need to analyze longitudinal data.

This book is based on the view that cognitive skills are best acquired by solving challenging, non-standard probability problems.

Many puzzles and problems presented here are either new within a problem solving context (although as topics in fundamental research they are long known) or are variations of classical problems which follow directly from elementary concepts. A small number of particularly instructive problems is taken from previous sources which in this case are generally given. This book will be a handy resource for professors looking for problems to assign, for undergraduate math students, and for a more general audience of amateur scientists.

A friendly and systematic introduction to the theory and applications. The book begins with the sums of independent random variables and vectors, with maximal inequalities and sharp estimates on moments, which are later used to develop and interpret decoupling inequalities. Decoupling is first introduced as it applies to randomly stopped processes and unbiased estimation. The authors then proceed with the theory of decoupling in full generality, paying special attention to comparison and interplay between martingale and decoupling theory, and to applications. These include limit theorems, moment and exponential inequalities for martingales and more general dependence structures, biostatistical implications, and moment convergence in Anscombe's theorem and Wald's equation for U--statistics. Addressed to researchers in probability and statistics and to graduates, the expositon is at the level of a second graduate probability course, with a good portion of the material fit for use in a first year course.

Each year hundreds of new drugs are approved for the marketplace. The approval of a single new drug is the result of years of screening tens of thousands of compounds, performing pre-clinical research on their effects, and designing, implementing, and analyzing the results of clinical trials. This book provides a general guide to statistical methods used in the pharmaceutical industry, and is aimed at graduate students and researchers who want to know more about statistical applications in all phases of the drug development process. The 19 chapters authored by over 30 statisticians working in the industry follow the general sequence of drug development, from pre-clinical research and saftey assessment to dose finding, safety studies, large clinical trials, analysis of health economic data, and fianlly manufacturing and production. Special topics such as single patient analysis and the impact of patient compliance show the broad spectrum of applications of data analysis methods. Each chapter illustrates a practical problem using data from actual studies by describing the study, the data, the methods, and the results. All of the analyses are done with S-PLUS, and the data and code are provided both in appendices to the chapters and on the companion Springer-Verlag web site, making it possible to reproduce the results and extend the analyses. Prior knowledge of the software is not required to follow the analyses. Steven P. Millard is a statistical consultant and also Manager of Consulting Services for MathSoft, Inc. (Data Analysis Products Division.) He has applied statistical methods to projects ranging from quality control in bioassay to measuring water quality to automating home appraisal, and has taught courses in S-PLUS for over 10 years. He is the author of the book Environmental Statistics with S-PLUS (CRC Press) as well as the S-PLUS add-in module ENVIRONMENTALSTATS for S-PLUS. Andreas Krause is a statistical consultant in the pharmaceutical industry and works for Novartis Pharma AG. He has extensive experience in graphical and numerical data analysis as well as programming, has taught numerous classes with and on S-PLUS, and is an S_PLUS user from the early days on. He is also author of the book The Basics of S and S-PLUS (Springer).

The book shows that the analytic combinatorics (AC) method encodes the combinatorial problems of multiple object tracking-without information loss-into the derivatives of a generating function (GF). The book lays out an easy-to-follow path from theory to practice and includes salient AC application examples. Since GFs are not widely utilized amongst the tracking community, the book takes the reader from the basics of the subject to applications of theory starting from the simplest problem of single object tracking, and advancing chapter by chapter to more challenging multi-object tracking problems. Many established tracking filters (e.g., Bayes-Markov, PDA, JPDA, IPDA, JIPDA, CPHD, PHD, multi-Bernoulli, MBM, LMBM, and MHT) are derived in this manner with simplicity, economy, and considerable clarity. The AC method gives significant and fresh insights into the modeling assumptions of these filters and, thereby, also shows the potential utility of various approximation methods that are well established techniques in applied mathematics and physics, but are new to tracking. These unexplored possibilities are reviewed in the final chapter of the book.

This fairly self-contained work embraces a broad range of topics in analysis at the graduate level, requiring only a sound knowledge of calculus and the functions of one variable. A key feature of this lively yet rigorous and systematic exposition is the historical accounts of ideas and methods pertaining to the relevant topics. Most interesting and useful are the connections developed between analysis and other mathematical disciplines, in this case, numerical analysis and probability theory.

The text is divided into two parts: The first examines the systems of real and complex numbers and deals with the notion of sequences in this context. After the presentation of natural numbers as a subset of the reals, elements of combinatorics and a discussion of the mathematical notion of the infinite are introduced. The second part is dedicated to discrete processes starting with a study of the processes of infinite summation both in the case of numerical series and of power series.