Volume 1: (edited by Keith W. Hipel) In this landmark collection of papers, highly respected scientists and engineers from around the world present the latest research results in extreme value analyses for floods and droughts. Two approaches that are commonly employed in flood frequency analyses are the maximum annual flood and partial duration series or peak over threshold procedures. Recent theoretical advances as well as illustrative applications are described in detail for each of these approaches. Additionally, droughts and storms are systematically studied using appropriate probabilistic models. A major part of the volume is devoted to frequency analyses and fitting extreme value distributions to hydrological data. Other thought-provoking topics include regionalization techniques, distributed models, entropy and fractal analysis. Volume 1 is of interest to researchers, teachers, students and practitioners who wish to place themselves at the leading edge of flood frequency and drought analyses. Volume 2: (edited by Keith W. Hipel) World renowned scientists present valuable contributions to stochastic and statistical modelling of groundwater and surface water systems. The philosophy of probabilistic modelling in the hydrological sciences is put into proper perspective and the importance of stochastic differential equations in the environmental sciences is explained and illustrated. The new research ideas put forward in groundwater modelling will assist decision makers in tackling challenging problems such as controlling pollution of underground aquifers and obtaining adequate water supplies. Additionally, different types of stochastic models are used in modelling a range ofinteresting surface water problems. Other topics covered in this landmark volume include stochastic optimization, moment analysis, carbon dioxide modelling and rainfall prediction. Volume 2 is of interest to researchers, teachers, students and practitioners who wish to be at the leading edge of stochastic and statistical modelling in the environmental sciences. Volume 3: (edited by Keith W. Hipel; A. Ian McLeod; U.S. Panu; Vijay P. Singh) International experts from around the globe present a rich variety of intriguing developments in time series analysis in hydrology and environmental engineering. Climatic change is of great concern to everyone and significant contributions to this challenging research topic are put forward by internationally renowned authors. A range of interesting applications in hydrological forecasting are given for case studies in reservoir operation in North America, Asia and South America. Additionally, progress in entropy research is described and entropy concepts are applied to various water resource systems problems. Neural networks are employed for forecasting runoff and water demand. Moreover, graphical, nonparametric and parametric trend analyses methods are compared and applied to water quality time series. Other topics covered in this landmark volume include spatial analyses, spectral analyses and different methods for stream-flow modelling. Volume 3 constitutes an invaluable resource for researchers, teachers, students and practitioners who wish to be at the forefront of time series analysis in the environmental sciences. Volume 4: (edited by Keith W. Hipel; Liping Fang) In this landmark set of papers, experts from around the world present the latest andmost promising approaches to both the theory and practice of effective environmental management. To achieve sustainable development, organizations and individual citizens must comply with environmental laws and regulations. Accordingly, a major contribution of this book is the presentation of original techniques for designing effective environmental policies, regulations, inspection procedures and monitoring systems. Interesting methods for modelling risk and decision making problems are discussed from an environmental management perspective. Moreover, knowledge-based techniques for handling environmental problems are also investigated. Finally, the last main part of the book describes optimal approaches to reservoir operation and control that take into account appropriate multiple objectives. Volume 4 is of direct interest to researchers, teachers, students and practitioners concerned with the latest developments in environmental management and sustainable development.

Statistics for Sport and Exercise Studies guides the student through the full research process, from selecting the most appropriate statistical procedure, to analysing data, to the presentation of results, illustrating every key step in the process with clear examples, case-studies and data taken from real sport and exercise settings. Every chapter includes a range of features designed to help the student grasp the underlying concepts and relate each statistical procedure to their own research project, including definitions of key terms, practical exercises, worked examples and clear summaries. The book also offers an in-depth and practical guide to using SPSS in sport and exercise research, the most commonly used data analysis software in sport and exercise departments. In addition, a companion website includes more than 100 downloadable data sets and work sheets for use in or out of the classroom, full solutions to exercises contained in the book, plus over 1,300 PowerPoint slides for use by tutors and lecturers. Statistics for Sport and Exercise Studies is a complete, user-friendly introduction to the use of statistical tests, techniques and procedures in sport, exercise and related subjects. Visit the companion website at: www.routledge.com/cw/odonoghue

The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 35 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob.

Graduate students and postgraduates in Mathematics, Engineering and the Natural Sciences want to understand Applied Mathematics for the solution of everyday problems. Scholars of Roland Bulirsch working at universities, at research institutions and in industry combine research and review papers in this anthology. Their work is summed up under the title "From Nano to Space Applied Mathematics Inspired by Roland Bulirsch." More than 20 contributions are divided into scales: nano, micro, macro, space and real life. The contributions survey current research and present case studies very interesting and informative for both graduate students and postgraduates. The contributions show how modern Applied Mathematics influences our everyday lives. Several contributions include complex graphics and illustrations, many of them in color."

This is the second volume of the reworked second edition of a key work on Point Process Theory. Fully revised and updated by the authors who have reworked their 1988 first edition, it brings together the basic theory of random measures and point processes in a unified setting and continues with the more theoretical topics of the first edition: limit theorems, ergodic theory, Palm theory, and evolutionary behaviour via martingales and conditional intensity. The very substantial new material in this second volume includes expanded discussions of marked point processes, convergence to equilibrium, and the structure of spatial point processes.

This monograph deals with spatially dependent nonstationary time series in a way accessible to both time series econometricians wanting to understand spatial econometics, and spatial econometricians lacking a grounding in time series analysis. After charting key concepts in both time series and spatial econometrics, the book discusses how the spatial connectivity matrix can be estimated using spatial panel data instead of assuming it to be exogenously fixed. This is followed by a discussion of spatial nonstationarity in spatial cross-section data, and a full exposition of non-stationarity in both single and multi-equation contexts, including the estimation and simulation of spatial vector autoregression (VAR) models and spatial error correction (ECM) models. The book reviews the literature on panel unit root tests and panel cointegration tests for spatially independent data, and for data that are strongly spatially dependent. It provides for the first time critical values for panel unit root tests and panel cointegration tests when the spatial panel data are weakly or spatially dependent. The volume concludes with a discussion of incorporating strong and weak spatial dependence in non-stationary panel data models. All discussions are accompanied by empirical testing based on a spatial panel data of house prices in Israel.

This volume contains a unique collection of mathematical essays that resent a battery of techniques and approaches for the statistical analysis of heavy tailed distributions and processes. The articles cover a number of applications of heavy tailed modeling, running the gamut from insurance and finance, to telecommunications and the World Wide Web, and classical signal/noise detection problems.

Illustrate the usefulness and abuse of statistics in automotive safety arguments that are hidden from public view Show the importance of data and statistics in making safety-related changes that ultimately save or cost lives Discuss the impact of electric vehicles and autonomous vehicles on car safety

A "health disparity" refers to a higher burden of illness, injury, disability, or mortality experienced by one group relative to another. These disparities may be due to many factors including age, income, race, etc. This book will focus on their estimation, ranging from classical approaches including the quantification of a disparity, to more formal modelling, to modern approaches involving more flexible computational approaches. Features: * Presents an overview of methods and applications of health disparity estimation * First book to synthesize research in this field in a unified statistical framework * Covers classical approaches, and builds to more modern computational techniques * Includes many worked examples and case studies using real data * Discusses available software for estimation The book is designed primarily for researchers and graduate students in biostatistics, data science, and computer science. It will also be useful to many quantitative modelers in genetics, biology, sociology, and epidemiology.

Develops insights into solving complex problems in engineering, biomedical sciences, social science and economics based on artificial intelligence. Some of the problems studied are in interstate conflict, credit scoring, breast cancer diagnosis, condition monitoring, wine testing, image processing and optical character recognition. The author discusses and applies the concept of flexibly-bounded rationality which prescribes that the bounds in Nobel Laureate Herbert Simon's bounded rationality theory are flexible due to advanced signal processing techniques, Moore's Law and artificial intelligence. Artificial Intelligence Techniques for Rational Decision Making examines and defines the concepts of causal and correlation machines and applies the transmission theory of causality as a defining factor that distinguishes causality from correlation. It develops the theory of rational counterfactuals which are defined as counterfactuals that are intended to maximize the attainment of a particular goal within the context of a bounded rational decision making process. Furthermore, it studies four methods for dealing with irrelevant information in decision making: Theory of the marginalization of irrelevant information Principal component analysis Independent component analysis Automatic relevance determination method In addition it studies the concept of group decision making and various ways of effecting group decision making within the context of artificial intelligence. Rich in methods of artificial intelligence including rough sets, neural networks, support vector machines, genetic algorithms, particle swarm optimization, simulated annealing, incremental learning and fuzzy networks, this book will be welcomed by researchers and students working in these areas.

Applied Linear Regression for Business Analytics with R introduces regression analysis to business students using the R programming language with a focus on illustrating and solving real-time, topical problems. Specifically, this book presents modern and relevant case studies from the business world, along with clear and concise explanations of the theory, intuition, hands-on examples, and the coding required to employ regression modeling. Each chapter includes the mathematical formulation and details of regression analysis and provides in-depth practical analysis using the R programming language.

Noted for its comprehensive coverage, this greatly expanded new edition now covers the use of univariate and multivariate effect sizes. Many measures and estimators are reviewed along with their application, interpretation, and limitations. Noted for its practical approach, the book features numerous examples using real data for a variety of variables and designs, to help readers apply the material to their own data. Tips on the use of SPSS, SAS, R, and S-Plus are provided. The book's broad disciplinary appeal results from its inclusion of a variety of examples from psychology, medicine, education, and other social sciences. Special attention is paid to confidence intervals, the statistical assumptions of the methods, and robust estimators of effect sizes. The extensive reference section is appreciated by all.

With more than 40% new material, highlights of the new editon include:

• three new multivariate chapters covering effect sizes for analysis of covariance, multiple regression/correlation, and multivariate analysis of variance
• more learning tools in each chapter including introductions, summaries, "Tips and Pitfalls" and more conceptual and computational questions
• more coverage of univariate effect sizes, confidence intervals, and effect sizes for repeated measures to reflect their increased use in research
• more software references for calculating effect sizes and their confidence intervals including SPSS, SAS, R, and S-Plus
• the data used in the book are now provided on the web along with new data and suggested calculations with IBM SPSS syntax for computational practice.

Effect Sizes for Research covers standardized and unstandardized differences between means, correlational measures, strength of association, and parametric and nonparametric measures for between- and within-groups data.

Intended as a resource for professionals, researchers, and advanced students in a variety of fields, this book is also an excellent supplement for advanced statistics courses in psychology, education, the social sciences, business, and medicine. A prerequisite of introductory statistics through factorial analysis of variance and chi-square is recommended.

Given the rapid pace of development in economics and finance, a concise and up-to-date introduction to mathematical methods has become a prerequisite for all graduate students, even those not specializing in quantitative finance. This book offers an introductory text on mathematical methods for graduate students of economics and finance-and leading to the more advanced subject of quantum mathematics. The content is divided into five major sections: mathematical methods are covered in the first four sections, and can be taught in one semester. The book begins by focusing on the core subjects of linear algebra and calculus, before moving on to the more advanced topics of probability theory and stochastic calculus. Detailed derivations of the Black-Scholes and Merton equations are provided - in order to clarify the mathematical underpinnings of stochastic calculus. Each chapter of the first four sections includes a problem set, chiefly drawn from economics and finance. In turn, section five addresses quantum mathematics. The mathematical topics covered in the first four sections are sufficient for the study of quantum mathematics; Black-Scholes option theory and Merton's theory of corporate debt are among topics analyzed using quantum mathematics.

The first comprehensive account of the theory of mass transportation problems and its applications. In Volume I, the authors systematically develop the theory with emphasis on the Monge-Kantorovich mass transportation and the Kantorovich-Rubinstein mass transshipment problems. They then discuss a variety of different approaches towards solving these problems and exploit the rich interrelations to several mathematical sciences - from functional analysis to probability theory and mathematical economics. The second volume is devoted to applications of the above problems to topics in applied probability, theory of moments and distributions with given marginals, queuing theory, risk theory of probability metrics and its applications to various fields, among them general limit theorems for Gaussian and non-Gaussian limiting laws, stochastic differential equations and algorithms, and rounding problems. Useful to graduates and researchers in theoretical and applied probability, operations research, computer science, and mathematical economics, the prerequisites for this book are graduate level probability theory and real and functional analysis.

The study of quantum disorder has generated considerable research activity in mathematics and physics over past 40 years. While single-particle models have been extensively studied at a rigorous mathematical level, little was known about systems of several interacting particles, let alone systems with positive spatial particle density. Creating a consistent theory of disorder in multi-particle quantum systems is an important and challenging problem that largely remains open. Multi-scale Analysis for Random Quantum Systems with Interaction presents the progress that had been recently achieved in this area. The main focus of the book is on a rigorous derivation of the multi-particle localization in a strong random external potential field. To make the presentation accessible to a wider audience, the authors restrict attention to a relatively simple tight-binding Anderson model on a cubic lattice Zd. This book includes the following cutting-edge features: an introduction to the state-of-the-art single-particle localization theory an extensive discussion of relevant technical aspects of the localization theory a thorough comparison of the multi-particle model with its single-particle counterpart a self-contained rigorous derivation of both spectral and dynamical localization in the multi-particle tight-binding Anderson model. Required mathematical background for the book includes a knowledge of functional calculus, spectral theory (essentially reduced to the case of finite matrices) and basic probability theory. This is an excellent text for a year-long graduate course or seminar in mathematical physics. It also can serve as a standard reference for specialists.

First published in 1990, this is a reissue of Professor Hilary Putnam 's dissertation thesis, written in 1951, which concerns itself with The Meaning of the Concept of Probability in Application to Finite Sequences and the problems of the deductive justification for induction. Written under the direction of Putnam 's mentor, Hans Reichenbach, the book considers Reichenbach 's idealization of very long finite sequences as infinite sequences and the bearing this has upon Reichenbach 's pragmatic vindication of induction.

Beginning graduate students in mathematical sciences and related areas in physical and computer sciences and engineering are expected to be familiar with a daunting breadth of mathematics, but few have such a background. This bestselling book helps students fill in the gaps in their knowledge. Thomas A. Garrity explains the basic points and a few key results of all the most important undergraduate topics in mathematics, emphasizing the intuitions behind the subject. The explanations are accompanied by numerous examples, exercises and suggestions for further reading that allow the reader to test and develop their understanding of these core topics. Featuring four new chapters and many other improvements, this second edition of All the Math You Missed is an essential resource for advanced undergraduates and beginning graduate students who need to learn some serious mathematics quickly.

This book offers an exploration of the relationships between epistemology and probability in the work of Niels Bohr, Werner Heisenberg, and Erwin Schro- ] dinger, and in quantum mechanics and in modern physics as a whole. It also considers the implications of these relationships and of quantum theory itself for our understanding of the nature of human thinking and knowledge in general, or the ''epistemological lesson of quantum mechanics, '' as Bohr liked 1 to say. These implications are radical and controversial. While they have been seen as scientifically productive and intellectually liberating to some, Bohr and Heisenberg among them, they have been troublesome to many others, such as Schro] dinger and, most prominently, Albert Einstein. Einstein famously refused to believe that God would resort to playing dice or rather to playing with nature in the way quantum mechanics appeared to suggest, which is indeed quite different from playing dice. According to his later (sometime around 1953) remark, a lesser known or commented upon but arguably more important one: ''That the Lord should play dice], all right; but that He should gamble according to definite rules i. e., according to the rules of quantum mechanics, rather than 2 by merely throwing dice], that is beyond me. '' Although Einstein's invocation of God is taken literally sometimes, he was not talking about God but about the way nature works. Bohr's reply on an earlier occasion to Einstein's question 1 Cf."

With the critical role of statistics in the design, conduct, analysis and reporting of clinical trials or observational studies intended for regulatory purposes, numerous guidelines have been issued by regulatory authorities around the world focusing on statistical issues related to drug development. However, the available literature on this important topic is sporadic, and often not readily accessible to drug developers or regulatory personnel. This book provides a systematic exposition of the interplay between the two disciplines, including emerging themes pertaining to the acceleration of the development of pharmaceutical medicines to serve patients with unmet needs. Features: Regulatory and statistical interactions throughout the drug development continuum The critical role of the statistician in relation to the changing regulatory and healthcare landscapes Statistical issues that commonly arise in the course of drug development and regulatory interactions Trending topics in drug development, with emphasis on current regulatory thinking and the associated challenges and opportunities The book is designed to be accessible to readers with an intermediate knowledge of statistics, and can be a useful resource to statisticians, medical researchers, and regulatory personnel in drug development, as well as graduate students in the health sciences. The authors' decades of experience in the pharmaceutical industry and academia, and extensive regulatory experience, comes through in the many examples throughout the book.

Computer-aided modelling is one of the most effective means of getting to the root of a natural phenomenon and of predicting the consequences of human impact on the environment. General methods of numerical modelling of random processes have been effectively developed and the area of applications has rapidly expanded in recent years. This book deals with the development and investigation of numerical methods for simulation of random processes and fields. The book opens with a description of scalar and vector-valued Gaussian models, followed by non-Gaussian models. Furthermore, issues of convergence of approximate models of random fields are studied. The last part of this book is devoted to applications of stochastic modelling, in which new application areas such as simulation of meteorological processes and fields, sea surface undulation, and stochastic structure of clouds, are presented.

This book is an undergraduate text that introduces students to commonly used statistical methods in economics. Using examples based on contemporary economic issues and readily available data, it not only explains the mechanics of the various methods, but also guides students to connect statistical results to detailed economic interpretations. Because the goal is for students to be able to apply the statistical methods presented, online sources for economic data and directions for performing each task in Excel are also included.

Classical probability theory provides information about random walks after a fixed number of steps. For applications, however, it is more natural to consider random walks evaluated after a random number of steps. Examples are sequential analysis, queuing theory, storage and inventory theory, insurance risk theory, reliability theory, and the theory of contours. Stopped Random Walks: Limit Theorems and Applications shows how this theory can be used to prove limit theorems for renewal counting processes, first passage time processes, and certain two-dimenstional random walks, and to how these results are useful in various applications.

This second edition offers updated content and an outlook on further results, extensions and generalizations. A new chapter examines nonlinear renewal processes in order to present the analagous theory for perturbed random walks, modeled as a random walk plus "noise."

This monograph is a slightly revised version of my PhD thesis [86], com pleted in the Department of Computer Science at the University of Edin burgh in June 1988, with an additional chapter summarising more recent developments. Some of the material has appeared in the form of papers [50,88]. The underlying theme of the monograph is the study of two classical problems: counting the elements of a finite set of combinatorial structures, and generating them uniformly at random. In their exact form, these prob lems appear to be intractable for many important structures, so interest has focused on finding efficient randomised algorithms that solve them ap proxim~ly, with a small probability of error. For most natural structures the two problems are intimately connected at this level of approximation, so it is natural to study them together. At the heart of the monograph is a single algorithmic paradigm: sim ulate a Markov chain whose states are combinatorial structures and which converges to a known probability distribution over them. This technique has applications not only in combinatorial counting and generation, but also in several other areas such as statistical physics and combinatorial optimi sation. The efficiency of the technique in any application depends crucially on the rate of convergence of the Markov chain.

This book aims to present the impact of Artificial Intelligence (AI) and Big Data in healthcare for medical decision making and data analysis in myriad fields including Radiology, Radiomics, Radiogenomics, Oncology, Pharmacology, COVID-19 prognosis, Cardiac imaging, Neuroradiology, Psychiatry and others. This will include topics such as Artificial Intelligence of Thing (AIOT), Explainable Artificial Intelligence (XAI), Distributed learning, Blockchain of Internet of Things (BIOT), Cybersecurity, and Internet of (Medical) Things (IoTs). Healthcare providers will learn how to leverage Big Data analytics and AI as methodology for accurate analysis based on their clinical data repositories and clinical decision support. The capacity to recognize patterns and transform large amounts of data into usable information for precision medicine assists healthcare professionals in achieving these objectives. Intelligent Health has the potential to monitor patients at risk with underlying conditions and track their progress during therapy. Some of the greatest challenges in using these technologies are based on legal and ethical concerns of using medical data and adequately representing and servicing disparate patient populations. One major potential benefit of this technology is to make health systems more sustainable and standardized. Privacy and data security, establishing protocols, appropriate governance, and improving technologies will be among the crucial priorities for Digital Transformation in Healthcare.

Newcomers to R are often intimidated by the command-line interface, the vast number of functions and packages, or the processes of importing data and performing a simple statistical analysis. The R Primer provides a collection of concise examples and solutions to R problems frequently encountered by new users of this statistical software.

Rather than explore the many options available for every command as well as the ever-increasing number of packages, the book focuses on the basics of data preparation and analysis and gives examples that can be used as a starting point. The numerous examples illustrate a specific situation, topic, or problem, including data importing, data management, classical statistical analyses, and high-quality graphics production. Each example is self-contained and includes R code that can be run exactly as shown, enabling results from the book to be replicated. While base R is used throughout, other functions or packages are listed if they cover or extend the functionality.

After working through the examples found in this text, new users of R will be able to better handle data analysis and graphics applications in R. Additional topics and R code are available from the book s supporting website at www.statistics.life.ku.dk/primer/