The contributions by leading experts in this book focus on a variety of topics of current interest related to information-based complexity, ranging from function approximation, numerical integration, numerical methods for the sphere, and algorithms with random information, to Bayesian probabilistic numerical methods and numerical methods for stochastic differential equations.

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 volume focuses on the analysis and measurement of business cycles in Brazil, Russia, India, China and South Africa (BRICS). Divided into five parts, it begins with an overview of the main concepts and problems involved in monitoring and forecasting business cycles. Then it highlights the role of BRICS in the global economy and explores the interrelatedness of business cycles within BRICS. In turn, part two provides studies on the historical development of business cycles in the individual BRICS countries and describes the driving forces behind those cycles. Parts three and four present national business tendency surveys and composite cyclical indices for real-time monitoring and forecasting of various BRICS economies, while the final part discusses how the lessons learned in the BRICS countries can be used for the analysis of business cycles and their socio-political consequences in other emerging countries.

Statistical Methods for Dynamic Treatment Regimes shares state of the art of statistical methods developed to address questions of estimation and inference for dynamic treatment regimes, a branch of personalized medicine. This volume demonstrates these methods with their conceptual underpinnings and illustration through analysis of real and simulated data. These methods are immediately applicable to the practice of personalized medicine, which is a medical paradigm that emphasizes the systematic use of individual patient information to optimize patient health care. This is the first single source to provide an overview of methodology and results gathered from journals, proceedings, and technical reports with the goal of orienting researchers to the field. The first chapter establishes context for the statistical reader in the landscape of personalized medicine. Readers need only have familiarity with elementary calculus, linear algebra, and basic large-sample theory to use this text. Throughout the text, authors direct readers to available code or packages in different statistical languages to facilitate implementation. In cases where code does not already exist, the authors provide analytic approaches in sufficient detail that any researcher with knowledge of statistical programming could implement the methods from scratch. This will be an important volume for a wide range of researchers, including statisticians, epidemiologists, medical researchers, and machine learning researchers interested in medical applications. Advanced graduate students in statistics and biostatistics will also find material in Statistical Methods for Dynamic Treatment Regimes to be a critical part of their studies.

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.

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

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.

Features: Second edition has been updated with a new chapter on Nonparametric Estimation; a significant update to the chapter on Statistical Decision Theory; and other updates throughout No requirement for heavy calculus, and simple questions throughout the text help students check their understanding of the material Each chapter also includes a set of exercises that range in level of difficulty Self-contained, and can be used by the students to understand the theory Chapters and sections marked by asterisks contain more advanced topics and may be omitted Special chapters on linear models and nonparametric statistics show how the main theoretical concepts can be applied to well-known and frequently used statistical tools

This book explores widely used seasonal adjustment methods and recent developments in real time trend-cycle estimation. It discusses in detail the properties and limitations of X12ARIMA, TRAMO-SEATS and STAMP - the main seasonal adjustment methods used by statistical agencies. Several real-world cases illustrate each method and real data examples can be followed throughout the text. The trend-cycle estimation is presented using nonparametric techniques based on moving averages, linear filters and reproducing kernel Hilbert spaces, taking recent advances into account. The book provides a systematical treatment of results that to date have been scattered throughout the literature. Seasonal adjustment and real time trend-cycle prediction play an essential part at all levels of activity in modern economies. They are used by governments to counteract cyclical recessions, by central banks to control inflation, by decision makers for better modeling and planning and by hospitals, manufacturers, builders, transportation, and consumers in general to decide on appropriate action. This book appeals to practitioners in government institutions, finance and business, macroeconomists, and other professionals who use economic data as well as academic researchers in time series analysis, seasonal adjustment methods, filtering and signal extraction. It is also useful for graduate and final-year undergraduate courses in econometrics and time series with a good understanding of linear regression and matrix algebra, as well as ARIMA modelling.

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.

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.

Contains fully worked-out solutions to all of the odd-numbered exercises in the text, giving students a way to check their answers and ensure that they took the correct steps to arrive at an answer.

-Includes several real-life examples from health and clinical studies -Introduces statistical concepts of longitudinal data analysis strategies through visualization -Provides datasets and exercises online

Mathematical Puzzle Tales from Mount Olympus uses fascinating tales from Greek Mythology as the background for introducing mathematics puzzles to the general public. A background in high school mathematics will be ample preparation for using this book, and it should appeal to anyone who enjoys puzzles and recreational mathematics. Features: Combines the arts and science, and emphasizes the fact that mathematics straddles both domains. Great resource for students preparing for mathematics competitions, and the trainers of such students.

TThis book illustrates recent advances in applications of partial order theory and Hasse diagram techniques to data analysis, mainly in the socio-economic and environmental sciences. For years, partial order theory has been considered a fundamental branch of mathematics of only theoretical interest. In recent years, its effectiveness as a tool for data analysis is increasingly being realized and many applications of partially ordered sets to real problems in statistics and applied sciences have appeared. Main examples pertain to the analysis of complex and multidimensional systems of ordinal data and to problems of multi-criteria decision making, so relevant in social and environmental sciences. Partial Order Concepts in Applied Sciences presents new theoretical and methodological developments in partial order for data analysis, together with a wide range of applications to different topics: multidimensional poverty, economic development, inequality measurement, ecology and pollution, and biology, to mention a few. The book is of interest for applied mathematicians, statisticians, social scientists, environmental scientists and all those aiming at keeping pace with innovation in this interesting, growing and promising research field.

This monograph concisely but thoroughly introduces the reader to the field of mathematical immunology. The book covers first basic principles of formulating a mathematical model, and an outline on data-driven parameter estimation and model selection. The authors then introduce the modeling of experimental and human infections and provide the reader with helpful exercises. The target audience primarily comprises researchers and graduate students in the field of mathematical biology who wish to be concisely introduced into mathematical immunology.

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.

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.

The present volume contains the transactions of the lOth Oberwolfach Conference on "Probability Measures on Groups." The series of these meetings inaugurated in 1970 by L. Schmetterer and the editor is devoted to an intensive exchange of ideas on a subject which developed from the relations between various topics of mathematics: measure theory, probability theory, group theory, harmonic analysis, special functions, partial differential operators, quantum stochastics, just to name the most significant ones. Over the years the fruitful interplay broadened in various directions: new group-related structures such as convolution algebras, generalized translation spaces, hypercomplex systems, and hypergroups arose from generalizations as well as from applications, and a gradual refinement of the combinatorial, Banach-algebraic and Fourier analytic methods led to more precise insights into the theory. In a period of highest specialization in scientific thought the separated minds should be reunited by actively emphasizing similarities, analogies and coincidences between ideas in their fields of research. Although there is no real separation between one field and another - David Hilbert denied even the existence of any difference between pure and applied mathematics - bridges between probability theory on one side and algebra, topology and geometry on the other side remain absolutely necessary. They provide a favorable ground for the communication between apparently disjoint research groups and motivate the framework of what is nowadays called "Structural probability theory."

Statistics and their analysis are key to making mathematical sense of the world around us. In this textbook the authors underscore the importance of statistical methods and calculation skills and explain clearly and simply the key concepts and principles of statistics, so that they are easy to understand. The main purpose of the book is to make students more confident about handling statistical data and enable them to understand the meaning of the results obtained.

Statistical methods cover the collection of data, descriptive methods and inferential methods of analysis. Calculation skills cover elementary calculations, percentages and ratios, equations, graphs and interest calculations. The elementary calculations include basic calculations, such as exponents, decimals, scientific notation, logarithms, rounding and VAT calculations. This book teaches students with no mathematics background how to do basic calculations before concentrating on the statistical applications. For some courses, calculations such as interest, future values of investments, graphs and ratios form part of the core module and are also covered in this book.

The series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking effective mathematical tools for their research. A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories.

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.

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."

For courses in Probability and Random Processes. "Probability, Statistics, and Random Processes for Engineers, 4e "is a useful text for electrical and computer engineers. This book is a comprehensive treatment of probability and random processes that, more than any other available source, combines "rigor" with "accessibility." Beginning with the fundamentals of probability theory and requiring only college-level calculus, the book develops all the tools needed to understand more advanced topics such as random sequences, continuous-time random processes, and statistical signal processing. The book progresses at a leisurely pace, never assuming more knowledge than contained in the material already covered. Rigor is established by developing all results from the basic axioms and carefully defining and discussing such advanced notions as stochastic convergence, stochastic integrals and resolution of stochastic processes.