Математика
Различные книги в жанре МатематикаStatistical Inference for Fractional Diffusion Processes
Stochastic processes are widely used for model building in the social, physical, engineering and life sciences as well as in financial economics. In model building, statistical inference for stochastic processes is of great importance from both a theoretical and an applications point of view. This book deals with Fractional Diffusion Processes and statistical inference for such stochastic processes. The main focus of the book is to consider parametric and nonparametric inference problems for fractional diffusion processes when a complete path of the process over a finite interval is observable. Key features: Introduces self-similar processes, fractional Brownian motion and stochastic integration with respect to fractional Brownian motion. Provides a comprehensive review of statistical inference for processes driven by fractional Brownian motion for modelling long range dependence. Presents a study of parametric and nonparametric inference problems for the fractional diffusion process. Discusses the fractional Brownian sheet and infinite dimensional fractional Brownian motion. Includes recent results and developments in the area of statistical inference of fractional diffusion processes. Researchers and students working on the statistics of fractional diffusion processes and applied mathematicians and statisticians involved in stochastic process modelling will benefit from this book.
Fourier Series and Numerical Methods for Partial Differential Equations
The importance of partial differential equations (PDEs) in modeling phenomena in engineering as well as in the physical, natural, and social sciences is well known by students and practitioners in these fields. Striking a balance between theory and applications, Fourier Series and Numerical Methods for Partial Differential Equations presents an introduction to the analytical and numerical methods that are essential for working with partial differential equations. Combining methodologies from calculus, introductory linear algebra, and ordinary differential equations (ODEs), the book strengthens and extends readers' knowledge of the power of linear spaces and linear transformations for purposes of understanding and solving a wide range of PDEs. The book begins with an introduction to the general terminology and topics related to PDEs, including the notion of initial and boundary value problems and also various solution techniques. Subsequent chapters explore: The solution process for Sturm-Liouville boundary value ODE problems and a Fourier series representation of the solution of initial boundary value problems in PDEs The concept of completeness, which introduces readers to Hilbert spaces The application of Laplace transforms and Duhamel's theorem to solve time-dependent boundary conditions The finite element method, using finite dimensional subspaces The finite analytic method with applications of the Fourier series methodology to linear version of non-linear PDEs Throughout the book, the author incorporates his own class-tested material, ensuring an accessible and easy-to-follow presentation that helps readers connect presented objectives with relevant applications to their own work. Maple is used throughout to solve many exercises, and a related Web site features Maple worksheets for readers to use when working with the book's one- and multi-dimensional problems. Fourier Series and Numerical Methods for Partial Differential Equations is an ideal book for courses on applied mathematics and partial differential equations at the upper-undergraduate and graduate levels. It is also a reliable resource for researchers and practitioners in the fields of mathematics, science, and engineering who work with mathematical modeling of physical phenomena, including diffusion and wave aspects.
An Introduction to Critical Thinking and Creativity. Think More, Think Better
A valuable guide on creativity and critical thinking to improve reasoning and decision-making skills Critical thinking skills are essential in virtually any field of study or practice where individuals need to communicate ideas, make decisions, and analyze and solve problems. An Introduction to Critical Thinking and Creativity: Think More, Think Better outlines the necessary tools for readers to become critical as well as creative thinkers. By gaining a practical and solid foundation in the basic principles that underlie critical thinking and creativity, readers will become equipped to think in a more systematic, logical, and imaginative manner. Creativity is needed to generate new ideas to solve problems, and critical thinking evaluates and improves an idea. These concepts are uniquely introduced as a unified whole due to their dependence on each other. Each chapter introduces relevant theories in conjunction with real-life examples and findings from cognitive science and psychology to illustrate how the theories can be applied in numerous fields and careers. An emphasis on how theoretical principles of reasoning can be practical and useful in everyday life is featured, and special sections on presentation techniques, the analysis of meaning, decision-making, and reasoning about personal and moral values are also highlighted. All chapters conclude with a set of exercises, and detailed solutions are provided at the end of the book. A companion website features online tutorials that further explore topics including meaning analysis, argument analysis, logic, statistics, and strategic thinking, along with additional exercises and multimedia resources for continued study. An Introduction to Critical Thinking and Creativity is an excellent book for courses on critical thinking and logic at the undergraduate and graduate levels. The book also serves as a self-contained study guide for readers interested in the topics of critical thinking and creativity as a unified whole.
Risk Assessment. Theory, Methods, and Applications
An introduction to risk assessment that utilizes key theory and state-of-the-art applications With its balanced coverage of theory and applications along with standards and regulations, Risk Assessment: Theory, Methods, and Applications serves as a comprehensive introduction to the topic. The book serves as a practical guide to current risk analysis and risk assessment, emphasizing the possibility of sudden, major accidents across various areas of practice from machinery and manufacturing processes to nuclear power plants and transportation systems. The author applies a uniform framework to the discussion of each method, setting forth clear objectives and descriptions, while also shedding light on applications, essential resources, and advantages and disadvantages. Following an introduction that provides an overview of risk assessment, the book is organized into two sections that outline key theory, methods, and applications. Introduction to Risk Assessment defines key concepts and details the steps of a thorough risk assessment along with the necessary quantitative risk measures. Chapters outline the overall risk assessment process, and a discussion of accident models and accident causation offers readers new insights into how and why accidents occur to help them make better assessments. Risk Assessment Methods and Applications carefully describes the most relevant methods for risk assessment, including preliminary hazard analysis, HAZOP, fault tree analysis, and event tree analysis. Here, each method is accompanied by a self-contained description as well as workflow diagrams and worksheets that illustrate the use of discussed techniques. Important problem areas in risk assessment, such as barriers and barrier analysis, human errors, and human reliability, are discussed along with uncertainty and sensitivity analysis. Each chapter concludes with a listing of resources for further study of the topic, and detailed appendices outline main results from probability and statistics, related formulas, and a listing of key terms used in risk assessment. A related website features problems that allow readers to test their comprehension of the presented material and supplemental slides to facilitate the learning process. Risk Assessment is an excellent book for courses on risk analysis and risk assessment at the upper-undergraduate and graduate levels. It also serves as a valuable reference for engineers, researchers, consultants, and practitioners who use risk assessment techniques in their everyday work.
Visual Data Mining. The VisMiner Approach
A visual approach to data mining. Data mining has been defined as the search for useful and previously unknown patterns in large datasets, yet when faced with the task of mining a large dataset, it is not always obvious where to start and how to proceed. This book introduces a visual methodology for data mining demonstrating the application of methodology along with a sequence of exercises using VisMiner. VisMiner has been developed by the author and provides a powerful visual data mining tool enabling the reader to see the data that they are working on and to visually evaluate the models created from the data. Key features: Presents visual support for all phases of data mining including dataset preparation. Provides a comprehensive set of non-trivial datasets and problems with accompanying software. Features 3-D visualizations of multi-dimensional datasets. Gives support for spatial data analysis with GIS like features. Describes data mining algorithms with guidance on when and how to use. Accompanied by VisMiner, a visual software tool for data mining, developed specifically to bridge the gap between theory and practice. Visual Data Mining: The VisMiner Approach is designed as a hands-on work book to introduce the methodologies to students in data mining, advanced statistics, and business intelligence courses. This book provides a set of tutorials, exercises, and case studies that support students in learning data mining processes. In praise of the VisMiner approach: «What we discovered among students was that the visualization concepts and tools brought the analysis alive in a way that was broadly understood and could be used to make sound decisions with greater certainty about the outcomes» —Dr. James V. Hansen, J. Owen Cherrington Professor, Marriott School, Brigham Young University, USA «Students learn best when they are able to visualize relationships between data and results during the data mining process. VisMiner is easy to learn and yet offers great visualization capabilities throughout the data mining process. My students liked it very much and so did I.» —Dr. Douglas Dean, Assoc. Professor of Information Systems, Marriott School, Brigham Young University, USA
Der perfekte Tipp. Statistik des Fußballspiels
How predictable is a soccer game, what good does the change of a coach, which role does the salary of soccer players have? Andreas Heuer surprises us with his analysis of soccer statistics. He shows that many beloved soccer sayings will vanish into thin air at a closer look.
Biostatistical Methods. The Assessment of Relative Risks
Praise for the First Edition «. . . an excellent textbook . . . an indispensable reference for biostatisticians and epidemiologists.» —International Statistical Institute A new edition of the definitive guide to classical and modern methods of biostatistics Biostatistics consists of various quantitative techniques that are essential to the description and evaluation of relationships among biologic and medical phenomena. Biostatistical Methods: The Assessment of Relative Risks, Second Edition develops basic concepts and derives an expanded array of biostatistical methods through the application of both classical statistical tools and more modern likelihood-based theories. With its fluid and balanced presentation, the book guides readers through the important statistical methods for the assessment of absolute and relative risks in epidemiologic studies and clinical trials with categorical, count, and event-time data. Presenting a broad scope of coverage and the latest research on the topic, the author begins with categorical data analysis methods for cross-sectional, prospective, and retrospective studies of binary, polychotomous, and ordinal data. Subsequent chapters present modern model-based approaches that include unconditional and conditional logistic regression; Poisson and negative binomial models for count data; and the analysis of event-time data including the Cox proportional hazards model and its generalizations. The book now includes an introduction to mixed models with fixed and random effects as well as expanded methods for evaluation of sample size and power. Additional new topics featured in this Second Edition include: Establishing equivalence and non-inferiority Methods for the analysis of polychotomous and ordinal data, including matched data and the Kappa agreement index Multinomial logistic for polychotomous data and proportional odds models for ordinal data Negative binomial models for count data as an alternative to the Poisson model GEE models for the analysis of longitudinal repeated measures and multivariate observations Throughout the book, SAS is utilized to illustrate applications to numerous real-world examples and case studies. A related website features all the data used in examples and problem sets along with the author's SAS routines. Biostatistical Methods, Second Edition is an excellent book for biostatistics courses at the graduate level. It is also an invaluable reference for biostatisticians, applied statisticians, and epidemiologists.
Cross Section and Experimental Data Analysis Using EViews
A practical guide to selecting and applying the most appropriate model for analysis of cross section data using EViews. «This book is a reflection of the vast experience and knowledge of the author. It is a useful reference for students and practitioners dealing with cross sectional data analysis … The strength of the book lies in its wealth of material and well structured guidelines …» Prof. Yohanes Eko Riyanto, Nanyang Technological University, Singapore «This is superb and brilliant. Prof. Agung has skilfully transformed his best experiences into new knowledge … creating a new way of understanding data analysis.» Dr. I Putu Gede Ary Suta, The Ary Suta Center, Jakarta Basic theoretical concepts of statistics as well as sampling methods are often misinterpreted by students and less experienced researchers. This book addresses this issue by providing a hands-on practical guide to conducting data analysis using EViews combined with a variety of illustrative models (and their extensions). Models having numerically dependent variables based on a cross-section data set (such as univariate, multivariate and nonlinear models as well as non-parametric regressions) are concentrated on. It is shown that a wide variety of hypotheses can easily be tested using EViews. Cross Section and Experimental Data Analysis Using EViews: Provides step-by-step directions on how to apply EViews to cross section data analysis – from multivariate analysis and nonlinear models to non-parametric regression Presents a method to test for all possible hypotheses based on each model Proposes a new method for data analysis based on a multifactorial design model Demonstrates that statistical summaries in the form of tabulations are invaluable inputs for strategic decision making Contains 200 examples with special notes and comments based on the author’s own empirical findings as well as over 400 illustrative outputs of regressions from EViews Techniques are illustrated through practical examples from real situations Comes with supplementary material, including work-files containing selected equation and system specifications that have been applied in the book This user-friendly introduction to EViews is ideal for Advanced undergraduate and graduate students taking finance, econometrics, population, or public policy courses, as well as applied policy researchers.
Approximate Dynamic Programming. Solving the Curses of Dimensionality
Praise for the First Edition «Finally, a book devoted to dynamic programming and written using the language of operations research (OR)! This beautiful book fills a gap in the libraries of OR specialists and practitioners.» —Computing Reviews This new edition showcases a focus on modeling and computation for complex classes of approximate dynamic programming problems Understanding approximate dynamic programming (ADP) is vital in order to develop practical and high-quality solutions to complex industrial problems, particularly when those problems involve making decisions in the presence of uncertainty. Approximate Dynamic Programming, Second Edition uniquely integrates four distinct disciplines—Markov decision processes, mathematical programming, simulation, and statistics—to demonstrate how to successfully approach, model, and solve a wide range of real-life problems using ADP. The book continues to bridge the gap between computer science, simulation, and operations research and now adopts the notation and vocabulary of reinforcement learning as well as stochastic search and simulation optimization. The author outlines the essential algorithms that serve as a starting point in the design of practical solutions for real problems. The three curses of dimensionality that impact complex problems are introduced and detailed coverage of implementation challenges is provided. The Second Edition also features: A new chapter describing four fundamental classes of policies for working with diverse stochastic optimization problems: myopic policies, look-ahead policies, policy function approximations, and policies based on value function approximations A new chapter on policy search that brings together stochastic search and simulation optimization concepts and introduces a new class of optimal learning strategies Updated coverage of the exploration exploitation problem in ADP, now including a recently developed method for doing active learning in the presence of a physical state, using the concept of the knowledge gradient A new sequence of chapters describing statistical methods for approximating value functions, estimating the value of a fixed policy, and value function approximation while searching for optimal policies The presented coverage of ADP emphasizes models and algorithms, focusing on related applications and computation while also discussing the theoretical side of the topic that explores proofs of convergence and rate of convergence. A related website features an ongoing discussion of the evolving fields of approximation dynamic programming and reinforcement learning, along with additional readings, software, and datasets. Requiring only a basic understanding of statistics and probability, Approximate Dynamic Programming, Second Edition is an excellent book for industrial engineering and operations research courses at the upper-undergraduate and graduate levels. It also serves as a valuable reference for researchers and professionals who utilize dynamic programming, stochastic programming, and control theory to solve problems in their everyday work.
Digital Spectral Analysis. Parametric, Non-Parametric and Advanced Methods
Digital Spectral Analysis provides a single source that offers complete coverage of the spectral analysis domain. This self-contained work includes details on advanced topics that are usually presented in scattered sources throughout the literature. The theoretical principles necessary for the understanding of spectral analysis are discussed in the first four chapters: fundamentals, digital signal processing, estimation in spectral analysis, and time-series models. An entire chapter is devoted to the non-parametric methods most widely used in industry. High resolution methods are detailed in a further four chapters: spectral analysis by stationary time series modeling, minimum variance, and subspace-based estimators. Finally, advanced concepts are the core of the last four chapters: spectral analysis of non-stationary random signals, space time adaptive processing: irregularly sampled data processing, particle filtering and tracking of varying sinusoids. Suitable for students, engineers working in industry, and academics at any level, this book provides a rare complete overview of the spectral analysis domain.