Математика
Различные книги в жанре МатематикаSpatial Statistics and Spatio-Temporal Data. Covariance Functions and Directional Properties
In the spatial or spatio-temporal context, specifying the correct covariance function is fundamental to obtain efficient predictions, and to understand the underlying physical process of interest. This book focuses on covariance and variogram functions, their role in prediction, and appropriate choice of these functions in applications. Both recent and more established methods are illustrated to assess many common assumptions on these functions, such as, isotropy, separability, symmetry, and intrinsic correlation. After an extensive introduction to spatial methodology, the book details the effects of common covariance assumptions and addresses methods to assess the appropriateness of such assumptions for various data structures. Key features: An extensive introduction to spatial methodology including a survey of spatial covariance functions and their use in spatial prediction (kriging) is given. Explores methodology for assessing the appropriateness of assumptions on covariance functions in the spatial, spatio-temporal, multivariate spatial, and point pattern settings. Provides illustrations of all methods based on data and simulation experiments to demonstrate all methodology and guide to proper usage of all methods. Presents a brief survey of spatial and spatio-temporal models, highlighting the Gaussian case and the binary data setting, along with the different methodologies for estimation and model fitting for these two data structures. Discusses models that allow for anisotropic and nonseparable behaviour in covariance functions in the spatial, spatio-temporal and multivariate settings. Gives an introduction to point pattern models, including testing for randomness, and fitting regular and clustered point patterns. The importance and assessment of isotropy of point patterns is detailed. Statisticians, researchers, and data analysts working with spatial and space-time data will benefit from this book as well as will graduate students with a background in basic statistics following courses in engineering, quantitative ecology or atmospheric science.
A Practical Guide to Data Mining for Business and Industry
Data mining is well on its way to becoming a recognized discipline in the overlapping areas of IT, statistics, machine learning, and AI. Practical Data Mining for Business presents a user-friendly approach to data mining methods, covering the typical uses to which it is applied. The methodology is complemented by case studies to create a versatile reference book, allowing readers to look for specific methods as well as for specific applications. The book is formatted to allow statisticians, computer scientists, and economists to cross-reference from a particular application or method to sectors of interest.
Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators
Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators provides a uniquely broad compendium of the key mathematical concepts and results that are relevant for the theoretical development of functional data analysis (FDA). The self–contained treatment of selected topics of functional analysis and operator theory includes reproducing kernel Hilbert spaces, singular value decomposition of compact operators on Hilbert spaces and perturbation theory for both self–adjoint and non self–adjoint operators. The probabilistic foundation for FDA is described from the perspective of random elements in Hilbert spaces as well as from the viewpoint of continuous time stochastic processes. Nonparametric estimation approaches including kernel and regularized smoothing are also introduced. These tools are then used to investigate the properties of estimators for the mean element, covariance operators, principal components, regression function and canonical correlations. A general treatment of canonical correlations in Hilbert spaces naturally leads to FDA formulations of factor analysis, regression, MANOVA and discriminant analysis. This book will provide a valuable reference for statisticians and other researchers interested in developing or understanding the mathematical aspects of FDA. It is also suitable for a graduate level special topics course.
Dispersion Decay and Scattering Theory
A simplified, yet rigorous treatment of scattering theory methods and their applications Dispersion Decay and Scattering Theory provides thorough, easy-to-understand guidance on the application of scattering theory methods to modern problems in mathematics, quantum physics, and mathematical physics. Introducing spectral methods with applications to dispersion time-decay and scattering theory, this book presents, for the first time, the Agmon-Jensen-Kato spectral theory for the Schr?dinger equation, extending the theory to the Klein-Gordon equation. The dispersion decay plays a crucial role in the modern application to asymptotic stability of solitons of nonlinear Schr?dinger and Klein-Gordon equations. The authors clearly explain the fundamental concepts and formulas of the Schr?dinger operators, discuss the basic properties of the Schr?dinger equation, and offer in-depth coverage of Agmon-Jensen-Kato theory of the dispersion decay in the weighted Sobolev norms. The book also details the application of dispersion decay to scattering and spectral theories, the scattering cross section, and the weighted energy decay for 3D Klein-Gordon and wave equations. Complete streamlined proofs for key areas of the Agmon-Jensen-Kato approach, such as the high-energy decay of the resolvent and the limiting absorption principle are also included. Dispersion Decay and Scattering Theory is a suitable book for courses on scattering theory, partial differential equations, and functional analysis at the graduate level. The book also serves as an excellent resource for researchers, professionals, and academics in the fields of mathematics, mathematical physics, and quantum physics who would like to better understand scattering theory and partial differential equations and gain problem-solving skills in diverse areas, from high-energy physics to wave propagation and hydrodynamics.
Optimal Learning
Learn the science of collecting information to make effective decisions Everyday decisions are made without the benefit of accurate information. Optimal Learning develops the needed principles for gathering information to make decisions, especially when collecting information is time-consuming and expensive. Designed for readers with an elementary background in probability and statistics, the book presents effective and practical policies illustrated in a wide range of applications, from energy, homeland security, and transportation to engineering, health, and business. This book covers the fundamental dimensions of a learning problem and presents a simple method for testing and comparing policies for learning. Special attention is given to the knowledge gradient policy and its use with a wide range of belief models, including lookup table and parametric and for online and offline problems. Three sections develop ideas with increasing levels of sophistication: Fundamentals explores fundamental topics, including adaptive learning, ranking and selection, the knowledge gradient, and bandit problems Extensions and Applications features coverage of linear belief models, subset selection models, scalar function optimization, optimal bidding, and stopping problems Advanced Topics explores complex methods including simulation optimization, active learning in mathematical programming, and optimal continuous measurements Each chapter identifies a specific learning problem, presents the related, practical algorithms for implementation, and concludes with numerous exercises. A related website features additional applications and downloadable software, including MATLAB and the Optimal Learning Calculator, a spreadsheet-based package that provides an introduction to learning and a variety of policies for learning.
Statistical and Machine Learning Approaches for Network Analysis
Explore the multidisciplinary nature of complex networks through machine learning techniques Statistical and Machine Learning Approaches for Network Analysis provides an accessible framework for structurally analyzing graphs by bringing together known and novel approaches on graph classes and graph measures for classification. By providing different approaches based on experimental data, the book uniquely sets itself apart from the current literature by exploring the application of machine learning techniques to various types of complex networks. Comprised of chapters written by internationally renowned researchers in the field of interdisciplinary network theory, the book presents current and classical methods to analyze networks statistically. Methods from machine learning, data mining, and information theory are strongly emphasized throughout. Real data sets are used to showcase the discussed methods and topics, which include: A survey of computational approaches to reconstruct and partition biological networks An introduction to complex networks—measures, statistical properties, and models Modeling for evolving biological networks The structure of an evolving random bipartite graph Density-based enumeration in structured data Hyponym extraction employing a weighted graph kernel Statistical and Machine Learning Approaches for Network Analysis is an excellent supplemental text for graduate-level, cross-disciplinary courses in applied discrete mathematics, bioinformatics, pattern recognition, and computer science. The book is also a valuable reference for researchers and practitioners in the fields of applied discrete mathematics, machine learning, data mining, and biostatistics.
Introduction to the Explicit Finite Element Method for Nonlinear Transient Dynamics
A systematic introduction to the theories and formulations of the explicit finite element method As numerical technology continues to grow and evolve with industrial applications, understanding the explicit finite element method has become increasingly important, particularly in the areas of crashworthiness, metal forming, and impact engineering. Introduction to the Explicit Finite Element Method for Nonlinear Transient Dynamics is the first book to address specifically what is now accepted as the most successful numerical tool for nonlinear transient dynamics. The book aids readers in mastering the explicit finite element method and programming code without requiring extensive background knowledge of the general finite element. The authors present topics relating to the variational principle, numerical procedure, mechanical formulation, and fundamental achievements of the convergence theory. In addition, key topics and techniques are provided in four clearly organized sections: • Fundamentals explores a framework of the explicit finite element method for nonlinear transient dynamics and highlights achievements related to the convergence theory • Element Technology discusses four-node, three-node, eight-node, and two-node element theories • Material Models outlines models of plasticity and other nonlinear materials as well as the mechanics model of ductile damage • Contact and Constraint Conditions covers subjects related to three-dimensional surface contact, with examples solved analytically, as well as discussions on kinematic constraint conditions Throughout the book, vivid figures illustrate the ideas and key features of the explicit finite element method. Examples clearly present results, featuring both theoretical assessments and industrial applications. Introduction to the Explicit Finite Element Method for Nonlinear Transient Dynamics is an ideal book for both engineers who require more theoretical discussions and for theoreticians searching for interesting and challenging research topics. The book also serves as an excellent resource for courses on applied mathematics, applied mechanics, and numerical methods at the graduate level.
A Career in Statistics. Beyond the Numbers
A valuable guide to a successful career as a statistician A Career in Statistics: Beyond the Numbers prepares readers for careers in statistics by emphasizing essential concepts and practices beyond the technical tools provided in standard courses and texts. This insider's guide from internationally recognized applied statisticians helps readers decide whether a career in statistics is right for them, provides hands-on guidance on how to prepare for such a career, and shows how to succeed on the job. The book provides non-technical guidance for a successful career. The authors' extensive industrial experience is supplemented by insights from contributing authors from government and academia, Carol Joyce Blumberg, Leonard M. Gaines, Lynne B. Hare, William Q. Meeker, and Josef Schmee. Following an introductory chapter that provides an overview of the field, the authors discuss the various dimensions of a career in applied statistics in three succinct parts: The Work of a Statistician describes the day-to-day activities of applied statisticians in business and industry, official government, and various other application areas, highlighting the work environment and major on-the-job challenges Preparing for a Successful Career in Statistics describes the personal traits that characterize successful statisticians, the education that they need to acquire, and approaches for securing the right job Building a Successful Career as a Statistician offers practical guidance for addressing key challenges that statisticians face on the job, such as project initiation and execution, effective communication, publicizing successes, ethical considerations, and gathering good data; alternative career paths are also described The book concludes with an in-depth examination of careers for statisticians in academia as well as tips to help them stay on top of their field throughout their careers. Each chapter includes thought-provoking discussion questions and a Major Takeaways section that outlines key concepts. Real-world examples illustrate key points, and an FTP site provides additional information on selected topics. A Career in Statistics is an invaluable guide for individuals who are considering or have decided on a career in statistics as well as for statisticians already on the job who want to accelerate their path to success. It also serves as a suitable book for courses on statistical consulting, statistical practice, and statistics in the workplace at the undergraduate and graduate levels.
Bayesian Networks. An Introduction
Bayesian Networks: An Introduction provides a self-contained introduction to the theory and applications of Bayesian networks, a topic of interest and importance for statisticians, computer scientists and those involved in modelling complex data sets. The material has been extensively tested in classroom teaching and assumes a basic knowledge of probability, statistics and mathematics. All notions are carefully explained and feature exercises throughout. Features include: An introduction to Dirichlet Distribution, Exponential Families and their applications. A detailed description of learning algorithms and Conditional Gaussian Distributions using Junction Tree methods. A discussion of Pearl's intervention calculus, with an introduction to the notion of see and do conditioning. All concepts are clearly defined and illustrated with examples and exercises. Solutions are provided online. This book will prove a valuable resource for postgraduate students of statistics, computer engineering, mathematics, data mining, artificial intelligence, and biology. Researchers and users of comparable modelling or statistical techniques such as neural networks will also find this book of interest.
GARCH Models. Structure, Statistical Inference and Financial Applications
This book provides a comprehensive and systematic approach to understanding GARCH time series models and their applications whilst presenting the most advanced results concerning the theory and practical aspects of GARCH. The probability structure of standard GARCH models is studied in detail as well as statistical inference such as identification, estimation and tests. The book also provides coverage of several extensions such as asymmetric and multivariate models and looks at financial applications. Key features: Provides up-to-date coverage of the current research in the probability, statistics and econometric theory of GARCH models. Numerous illustrations and applications to real financial series are provided. Supporting website featuring R codes, Fortran programs and data sets. Presents a large collection of problems and exercises. This authoritative, state-of-the-art reference is ideal for graduate students, researchers and practitioners in business and finance seeking to broaden their skills of understanding of econometric time series models.