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Список книг автора Группа авторовMarkov Processes and Applications
This well-written book provides a clear and accessible treatment of the theory of discrete and continuous-time Markov chains, with an emphasis towards applications. The mathematical treatment is precise and rigorous without superfluous details, and the results are immediately illustrated in illuminating examples. This book will be extremely useful to anybody teaching a course on Markov processes. Jean-François Le Gall, Professor at Université de Paris-Orsay, France. Markov processes is the class of stochastic processes whose past and future are conditionally independent, given their present state. They constitute important models in many applied fields. After an introduction to the Monte Carlo method, this book describes discrete time Markov chains, the Poisson process and continuous time Markov chains. It also presents numerous applications including Markov Chain Monte Carlo, Simulated Annealing, Hidden Markov Models, Annotation and Alignment of Genomic sequences, Control and Filtering, Phylogenetic tree reconstruction and Queuing networks. The last chapter is an introduction to stochastic calculus and mathematical finance. Features include: The Monte Carlo method, discrete time Markov chains, the Poisson process and continuous time jump Markov processes. An introduction to diffusion processes, mathematical finance and stochastic calculus. Applications of Markov processes to various fields, ranging from mathematical biology, to financial engineering and computer science. Numerous exercises and problems with solutions to most of them
Statistical Rules of Thumb
Praise for the First Edition: «For a beginner [this book] is a treasure trove; for an experienced person it can provide new ideas on how better to pursue the subject of applied statistics.» —Journal of Quality Technology Sensibly organized for quick reference, Statistical Rules of Thumb, Second Edition compiles simple rules that are widely applicable, robust, and elegant, and each captures key statistical concepts. This unique guide to the use of statistics for designing, conducting, and analyzing research studies illustrates real-world statistical applications through examples from fields such as public health and environmental studies. Along with an insightful discussion of the reasoning behind every technique, this easy-to-use handbook also conveys the various possibilities statisticians must think of when designing and conducting a study or analyzing its data. Each chapter presents clearly defined rules related to inference, covariation, experimental design, consultation, and data representation, and each rule is organized and discussed under five succinct headings: introduction; statement and illustration of the rule; the derivation of the rule; a concluding discussion; and exploration of the concept's extensions. The author also introduces new rules of thumb for topics such as sample size for ratio analysis, absolute and relative risk, ANCOVA cautions, and dichotomization of continuous variables. Additional features of the Second Edition include: Additional rules on Bayesian topics New chapters on observational studies and Evidence-Based Medicine (EBM) Additional emphasis on variation and causation Updated material with new references, examples, and sources A related Web site provides a rich learning environment and contains additional rules, presentations by the author, and a message board where readers can share their own strategies and discoveries. Statistical Rules of Thumb, Second Edition is an ideal supplementary book for courses in experimental design and survey research methods at the upper-undergraduate and graduate levels. It also serves as an indispensable reference for statisticians, researchers, consultants, and scientists who would like to develop an understanding of the statistical foundations of their research efforts. A related website www.vanbelle.org provides additional rules, author presentations and more.
Statistical Modeling by Wavelets
A comprehensive, step-by-step introduction to wavelets in statistics. What are wavelets? What makes them increasingly indispensable in statistical nonparametrics? Why are they suitable for «time-scale» applications? How are they used to solve such problems as denoising, regression, or density estimation? Where can one find up-to-date information on these newly «discovered» mathematical objects? These are some of the questions Brani Vidakovic answers in Statistical Modeling by Wavelets. Providing a much-needed introduction to the latest tools afforded statisticians by wavelet theory, Vidakovic compiles, organizes, and explains in depth research data previously available only in disparate journal articles. He carefully balances both statistical and mathematical techniques, supplementing the material with a wealth of examples, more than 100 illustrations, and extensive references-with data sets and S-Plus wavelet overviews made available for downloading over the Internet. Both introductory and data-oriented modeling topics are featured, including: * Continuous and discrete wavelet transformations. * Statistical optimality properties of wavelet shrinkage. * Theoretical aspects of wavelet density estimation. * Bayesian modeling in the wavelet domain. * Properties of wavelet-based random functions and densities. * Several novel and important wavelet applications in statistics. * Wavelet methods in time series. Accessible to anyone with a background in advanced calculus and algebra, Statistical Modeling by Wavelets promises to become the standard reference for statisticians and engineers seeking a comprehensive introduction to an emerging field.
Convergence of Probability Measures
A new look at weak-convergence methods in metric spaces-from a master of probability theory In this new edition, Patrick Billingsley updates his classic work Convergence of Probability Measures to reflect developments of the past thirty years. Widely known for his straightforward approach and reader-friendly style, Dr. Billingsley presents a clear, precise, up-to-date account of probability limit theory in metric spaces. He incorporates many examples and applications that illustrate the power and utility of this theory in a range of disciplines-from analysis and number theory to statistics, engineering, economics, and population biology. With an emphasis on the simplicity of the mathematics and smooth transitions between topics, the Second Edition boasts major revisions of the sections on dependent random variables as well as new sections on relative measure, on lacunary trigonometric series, and on the Poisson-Dirichlet distribution as a description of the long cycles in permutations and the large divisors of integers. Assuming only standard measure-theoretic probability and metric-space topology, Convergence of Probability Measures provides statisticians and mathematicians with basic tools of probability theory as well as a springboard to the «industrial-strength» literature available today.
Applied Multiway Data Analysis
From a preeminent authority—a modern and applied treatment of multiway data analysis This groundbreaking book is the first of its kind to present methods for analyzing multiway data by applying multiway component techniques. Multiway analysis is a specialized branch of the larger field of multivariate statistics that extends the standard methods for two-way data, such as component analysis, factor analysis, cluster analysis, correspondence analysis, and multidimensional scaling to multiway data. Applied Multiway Data Analysis presents a unique, thorough, and authoritative treatment of this relatively new and emerging approach to data analysis that is applicable across a range of fields, from the social and behavioral sciences to agriculture, environmental sciences, and chemistry. General introductions to multiway data types, methods, and estimation procedures are provided in addition to detailed explanations and advice for readers who would like to learn more about applying multiway methods. Using carefully laid out examples and engaging applications, the book begins with an introductory chapter that serves as a general overview of multiway analysis, including the types of problems it can address. Next, the process of setting up, carrying out, and evaluating multiway analyses is discussed along with commonly encountered issues, such as preprocessing, missing data, model and dimensionality selection, postprocessing, and transformation, as well as robustness and stability issues. Extensive examples are presented within a unified framework consisting of a five-step structure: objectives; data description and design; model and dimensionality selection; results and their interpretation; and validation. Procedures featured in the book are conducted using 3WayPack, which is software developed by the author, and analyses can also be carried out within the R and MATLAB systems. Several data sets and 3WayPack can be downloaded via the book's related Web site. The author presents the material in a clear, accessible style without unnecessary or complex formalism, assuring a smooth transition from well-known standard two-analysis to multiway analysis for readers from a wide range of backgrounds. An understanding of linear algebra, statistics, and principal component analyses and related techniques is assumed, though the author makes an effort to keep the presentation at a conceptual, rather than mathematical, level wherever possible. Applied Multiway Data Analysis is an excellent supplement for component analysis and statistical multivariate analysis courses at the upper-undergraduate and beginning graduate levels. The book can also serve as a primary reference for statisticians, data analysts, methodologists, applied mathematicians, and social science researchers working in academia or industry. Visit the Related Website: http://three-mode.leidenuniv.nl/, to view data from the book.
Simulation and Monte Carlo
Simulation and Monte Carlo is aimed at students studying for degrees in Mathematics, Statistics, Financial Mathematics, Operational Research, Computer Science, and allied subjects, who wish an up-to-date account of the theory and practice of Simulation. Its distinguishing features are in-depth accounts of the theory of Simulation, including the important topic of variance reduction techniques, together with illustrative applications in Financial Mathematics, Markov chain Monte Carlo, and Discrete Event Simulation. Each chapter contains a good selection of exercises and solutions with an accompanying appendix comprising a Maple worksheet containing simulation procedures. The worksheets can also be downloaded from the web site supporting the book. This encourages readers to adopt a hands-on approach in the effective design of simulation experiments. Arising from a course taught at Edinburgh University over several years, the book will also appeal to practitioners working in the finance industry, statistics and operations research.
Introduction to Mixed Modelling
Mixed modelling is one of the most promising and exciting areas of statistical analysis, enabling more powerful interpretation of data through the recognition of random effects. However, many perceive mixed modelling as an intimidating and specialized technique. This book introduces mixed modelling analysis in a simple and straightforward way, allowing the reader to apply the technique confidently in a wide range of situations. Introduction to Mixed Modelling shows that mixed modelling is a natural extension of the more familiar statistical methods of regression analysis and analysis of variance. In doing so, it provides the ideal introduction to this important statistical technique for those engaged in the statistical analysis of data. This essential book: Demonstrates the power of mixed modelling in a wide range of disciplines, including industrial research, social sciences, genetics, clinical research, ecology and agricultural research. Illustrates how the capabilities of regression analysis can be combined with those of ANOVA by the specification of a mixed model. Introduces the criterion of Restricted Maximum Likelihood (REML) for the fitting of a mixed model to data. Presents the application of mixed model analysis to a wide range of situations and explains how to obtain and interpret Best Linear Unbiased Predictors (BLUPs). Features a supplementary website containing solutions to exercises, further examples, and links to the computer software systems GenStat and R. This book provides a comprehensive introduction to mixed modelling, ideal for final year undergraduate students, postgraduate students and professional researchers alike. Readers will come from a wide range of scientific disciplines including statistics, biology, bioinformatics, medicine, agriculture, engineering, economics, and social sciences.
Risk and Financial Management
Financial risk management has become a popular practice amongst financial institutions to protect against the adverse effects of uncertainty caused by fluctuations in interest rates, exchange rates, commodity prices, and equity prices. New financial instruments and mathematical techniques are continuously developed and introduced in financial practice. These techniques are being used by an increasing number of firms, traders and financial risk managers across various industries. Risk and Financial Management: Mathematical and Computational Methods confronts the many issues and controversies, and explains the fundamental concepts that underpin financial risk management. Provides a comprehensive introduction to the core topics of risk and financial management. Adopts a pragmatic approach, focused on computational, rather than just theoretical, methods. Bridges the gap between theory and practice in financial risk management Includes coverage of utility theory, probability, options and derivatives, stochastic volatility and value at risk. Suitable for students of risk, mathematical finance, and financial risk management, and finance practitioners. Includes extensive reference lists, applications and suggestions for further reading. Risk and Financial Management: Mathematical and Computational Methods is ideally suited to both students of mathematical finance with little background in economics and finance, and students of financial risk management, as well as finance practitioners requiring a clearer understanding of the mathematical and computational methods they use every day. It combines the required level of rigor, to support the theoretical developments, with a practical flavour through many examples and applications.
The History of Mathematics
This new edition brings the fascinating and intriguing history of mathematics to life The Second Edition of this internationally acclaimed text has been thoroughly revised, updated, and reorganized to give readers a fresh perspective on the evolution of mathematics. Written by one of the world's leading experts on the history of mathematics, the book details the key historical developments in the field, providing an understanding and appreciation of how mathematics influences today's science, art, music, literature, and society. In the first edition, each chapter was devoted to a single culture. This Second Edition is organized by subject matter: a general survey of mathematics in many cultures, arithmetic, geometry, algebra, analysis, and mathematical inference. This new organization enables students to focus on one complete topic and, at the same time, compare how different cultures approached each topic. Many new photographs and diagrams have been added to this edition to enhance the presentation. The text is divided into seven parts: The World of Mathematics and the Mathematics of the World, including the origin and prehistory of mathematics, cultural surveys, and women mathematicians Numbers, including counting, calculation, ancient number theory, and numbers and number theory in modern mathematics Color Plates, illustrating the impact of mathematics on civilizations from Egypt to Japan to Mexico to modern Europe Space, including measurement, Euclidean geometry, post-Euclidean geometry, and modern geometrics Algebra, including problems leading to algebra, equations and methods, and modern algebra Analysis, including the calculus, real, and complex analysis Mathematical Inference, including probability and statistics, and logic and set theory As readers progress through the text, they learn about the evolution of each topic, how different cultures devised their own solutions, and how these solutions enabled the cultures to develop and progress. In addition, readers will meet some of the greatest mathematicians of the ages, who helped lay the groundwork for today's science and technology. The book's lively approach makes it appropriate for anyone interested in learning how the field of mathematics came to be what it is today. It can also serve as a textbook for undergraduate or graduate-level courses. An Instructor's Manual presenting detailed solutions to all the problems in the book is available upon request from the Wiley editorial department.
Affine and Projective Geometry
An important new perspective on AFFINE AND PROJECTIVE GEOMETRY This innovative book treats math majors and math education students to a fresh look at affine and projective geometry from algebraic, synthetic, and lattice theoretic points of view. Affine and Projective Geometry comes complete with ninety illustrations, and numerous examples and exercises, covering material for two semesters of upper-level undergraduate mathematics. The first part of the book deals with the correlation between synthetic geometry and linear algebra. In the second part, geometry is used to introduce lattice theory, and the book culminates with the fundamental theorem of projective geometry. While emphasizing affine geometry and its basis in Euclidean concepts, the book: * Builds an appreciation of the geometric nature of linear algebra * Expands students' understanding of abstract algebra with its nontraditional, geometry-driven approach * Demonstrates how one branch of mathematics can be used to prove theorems in another * Provides opportunities for further investigation of mathematics by various means, including historical references at the ends of chapters Throughout, the text explores geometry's correlation to algebra in ways that are meant to foster inquiry and develop mathematical insights whether or not one has a background in algebra. The insight offered is particularly important for prospective secondary teachers who must major in the subject they teach to fulfill the licensing requirements of many states. Affine and Projective Geometry's broad scope and its communicative tone make it an ideal choice for all students and professionals who would like to further their understanding of things mathematical.