Matrix Tricks for Linear Statistical Models

A First Course in Combinatorial Optimization is a text for a one-semester introductory graduate-level course for students of operations research, mathematics, and computer science. It is a self-contained treatment of the subject, requiring only some mathematical maturity. Topics include: linear and integer programming, polytopes, matroids and matroid optimization, shortest paths, and network flows. Central to the exposition is the polyhedral viewpoint, which is the key principle underlying the successful integer-programming approach to combinatorial-optimization problems. Another key unifying topic is matroids. The author does not dwell on data structures and implementation details, preferring to focus on the key mathematical ideas that lead to useful models and algorithms. Problems and exercises are included throughout as well as references for further study.

Risk control and derivative pricing have become of major concern to financial institutions, and there is a real need for adequate statistical tools to measure and anticipate the amplitude of the potential moves of the financial markets. Summarising theoretical developments in the field, this 2003 second edition has been substantially expanded. Additional chapters now cover stochastic processes, Monte-Carlo methods, Black-Scholes theory, the theory of the yield curve, and Minority Game. There are discussions on aspects of data analysis, financial products, non-linear correlations, and herding, feedback and agent based models. This book has become a classic reference for graduate students and researchers working in econophysics and mathematical finance, and for quantitative analysts working on risk management, derivative pricing and quantitative trading strategies.

Calantai (mathematics, U. of Miskolc, Hungary) offers a broad survey of projectors, a type of matrix and operator, for readers who are familiar with linear algebra and mathematical analysis at an unde

This book presents a systematic reassessment of the theoretical and empirical foundations of the democratic peace literature. Three distinct theoretical models of how domestic political institutions shape the foreign policy choices of state leaders are developed and Huth and Allee then test hypotheses from each model against an original data set of 348 territorial disputes from 1919–95. Each territorial dispute is divided into three separate but related phases for empirical analysis: Challenge the Status Quo Stage, Negotiation Stage and Military Escalation Stage. Their statistical results provide strong support for the importance of democratic accountability and norms in shaping decisions to negotiate and settle disputes as well as to threaten force and escalate to war. The findings of this book address central debates and provide many insights into understanding when and why democratic leaders engage in cooperative or confrontational foreign policies.

This book presents a systematic reassessment of the theoretical and empirical foundations of the democratic peace literature. Three distinct theoretical models of how domestic political institutions shape the foreign policy choices of state leaders are developed and Huth and Allee then test hypotheses from each model against an original data set of 348 territorial disputes from 1919–95. Each territorial dispute is divided into three separate but related phases for empirical analysis: Challenge the Status Quo Stage, Negotiation Stage and Military Escalation Stage. Their statistical results provide strong support for the importance of democratic accountability and norms in shaping decisions to negotiate and settle disputes as well as to threaten force and escalate to war. The findings of this book address central debates and provide many insights into understanding when and why democratic leaders engage in cooperative or confrontational foreign policies.

Structural equation modelling (SEM) is a technique that is used to estimate, analyse and test models that specify relationships among variables. The ability to conduct such analyses is essential for many problems in ecology and evolutionary biology. This book begins by explaining the theory behind the statistical methodology, including chapters on conceptual issues, the implementation of an SEM study and the history of the development of SEM. The second section provides examples of analyses on biological data including multi-group models, means models, P-technique and time-series. The final section of the book deals with computer applications and contrasts three popular SEM software packages. Aimed specifically at biological researchers and graduate students, this book will serve as valuable resource for both learning and teaching the SEM methodology. Moreover, data sets and programs that are presented in the book can also be downloaded from a website to assist the learning process.

In this short and very practical 2002 introduction to econometrics Philip Hans Franses guides the reader through the essential concepts of econometrics. Central to the book are practical questions in various economic disciplines, which can be answered using econometric methods and models. The book focuses on a limited number of the essential, most widely used methods, before going on to review the basics of econometrics. The book ends with a number of case studies drawn from recent empirical work to provide an intuitive illustration of what econometricians do when faced with practical questions. Throughout the book Franses emphasises the importance of specification, evaluation and implementation of models appropriate to the data. Assuming basic familiarity only with matrix algebra and calculus the book is designed to appeal as either a short stand-alone introduction for students embarking on an empirical research project or as a supplement to any standard introductory textbook.

This volume collects seven of Marc Nerlove's previously published, classic essays on panel data econometrics written over the past thirty-five years, together with a cogent essay on the history of the subject, which began with George Biddell Airey's monograph published in 1861. Since Professor Nerlove's 1966 Econometrica paper with Pietro Balestra, panel data and methods of econometric analysis appropriate to such data have become increasingly important in the discipline. The principal factors in the research environment affecting the future course of panel data econometrics are the phenomenal growth in the computational power available to the individual researcher at his or her desktop and the ready availability of data sets, both large and small, via the Internet. The best way to formulate statistical models for inference is motivated and shaped by substantive problems and understanding of the processes generating the data at hand to resolve them. The essays illustrate both the role

This 2002 book introduces the quantum theory of gauge fields. Emphasis is placed on four non-perturbative methods: path integrals, lattice gauge theories, the 1/N expansion, and reduced matrix models, all of which have important contemporary applications. Written as a textbook, it assumes a knowledge of quantum mechanics and elements of perturbation theory, while many relevant concepts are pedagogically introduced at a basic level in the first half of the book. The second half comprehensively covers large-N Yang-Mills theory. The book uses an approach to gauge theories based on path-dependent phase factors known as the Wilson loops, and contains problems with detailed solutions to aid understanding. Suitable for advanced graduate courses in quantum field theory, the book will also be of interest to researchers in high energy theory and condensed matter physics as a survey of recent developments in gauge theory.

Second order linear parabolic and elliptic equations arise frequently in mathematics and other disciplines. For example parabolic equations are to be found in statistical mechanics and solid state theory, their infinite dimensional counterparts are important in fluid mechanics, mathematical finance and population biology, whereas nonlinear parabolic equations arise in control theory. Here the authors present a state of the art treatment of the subject from a new perspective. The main tools used are probability measures in Hilbert and Banach spaces and stochastic evolution equations. There is then a discussion of how the results in the book can be applied to control theory. This area is developing very rapidly and there are numerous notes and references that point the reader to more specialised results not covered in the book. Coverage of some essential background material will help make the book self-contained and increase its appeal to those entering the subject.

The second edition of this book is unique in that it focuses on methods for making formal statistical inference from all the models in an a priori set (Multi-Model Inference). A philosophy is presente

Covering sex allocation, sex determination and operational sex ratios, this multi-author volume provides both a conceptual context and an instruction in methods for many aspects of sex ratio research. Theory, statistical analysis and genetics are each explained and discussed in the first three sections. The remaining chapters each focus on research in one of a wide spectrum of animal, plant and microbial taxa, including sex ratio distorting bacteria in invertebrates, malarial parasites, birds, human and other mammals, giving critical appraisals of such research. Sex Ratios: Concepts and Research Methods is primarily intended for graduate and professional behavioural and evolutionary ecologists in this field, but it will also be useful to biologists building evolutionary models, and researchers analysing data involving proportions or comparisons across phylogenetically related species.

Covering sex allocation, sex determination and operational sex ratios, this multi-author volume provides both a conceptual context and an instruction in methods for many aspects of sex ratio research. Theory, statistical analysis and genetics are each explained and discussed in the first three sections. The remaining chapters each focus on research in one of a wide spectrum of animal, plant and microbial taxa, including sex ratio distorting bacteria in invertebrates, malarial parasites, birds, human and other mammals, giving critical appraisals of such research. Sex Ratios: Concepts and Research Methods is primarily intended for graduate and professional behavioural and evolutionary ecologists in this field, but it will also be useful to biologists building evolutionary models, and researchers analysing data involving proportions or comparisons across phylogenetically related species.

Phase transition dynamics is centrally important to condensed matter physics. This 2002 book treats a wide variety of topics systematically by constructing time-dependent Ginzburg-Landau models for various systems in physics, metallurgy and polymer science. Beginning with a summary of advanced statistical-mechanical theories including the renormalization group theory, the book reviews dynamical theories, and covers the kinetics of phase ordering, spinodal decomposition and nucleation in depth. The phase transition dynamics of real systems are discussed, treating interdisciplinary problems in a unified manner. Topics include supercritical fluid dynamics, stress-diffusion coupling in polymers and mesoscopic dynamics at structural phase transitions in solids. Theoretical and experimental approaches to shear flow problems in fluids are reviewed. Phase Transition Dynamics provides a comprehensive account, building on the statistical mechanics of phase transitions covered in many introductor

Offering an integrated presentation of classical and statistical array processing, this book develops synthesis techniques for linear and planet arrays; it also provides a statistical characterization

Monitoring Ecological Impacts provides the tools needed by professional ecologists, scientists, engineers, planners and managers to design assessment programs that can reliably monitor, detect and allow management of human impacts on the natural environment. The procedures described are well grounded in inferential logic, and the statistical models needed to analyse complex data are given. Step-by-step guidelines and flow diagrams provide the reader with clear and useable protocols, which can be applied in any region of the world and to a wide range of human impacts. In addition, real examples are used to show how the theory can be put into practice. Although the context of this book is flowing water environments, especially rivers and streams, the advice for designing assessment programs can be applied to any ecosystem.

Statistics do not lie, nor is probability paradoxical. You just have to have the right intuition. In this lively look at both subjects, David Williams convinces mathematics students of the intrinsic interest of statistics and probability, and statistics students that the language of mathematics can bring real insight and clarity to their subject. He helps students build the intuition needed, in a presentation enriched with examples drawn from all manner of applications, e.g., genetics, filtering, the Black–Scholes option-pricing formula, quantum probability and computing, and classical and modern statistical models. Statistics chapters present both the Frequentist and Bayesian approaches, emphasising Confidence Intervals rather than Hypothesis Test, and include Gibbs-sampling techniques for the practical implementation of Bayesian methods. A central chapter gives the theory of Linear Regression and ANOVA, and explains how MCMC methods allow greater flexibility in modelling. C or WinBUG

Statistics do not lie, nor is probability paradoxical. You just have to have the right intuition. In this lively look at both subjects, David Williams convinces mathematics students of the intrinsic interest of statistics and probability, and statistics students that the language of mathematics can bring real insight and clarity to their subject. He helps students build the intuition needed, in a presentation enriched with examples drawn from all manner of applications, e.g., genetics, filtering, the Black–Scholes option-pricing formula, quantum probability and computing, and classical and modern statistical models. Statistics chapters present both the Frequentist and Bayesian approaches, emphasising Confidence Intervals rather than Hypothesis Test, and include Gibbs-sampling techniques for the practical implementation of Bayesian methods. A central chapter gives the theory of Linear Regression and ANOVA, and explains how MCMC methods allow greater flexibility in modelling. C or WinBUG

Eric Ghysels and Denise R. Osborn provide a thorough and timely review of the recent developments in the econometric analysis of seasonal economic time series, summarizing a decade of theoretical advances in the area. The authors discuss the asymptotic distribution theory for linear nonstationary seasonal stochastic processes. They also cover the latest contributions to the theory and practice of seasonal adjustment, together with its implications for estimation and hypothesis testing. Moreover, a comprehensive analysis of periodic models is provided, including stationary and nonstationary cases. The book concludes with a discussion of some nonlinear seasonal and periodic models. The treatment is designed for an audience of researchers and advanced graduate students.

Eric Ghysels and Denise R. Osborn provide a thorough and timely review of the recent developments in the econometric analysis of seasonal economic time series, summarizing a decade of theoretical advances in the area. The authors discuss the asymptotic distribution theory for linear nonstationary seasonal stochastic processes. They also cover the latest contributions to the theory and practice of seasonal adjustment, together with its implications for estimation and hypothesis testing. Moreover, a comprehensive analysis of periodic models is provided, including stationary and nonstationary cases. The book concludes with a discussion of some nonlinear seasonal and periodic models. The treatment is designed for an audience of researchers and advanced graduate students.

Independent Component Analysis (ICA) has recently become an important tool for modelling and understanding empirical datasets. It is a method of separating out independent sources from linearly mixed data, and belongs to the class of general linear models. ICA provides a better decomposition than other well-known models such as principal component analysis. This self-contained book contains a structured series of edited papers by leading researchers in the field, including an extensive introduction to ICA. The major theoretical bases are reviewed from a modern perspective, current developments are surveyed and many case studies of applications are described in detail. The latter include biomedical examples, signal and image denoising and mobile communications. ICA is discussed in the framework of general linear models, but also in comparison with other paradigms such as neural network and graphical modelling methods. The book is ideal for researchers and graduate students in the field.

Because of their intuitive layout, extensive mathematical capabilities, and convenient graphics, spreadsheets provide an easy, straightforward route to scientific computing. This textbook for undergraduate and entry-level graduate chemistry and chemical engineering students uses Excel, the most powerful available spreadsheet, to explore and solve problems in general and chemical data analysis. This is the only up-to-date text on the use of spreadsheets in chemistry. The book discusses topics including statistics, chemical equilibria, pH calculations, titrations, and instrumental methods such as chromatography, spectrometry, and electroanalysis. It contains many examples of data analysis, and uses spreadsheets for numerical simulations, and testing analytical procedures. It also treats modern data analysis methods such as linear and non-linear least squares in great detail, as well as methods based on Fourier transformation. The book shows how matrix methods can be powerful tools in dat

Because of their intuitive layout, extensive mathematical capabilities, and convenient graphics, spreadsheets provide an easy, straightforward route to scientific computing. This textbook for undergraduate and entry-level graduate chemistry and chemical engineering students uses Excel, the most powerful available spreadsheet, to explore and solve problems in general and chemical data analysis. This is the only up-to-date text on the use of spreadsheets in chemistry. The book discusses topics including statistics, chemical equilibria, pH calculations, titrations, and instrumental methods such as chromatography, spectrometry, and electroanalysis. It contains many examples of data analysis, and uses spreadsheets for numerical simulations, and testing analytical procedures. It also treats modern data analysis methods such as linear and non-linear least squares in great detail, as well as methods based on Fourier transformation. The book shows how matrix methods can be powerful tools in dat

A comprehensive, self-contained survey of the theory and applications of differential games, one of the most commonly used tools for modelling and analysing economics and management problems which are characterised by both multiperiod and strategic decision making. Although no prior knowledge of game theory is required, a basic knowledge of linear algebra, ordinary differential equations, mathematical programming and probability theory is necessary. Part One presents the theory of differential games, starting with the basic concepts of game theory and going on to cover control theoretic models, Markovian equilibria with simultaneous play, differential games with hierarchical play, trigger strategy equilibria, differential games with special structures, and stochastic differential games. Part Two offers applications to capital accumulation games, industrial organization and oligopoly games, marketing, resources and environmental economics.

New statistical methods and future directions of research in time series A Course in Time Series Analysis demonstrates how to build time series models for univariate and multivariate time series data.

Although geometry has always aided intuition in econometrics, more recently differential geometry has become a standard tool in the analysis of statistical models, offering a deeper appreciation of existing methodologies and highlighting the essential issues which can be hidden in an algebraic development of a problem. Originally published in 2000, this volume was an early example of the application of these techniques to econometrics. An introductory chapter provides a brief tutorial for those unfamiliar with the tools of Differential Geometry. The topics covered in the following chapters demonstrate the power of the geometric method to provide practical solutions and insight into problems of econometric inference.

This book provides an introduction to applied statistical mechanics by considering physically realistic models. It provides a simple and accessible introduction to theories of thermal fluctuations and diffusion, and goes on to apply them in a variety of physical contexts. The first part of the book is devoted to processes in thermal equilibrium, and considers linear systems. Ideas central to the subject, such as the fluctuation dissipation theorem, Fokker–Planck equations and the Kramers–Kroenig relations are introduced during the course of the exposition. The scope is then expanded to include non-equilibrium systems and also illustrates simple nonlinear systems. This book will be of interest to final year undergraduate and graduate students studying statistical mechanics, plasma physics, basic electronics, solid state physics and anyone who wants an accessible introduction to the subject.

This book provides an introduction to applied statistical mechanics by considering physically realistic models. It provides a simple and accessible introduction to theories of thermal fluctuations and diffusion, and goes on to apply them in a variety of physical contexts. The first part of the book is devoted to processes in thermal equilibrium, and considers linear systems. Ideas central to the subject, such as the fluctuation dissipation theorem, Fokker–Planck equations and the Kramers–Kroenig relations are introduced during the course of the exposition. The scope is then expanded to include non-equilibrium systems and also illustrates simple nonlinear systems. This book will be of interest to final year undergraduate and graduate students studying statistical mechanics, plasma physics, basic electronics, solid state physics and anyone who wants an accessible introduction to the subject.

The analysis of variance (ANOYA) models have become one of the most widely used tools of modern statistics for analyzing multifactor data. The ANOYA models provide versatile statistical tools for stud

Partial differential equations provide mathematical models of many important problems in the physical sciences and engineering. This book, first published in 2000, treats one class of such equations, concentrating on methods involving the use of surface potentials. It provided the first detailed exposition of the mathematical theory of boundary integral equations of the first kind on non-smooth domains. Included are chapters on three specific examples: the Laplace equation, the Helmholtz equation and the equations of linear elasticity. The book is designed to provide an ideal preparation for studying the modern research literature on boundary element methods.

Partial differential equations provide mathematical models of many important problems in the physical sciences and engineering. This book, first published in 2000, treats one class of such equations, concentrating on methods involving the use of surface potentials. It provided the first detailed exposition of the mathematical theory of boundary integral equations of the first kind on non-smooth domains. Included are chapters on three specific examples: the Laplace equation, the Helmholtz equation and the equations of linear elasticity. The book is designed to provide an ideal preparation for studying the modern research literature on boundary element methods.

David Epstein and Sharyn O'Halloran produce the first unified theory of policy making between the legislative and executive branches. Examining major US policy initiatives from 1947 to 1992, the authors describe the conditions under which the legislature narrowly constrains executive discretion, and when it delegates authority to the bureaucracy. In doing so, the authors synthesize diverse and competitive literatures, from transaction cost and principal-agent theory in economics, to information models developed in both economics and political science, to substantive and theoretical work on legislative organization and on bureaucratic discretion. Professors Epstein and O'Halloran produce their own deductive specification of the conditions for making or delegating policy, gather a rich, original data set on delegation and discretion in the postwar era to test the propositions derived from their model, and devise appropriate statistical tests to assess the validity of their propositions.

David Epstein and Sharyn O'Halloran produce the first unified theory of policy making between the legislative and executive branches. Examining major US policy initiatives from 1947 to 1992, the authors describe the conditions under which the legislature narrowly constrains executive discretion, and when it delegates authority to the bureaucracy. In doing so, the authors synthesize diverse and competitive literatures, from transaction cost and principal-agent theory in economics, to information models developed in both economics and political science, to substantive and theoretical work on legislative organization and on bureaucratic discretion. Professors Epstein and O'Halloran produce their own deductive specification of the conditions for making or delegating policy, gather a rich, original data set on delegation and discretion in the postwar era to test the propositions derived from their model, and devise appropriate statistical tests to assess the validity of their propositions.

This book describes theoretical advances in the study of artificial neural networks. It explores probabilistic models of supervised learning problems, and addresses the key statistical and computational questions. Research on pattern classification with binary-output networks is surveyed, including a discussion of the relevance of the Vapnik–Chervonenkis dimension, and calculating estimates of the dimension for several neural network models. A model of classification by real-output networks is developed, and the usefulness of classification with a 'large margin' is demonstrated. The authors explain the role of scale-sensitive versions of the Vapnik–Chervonenkis dimension in large margin classification, and in real prediction. They also discuss the computational complexity of neural network learning, describing a variety of hardness results, and outlining two efficient constructive learning algorithms. The book is self-contained and is intended to be accessible to researchers and gradua

This is an introduction to recent developments in algebraic combinatorics and an illustration of how research in mathematics actually progresses. The author recounts the story of the search for and discovery of a proof of a formula conjectured in the late 1970s: the number of n x n alternating sign matrices, objects that generalize permutation matrices. While apparent that the conjecture must be true, the proof was elusive. Researchers became drawn to this problem, making connections to aspects of invariant theory, to symmetric functions, to hypergeometric and basic hypergeometric series, and, finally, to the six-vertex model of statistical mechanics. All these threads are brought together in Zeilberger's 1996 proof of the original conjecture. The book is accessible to anyone with a knowledge of linear algebra. Students will learn what mathematicians actually do in an interesting and new area of mathematics, and even researchers in combinatorics will find something new here.

An integral part of engineering design is the development of models that describe physical behavior or phenomena in mathematical terms. As engineering systems have become more complex, classic linear methods of modeling and analysis have proved inadequate, creating a need for nonlinear models to solve design problems. This 1999 text provides an introduction to mathematical modeling of linear and nonlinear systems, with an emphasis on the solution of nonlinear design problems. While encouraging the use of the computer as a tool for modeling and analysis, the aim is to discuss the basic concepts underlying computer techniques and to seek analytical solutions. Among topics covered are exact solution, numerical solution, graphical solution, and approximate solution methods; and the stability of nonlinear systems. Numerous examples show how to apply modeling methods to real engineering systems. The book also includes end-of-chapter problems and case studies of challenging design problems. I

The Lund model, inspired by quantum chromodynamics, has provided a very promising approach to the dynamics of quark and gluon interactions. Starting with a brief reprise of basic concepts in relativity, quantum mechanics of fields and particle physics, this 1998 book discusses: the dynamics of the massless relativistic string; confinement; causality and relativistic covariance; Lund fragmentation processes; QED and QCD Bremsstrahlung; multiplicities and particle-parton distributions. Throughout the book, theory is confronted with current experimental data, and implications for future experiments are also considered. The book also explores the relationships between the Lund model and other models based on field theory (the Schwinger model, S-matrix models, light-cone algebra physics and variations of the parton model), and models based on statistical mechanics (the Feynman-Wilson gas, scaling, iterative cascade models).

Waves occur widely in nature and have innumerable commercial uses. Pressure waves are responsible for the transmission of speech, bow waves created by meteors can virtually ignite the earth's atmosphere, ultrasonic waves are used for medical imaging, and shock waves are used for the synthesis of new materials. This book provides a thorough, modern introduction to the study of linear and nonlinear waves. Beginning with fundamental concepts of motion, the book goes on to discuss linear and nonlinear mechanical waves, thermodynamics, and constitutive models. It covers gases, liquids, and solids as integral parts of the subject. Among the important areas of research and application are impact analysis, shock wave research, explosive detonation, nonlinear acoustics, and hypersonic aerodynamics. Graduate students, as well as professional engineers and applied physicists, will value this clear, comprehensive introduction to the study of wave phenomena.

This volume shows how odds ratios can be used as a framework for understanding log-linear models. Moving systematically from the paradigmatic 2x2 case to more complicated cases, the author defines the

Bootstrap methods are computer-intensive methods of statistical analysis, which use simulation to calculate standard errors, confidence intervals, and significance tests. The methods apply for any level of modelling, and so can be used for fully parametric, semiparametric, and completely nonparametric analysis. This 1997 book gives a broad and up-to-date coverage of bootstrap methods, with numerous applied examples, developed in a coherent way with the necessary theoretical basis. Applications include stratified data; finite populations; censored and missing data; linear, nonlinear, and smooth regression models; classification; time series and spatial problems. Special features of the book include: extensive discussion of significance tests and confidence intervals; material on various diagnostic methods; and methods for efficient computation, including improved Monte Carlo simulation. Each chapter includes both practical and theoretical exercises. S-Plus programs for implementing the