Matrix Tricks for Linear Statistical Models

With the current push toward educational reform, there is great potential for innovation and change, particularly in large scale testing. One area where change is possible is in cognitive diagnostic assessment. Researchers in educational measurement and cognitive psychology are finally in a position to design tests targeted specifically for providing valuable information about students' cognitive strengths and weaknesses. This self-contained volume organizes what is known about cognitive diagnostic assessment in education, including its conceptual and philosophical basis, methods, and applications. The complete list of topics includes educational demand, philosophical rationale, construct validity, cognitive methods, test construction, statistical models, and unresolved issues (e.g., how to best translate diagnostic information into teaching practices). Leighton and Gierl present a comprehensive and up-to-date examination of cognitive diagnostic assessment in education.

The 1980s and 1990s have seen several authoritarian governments voluntarily cede power to constitutionally elected democratic governments. John Londregan uses Chile as a case study of this phenomenon, exploring what sorts of guarantees are required for those who are ceding power and how those guarantees later work out in practice. He constructs an analytical model of a democratic transition and provides a new statistical technique for analysing legislative votes, based upon a detailed empirical analysis of Chile's legislative politics. Legislative Institutions and Ideology in Chile extends existing spatial models of policy preferences by incorporating a valence component to policy choices. The valence component enables an agenda setter, in Chile the democratically elected president, to overcome veto players' objections to reform. Londregan specifically also uses Senate committee voting records to study the impact of human rights concessions on the political debate.

With the current push toward educational reform, there is great potential for innovation and change, particularly in large scale testing. One area where change is possible is in cognitive diagnostic assessment. Researchers in educational measurement and cognitive psychology are finally in a position to design tests targeted specifically for providing valuable information about students' cognitive strengths and weaknesses. This self-contained volume organizes what is known about cognitive diagnostic assessment in education, including its conceptual and philosophical basis, methods, and applications. The complete list of topics includes educational demand, philosophical rationale, construct validity, cognitive methods, test construction, statistical models, and unresolved issues (e.g., how to best translate diagnostic information into teaching practices). Leighton and Gierl present a comprehensive and up-to-date examination of cognitive diagnostic assessment in education.

Filtering and system identification are powerful techniques for building models of complex systems. This 2007 book discusses the design of reliable numerical methods to retrieve missing information in models derived using these techniques. Emphasis is on the least squares approach as applied to the linear state-space model, and problems of increasing complexity are analyzed and solved within this framework, starting with the Kalman filter and concluding with the estimation of a full model, noise statistics and state estimator directly from the data. Key background topics, including linear matrix algebra and linear system theory, are covered, followed by different estimation and identification methods in the state-space model. With end-of-chapter exercises, MATLAB simulations and numerous illustrations, this book will appeal to graduate students and researchers in electrical, mechanical and aerospace engineering. It is also useful for practitioners. Additional resources for this title,

Decision Making and Operations Research Techniques for Construction Management challenges the traditional empirical approach to problem solving and provides construction practitioners with a seasoned account to resolving day-to-day complicated issues in construction project management. With over 150,000 workers at different levels working at dispersed project sites throughout the territory, construction managers have to look for optimal solutions to minimize the costs and to maximize the efficiencies. This book provides scientific tools for practitioners to resolve some practical problems which are administered empirically at present and may lead to inconsistent results and human errors. The modern decision-making tools introduced in this book include Multi-criteria Decision-making Models, Artificial Neural Network, Genetic Algorithms, Construction Simulation, Rough Set Theory and Advanced Statistical Techniques for construction. This book will serve as a useful companion for those m

Where did SARS come from? Have we inherited genes from Neanderthals? How do plants use their internal clock? The genomic revolution in biology enables us to answer such questions. But the revolution would have been impossible without the support of powerful computational and statistical methods that enable us to exploit genomic data. Many universities are introducing courses to train the next generation of bioinformaticians: biologists fluent in mathematics and computer science, and data analysts familiar with biology. This readable and entertaining book, based on successful taught courses, provides a roadmap to navigate entry to this field. It guides the reader through key achievements of bioinformatics, using a hands-on approach. Statistical sequence analysis, sequence alignment, hidden Markov models, gene and motif finding and more, are introduced in a rigorous yet accessible way. A companion website provides the reader with Matlab-related software tools for reproducing the steps de

This is a history of international monetary thought from the end of the nineteenth to the middle of the twentieth century. It provides a comprehensive survey of the literature produced on international macroeconomics for that period. It will be of interest to teachers of and graduate students in international monetary economics, monetary theory, and the history of economic thought. Professor Flanders argues that progress in the field of international monetary economics (or in the discipline as a whole) has not been linear. Instead of writing a sequential, chronological story, she has classified the literature according to groupings of ideas and classes of models. After a brief survey of the Classical doctrines, the book covers the developments of major approaches, which are labelled Neoclassical, Late Classical, and Keynesian. The models are conceptualized in two streams: stream F encompasses formal, long-run equilibrium models, all of which emerge from a common proto-model involving t

The architectures and mechanisms underlying language processing form one important part of the general structure of cognition. This book, written by leading experts in the field, brings together linguistic, psychological and computational perspectives on some of the fundamental issues. Several general introductory chapters offer overviews on important psycholinguistic research frameworks and highlight both shared assumptions and controversial issues. Subsequent chapters explore syntactic and lexical mechanisms; statistical and connectionist models of language understanding; the crucial importance of linguistic representations in explaining behavioural phenomena; evidence from a variety of studies and methodologies concerning the interaction of syntax and semantics; and the implications for cognitive architecture. The book concludes with a set of contributions on select issues of interpretation, including quantification, focus and anaphora in language understanding. Architectures and Me

Dynamic data assimilation is the assessment, combination and synthesis of observational data, scientific laws and mathematical models to determine the state of a complex physical system, for instance as a preliminary step in making predictions about the system's behaviour. The topic has assumed increasing importance in fields such as numerical weather prediction where conscientious efforts are being made to extend the term of reliable weather forecasts beyond the few days that are presently feasible. This book is designed to be a basic one-stop reference for graduate students and researchers. It is based on graduate courses taught over a decade to mathematicians, scientists, and engineers, and its modular structure accommodates the various audience requirements. Thus Part I is a broad introduction to the history, development and philosophy of data assimilation, illustrated by examples; Part II considers the classical, static approaches, both linear and nonlinear; and Part III describes

Macroeconomics is evolving in an almost dialectic fashion. The latest evolution is the development of a new synthesis that combines insights of new classical, new Keynesian and real business cycle traditions into a dynamic, stochastic general equilibrium (DSGE) model that serves as a foundation for thinking about macro policy. That new synthesis has opened up the door to a new antithesis, which is being driven by advances in computing power and analytic techniques. This new synthesis is coalescing around developments in complexity theory, automated general to specific econometric modeling, agent-based models, and non-linear and statistical dynamical models. This book thus provides the reader with an introduction to what might be called a Post Walrasian research program that is developing as the antithesis of the Walrasian DSGE synthesis.

Macroeconomics is evolving in an almost dialectic fashion. The latest evolution is the development of a new synthesis that combines insights of new classical, new Keynesian and real business cycle traditions into a dynamic, stochastic general equilibrium (DSGE) model that serves as a foundation for thinking about macro policy. That new synthesis has opened up the door to a new antithesis, which is being driven by advances in computing power and analytic techniques. This new synthesis is coalescing around developments in complexity theory, automated general to specific econometric modeling, agent-based models, and non-linear and statistical dynamical models. This book thus provides the reader with an introduction to what might be called a Post Walrasian research program that is developing as the antithesis of the Walrasian DSGE synthesis.

Geographical Information Systems has moved from the domain of the computer specialist into the wider archaeological community, providing it with an exciting new research method. This clearly written but rigorous book provides a comprehensive guide to that use. Topics covered include: the theoretical context and the basics of GIS; data acquisition including database design; interpolation of elevation models; exploratory data analysis including spatial queries; statistical spatial analysis; map algebra; spatial operations including the calculation of slope and aspect, filtering and erosion modeling; methods for analysing regions; visibility analysis; network analysis including hydrological modeling; the production of high quality output for paper and electronic publication; and the use and production of metadata. Offering an extensive range of archaeological examples, it is an invaluable source of practical information for all archaeologists, whether engaged in cultural resource manageme

The human brain contains billions of nerve cells whose activity plays a critical role in the way we behave, feel, perceive, and think. This two-volume set explains the basic properties of a neuron - an electrically active nerve cell - and develops mathematical theories for the way neurons respond to the various stimuli they receive. Volume 1 contains descriptions and analyses of the principal mathematical models that have been developed for neurons in the past thirty years. It provides a brief review of the basic neuroanatomical and neurophysiological facts that will form the focus of the mathematical treatment. Tuckwell discusses the mathematical theories, beginning with the theory of membrane potentials. He then goes on to treat the Lapicque model, linear cable theory, and time-dependent solutions of the cable equations. He concludes with a description of Rall's model nerve cell. Because the level of mathematics increases steadily upward from Chapter Two, some familiarity with differ

Optimal Design of Experiments offers a rare blend of linear algebra, convex analysis, and statistics. The optimal design for statistical experiments is first formulated as a concave matrix optimizatio

Suitable for advanced undergraduates and graduate students, this text presents selected aspects of matrix theory that are most useful in developing computational methods for solving linear equations a

element domain. A set of linear equations is obtained for each element in the discretized domain. A global matrix system is formed after the assembly of all elements. This lecture is divided into t

Correlation is a robust and general technique for pattern recognition and is used in many applications, such as automatic target recognition, biometric recognition and optical character recognition. The design, analysis and use of correlation pattern recognition algorithms requires background information, including linear systems theory, random variables and processes, matrix/vector methods, detection and estimation theory, digital signal processing and optical processing. This book provides a needed review of this diverse background material and develops the signal processing theory, the pattern recognition metrics, and the practical application know-how from basic premises. It shows both digital and optical implementations. It also contains technology presented by the team that developed it and includes case studies of significant interest, such as face and fingerprint recognition. Suitable for graduate students taking courses in pattern recognition theory, whilst reaching technical

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.

Inverse Modeling of the Ocean and Atmosphere is a graduate-level book for students of oceanography and meteorology, and anyone interested in combining computer models and observations of the hydrosphere or solid earth. A step-by-step development of maximally efficient inversion algorithms, using ideal models, is complemented by computer codes and comprehensive details for realistic models. Variational tools and statistical concepts are concisely introduced, and applications to contemporary research models, together with elaborate observing systems, are examined in detail. The book offers a review of the various alternative approaches, and further advanced research topics are discussed. Derived from the author's lecture notes, this book constitutes an ideal course companion for graduate students, as well as being a valuable reference source for researchers and managers in theoretical earth science, civil engineering and applied mathematics.

An important problem in computational biology is identifying short DNA sequences (mathematically, 'words') associated to a biological function. One approach consists in determining whether a particular word is simply random or is of statistical significance, for example, because of its frequency or location. This book introduces the mathematical and statistical ideas used in solving this so-called exceptional word problem. It begins with a detailed description of the principal models used in sequence analysis: Markovian models are central here and capture compositional information on the sequence being analysed. There follows an introduction to several statistical methods that are used for finding exceptional words with respect to the model used. The second half of the book is illustrated with numerous examples provided from the analysis of bacterial genomes, making this a practical guide for users facing a real situation and needing to make an adequate procedure choice.

The second part of this two-volume set contains advanced aspects of the quantitative theory of the dynamics of neurons. It begins with an introduction to the effects of reversal potentials on response to synaptic input. It then develops the theory of action potential generation based on the seminal Hodgkin-Huxley equations and gives methods for their solution in the space-clamped and non-space-clamped cases. The remainder of the book discusses stochastic models of neural activity and ends with a statistical analysis of neuronal data with emphasis on spike trains. The mathematics is more complex in this volume than in the first volume and involves numerical methods of solution of partial differential equations and the statistical analysis of point processes.

Tools developed by statistical physicists are of increasing importance in the analysis of complex biological systems. Physics in Molecular Biology, first published in 2005, discusses how physics can be used in modeling life. It begins by summarizing important biological concepts, emphasizing how they differ from the systems normally studied in physics. A variety of topics, ranging from the properties of single molecules to the dynamics of macro-evolution, are studied in terms of simple mathematical models. The main focus of the book is on genes and proteins and how they build systems that compute and respond. The discussion develops from simple to complex systems, and from small-scale to large-scale phenomena. This book will inspire advanced undergraduates and graduate students in physics to approach biological subjects from a physicist's point of view. It is self-contained, requiring no background knowledge of biology, and only familiarity with basic concepts from physics, such as for

This book is an introduction to the physics of highly excited, easily perturbed or interacting atoms. The book begins with a brief introduction to the traditional view of electron shells and their properties, and then goes on to discuss Rydberg states, quantum defect theory, atomic f-values, centrifugal barrier effects, autoionisation, inner shell and double excitation spectra, K-matrix theory, atoms in high laser fields, statistical methods, quantum chaos, and atomic effects in solids. The emphasis is throughout on radial properties, orbital collapse, many body effects, the breakdown of the independent particle approach, the emergence of chaos, and the behaviour of atoms inside clusters and solids. A very full account of autoionisation includes not only the standard treatment for isolated resonances, but also several alternative approaches. The book discusses many experimental examples and has many diagrams and a comprehensive reference list.

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).

This book provides a self-contained introduction to cellular automata and lattice Boltzmann techniques. Beginning with a chapter introducing the basic concepts of this developing field, a second chapter describes methods used in cellular automata modeling. Following chapters discuss the statistical mechanics of lattice gases, diffusion phenomena, reaction-diffusion processes and non-equilibrium phase transitions. A final chapter looks at other models and applications, such as wave propagation and multiparticle fluids. With a pedagogic approach, the volume focuses on the use of cellular automata in the framework of equilibrium and non-equilibrium statistical physics. It also emphasises application-oriented problems such as fluid dynamics and pattern formation. The book contains many examples and problems. A glossary and a detailed bibliography are also included. This will be a valuable book for graduate students and researchers working in statistical physics, solid state physics, chemic

Quantile regression is gradually emerging as a unified statistical methodology for estimating models of conditional quantile functions. By complementing the exclusive focus of classical least squares regression on the conditional mean, quantile regression offers a systematic strategy for examining how covariates influence the location, scale and shape of the entire response distribution. This monograph is the first comprehensive treatment of the subject, encompassing models that are linear and nonlinear, parametric and nonparametric. The author has devoted more than 25 years of research to this topic. The methods in the analysis are illustrated with a variety of applications from economics, biology, ecology and finance. The treatment will find its core audiences in econometrics, statistics, and applied mathematics in addition to the disciplines cited above.

Quantile regression is gradually emerging as a unified statistical methodology for estimating models of conditional quantile functions. By complementing the exclusive focus of classical least squares regression on the conditional mean, quantile regression offers a systematic strategy for examining how covariates influence the location, scale and shape of the entire response distribution. This monograph is the first comprehensive treatment of the subject, encompassing models that are linear and nonlinear, parametric and nonparametric. The author has devoted more than 25 years of research to this topic. The methods in the analysis are illustrated with a variety of applications from economics, biology, ecology and finance. The treatment will find its core audiences in econometrics, statistics, and applied mathematics in addition to the disciplines cited above.

The description of solids at a microscopic level is complex, involving the interaction of a huge number of its constituents, such as ions or electrons. It is impossible to solve the corresponding many-body problems analytically or numerically, although much insight can be gained from the analysis of simplified models. An important example is the Hubbard model, which describes interacting electrons in narrow energy bands, and which has been applied to problems as diverse as high-Tc superconductivity, band magnetism, and the metal-insulator transition. This book presents a coherent, self-contained account of the exact solution of the Hubbard model in one dimension. The early chapters will be accessible to beginning graduate students with a basic knowledge of quantum mechanics and statistical mechanics. The later chapters address more advanced topics, and are intended as a guide for researchers to some of the more topical results in the field of integrable models.

The third edition of this classic text maintains its focus on applications of demographic models, while extending its scope to matrix models for stage-classified populations. The authors first introdu

This focuses on models and data that arise from repeated observations of a cross-section of individuals, households or companies. These models have found important applications within business, economics, education, political science and other social science disciplines. The author introduces the foundations of longitudinal and panel data analysis at a level suitable for quantitatively oriented graduate social science students as well as individual researchers. He emphasizes mathematical and statistical fundamentals but also describes substantive applications from across the social sciences, showing the breadth and scope that these models enjoy. The applications are enhanced by real-world data sets and software programs in SAS and Stata.

This focuses on models and data that arise from repeated observations of a cross-section of individuals, households or companies. These models have found important applications within business, economics, education, political science and other social science disciplines. The author introduces the foundations of longitudinal and panel data analysis at a level suitable for quantitatively oriented graduate social science students as well as individual researchers. He emphasizes mathematical and statistical fundamentals but also describes substantive applications from across the social sciences, showing the breadth and scope that these models enjoy. The applications are enhanced by real-world data sets and software programs in SAS and Stata.

This book illustrates a set of tools - story grammars, relational data models, and network models - that can be profitably used for the collection, organization, and analysis of narrative data in socio-historical research. A story grammar, or Subject-Action-Object and their modifiers, is the linguistic tool the author uses to structure narrative for the purpose of collecting event data. Relational database models make such complex data collection schemes practically feasible in a computer environment. Finally, network models are a statistical tool best suited to analyze this type of data. Driven by the metaphors of the journal (from … to) and the alchemy (words into numbers), the book leads the reader throughout a number of paths, from substantive to methodological issues, across time and disciplines: sociology, linguistics, literary criticism, history, statistics, computer science, philosophy, cognitive psychology, political science.

This book illustrates a set of tools - story grammars, relational data models, and network models - that can be profitably used for the collection, organization, and analysis of narrative data in socio-historical research. A story grammar, or Subject-Action-Object and their modifiers, is the linguistic tool the author uses to structure narrative for the purpose of collecting event data. Relational database models make such complex data collection schemes practically feasible in a computer environment. Finally, network models are a statistical tool best suited to analyze this type of data. Driven by the metaphors of the journal (from … to) and the alchemy (words into numbers), the book leads the reader throughout a number of paths, from substantive to methodological issues, across time and disciplines: sociology, linguistics, literary criticism, history, statistics, computer science, philosophy, cognitive psychology, political science.

This book provides a pedagogical introduction to the perturbative and non-perturbative aspects of quantum chromodynamics (QCD). Introducing the basic theory and recent advances in QCD, it also reviews the historical development of the subject, covering pre-QCD ideas of strong interactions such as the quark and parton models, the notion of colours and the S-matrix approach. The author then discusses gauge theory, techniques of dimensional regularization and renormalization, deep inelastic scattering and hard processes in hadron collisions, hadron jets and e+e– annihilations. Other topics include power corrections and the technologies of the Shifman-Vainshtein-Zakharov operating product expansion. The final parts of the book are devoted to modern non-perturbative approaches to QCD and the phenomenological aspects of QCD spectral sum rules. The book will be a valuable reference for graduate students and researchers in high-energy particle and nuclear physics, both theoretical and experime

A basic problem in computer vision is to understand the structure of a real world scene given several images of it. Techniques for solving this problem are taken from projective geometry and photogrammetry. Here, the authors cover the geometric principles and their algebraic representation in terms of camera projection matrices, the fundamental matrix and the trifocal tensor. The theory and methods of computation of these entities are discussed with real examples, as is their use in the reconstruction of scenes from multiple images. The new edition features an extended introduction covering the key ideas in the book (which itself has been updated with additional examples and appendices) and significant new results which have appeared since the first edition. Comprehensive background material is provided, so readers familiar with linear algebra and basic numerical methods can understand the projective geometry and estimation algorithms presented, and implement the algorithms directly fr

Event History Modeling, first published in 2004, provides an accessible guide to event history analysis for researchers and advanced students in the social sciences. The substantive focus of many social science research problems leads directly to the consideration of duration models, and many problems would be better analyzed by using these longitudinal methods to take into account not only whether the event happened, but when. The foundational principles of event history analysis are discussed and ample examples are estimated and interpreted using standard statistical packages, such as STATA and S-Plus. Critical innovations in diagnostics are discussed, including testing the proportional hazards assumption, identifying outliers, and assessing model fit. The treatment of complicated events includes coverage of unobserved heterogeneity, repeated events, and competing risks models. The authors point out common problems in the analysis of time-to-event data in the social sciences and make

Event History Modeling, first published in 2004, provides an accessible guide to event history analysis for researchers and advanced students in the social sciences. The substantive focus of many social science research problems leads directly to the consideration of duration models, and many problems would be better analyzed by using these longitudinal methods to take into account not only whether the event happened, but when. The foundational principles of event history analysis are discussed and ample examples are estimated and interpreted using standard statistical packages, such as STATA and S-Plus. Critical innovations in diagnostics are discussed, including testing the proportional hazards assumption, identifying outliers, and assessing model fit. The treatment of complicated events includes coverage of unobserved heterogeneity, repeated events, and competing risks models. The authors point out common problems in the analysis of time-to-event data in the social sciences and make

Almost all the results available in the literature on multivariate t-distributions published in the last 50 years are now collected together in this comprehensive reference. Because these distributions are becoming more prominent in many applications, this book is a must for any serious researcher or consultant working in multivariate analysis and statistical distributions. Much of this material has never before appeared in book form. The first part of the book emphasizes theoretical results of a probabilistic nature. In the second part of the book, these are supplemented by a variety of statistical aspects. Various generalizations and applications are dealt with in the final chapters. The material on estimation and regression models is of special value for practitioners in statistics and economics. A comprehensive bibliography of over 350 references is included.