Matrix Tricks for Linear Statistical Models

As real estate forms a significant part of the asset portfolios of most investors and lenders, it is crucial that analysts and institutions employ sound techniques for modelling and forecasting the performance of real estate assets. Assuming no prior knowledge of econometrics, this book introduces and explains a broad range of quantitative techniques that are relevant for the analysis of real estate data. It includes numerous detailed examples, giving readers the confidence they need to estimate and interpret their own models. Throughout, the book emphasises how various statistical techniques may be used for forecasting and shows how forecasts can be evaluated. Written by a highly experienced teacher of econometrics and a senior real estate professional, both of whom are widely known for their research, Real Estate Modelling and Forecasting is the first book to provide a practical introduction to the econometric analysis of real estate for students and practitioners.

Presenting a rigorous treatment of the physical and mechanical basis for the modelling of sedimentary basins, this book supplies geoscientists with practical tools for creating their own models. It begins with a thorough grounding in properties of porous media, linear elasticity, continuum mechanics and rock compressibility. Chapters on heat flow, subsidence, rheology, flexure and gravity consider sedimentary basins in the context of the Earth's lithosphere, and the book concludes with coverage of pore space cementation, compaction and fluid flow. The volume introduces basic, state-of-the-art models and demonstrates how to reproduce results using tools like MATLAB® and Octave. Main equations are derived from first principles, and their basic solutions are obtained and then applied. Separate notes sections supply more technical details, and the text is illustrated throughout with real-world examples, applications and test exercises. This is an accessible introduction to quantitative mod

Maps of species' distributions or habitat suitability are required for many aspects of environmental research, resource management and conservation planning. These include biodiversity assessment, reserve design, habitat management and restoration, species and habitat conservation plans and predicting the effects of environmental change on species and ecosystems. The proliferation of methods and uncertainty regarding their effectiveness can be daunting to researchers, resource managers and conservation planners alike. Franklin summarises the methods used in species distribution modeling (also called niche modeling) and presents a framework for spatial prediction of species distributions based on the attributes (space, time, scale) of the data and questions being asked. The framework links theoretical ecological models of species distributions to spatial data on species and environment, and statistical models used for spatial prediction. Providing practical guidelines to students, resea

The book presents statistical methods and models that can usefully support the evaluation of educational services and quality of products. The evaluation of educational services, as well as the analys

The theory of empirical processes provides valuable tools for the development of asymptotic theory in (nonparametric) statistical models, and makes possible the unified treatment of a number of them. This book reveals the relation between the asymptotic behaviour of M-estimators and the complexity of parameter space. Virtually all results are proved using only elementary ideas developed within the book; there is minimal recourse to abstract theoretical results. To make the results concrete, a detailed treatment is presented for two important examples of M-estimation, namely maximum likelihood and least squares. The theory also covers estimation methods using penalties and sieves. Many illustrative examples are given, including the Grenander estimator, estimation of functions of bounded variation, smoothing splines, partially linear models, mixture models and image analysis. Graduate students and professionals in statistics as well as those with an interest in applications, to such area

This introductory text explores the theory of graph spectra: a topic with applications across a wide range of subjects, including computer science, quantum chemistry and electrical engineering. The spectra examined here are those of the adjacency matrix, the Seidel matrix, the Laplacian, the normalized Laplacian and the signless Laplacian of a finite simple graph. The underlying theme of the book is the relation between the eigenvalues and structure of a graph. Designed as an introductory text for graduate students, or anyone using the theory of graph spectra, this self-contained treatment assumes only a little knowledge of graph theory and linear algebra. The authors include many developments in the field which arise as a result of rapidly expanding interest in the area. Exercises, spectral data and proofs of required results are also provided. The end-of-chapter notes serve as a practical guide to the extensive bibliography of over 500 items.

This introductory text explores the theory of graph spectra: a topic with applications across a wide range of subjects, including computer science, quantum chemistry and electrical engineering. The spectra examined here are those of the adjacency matrix, the Seidel matrix, the Laplacian, the normalized Laplacian and the signless Laplacian of a finite simple graph. The underlying theme of the book is the relation between the eigenvalues and structure of a graph. Designed as an introductory text for graduate students, or anyone using the theory of graph spectra, this self-contained treatment assumes only a little knowledge of graph theory and linear algebra. The authors include many developments in the field which arise as a result of rapidly expanding interest in the area. Exercises, spectral data and proofs of required results are also provided. The end-of-chapter notes serve as a practical guide to the extensive bibliography of over 500 items.

Actuaries must pass exams, but more than that: they must put knowledge into practice. This coherent book gives complete syllabus coverage for Exam C of the Society of Actuaries (SOA) while emphasizing the concepts and practical application of nonlife actuarial models. Ideal for those approaching their professional exams, it is also a class-tested textbook for undergraduate university courses in actuarial science. All the topics that students need to prepare for Exam C are here, including modeling of losses, risk and ruin theory, credibility theory and applications, and empirical implementation of loss models. The book also covers more recent topics, such as risk measures and bootstrapping. Readers are assumed to have studied statistical inference and probability at the introductory undergraduate level. Numerous examples and exercises are provided, with many exercises adapted from past Exam C questions. Computational notes on the use of Excel are included. Teaching slides are available

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

With mathematical and computational models furthering our understanding of lung mechanics, function and disease, this book provides an all-inclusive introduction to the topic from a quantitative standpoint. Focusing on inverse modeling, the reader is guided through the theory in a logical progression, from the simplest models up to state-of-the-art models that are both dynamic and nonlinear. Key tools used in biomedical engineering research, such as regression theory, linear and nonlinear systems theory, and the Fourier transform, are explained. Derivations of important physical principles, such as the Poiseuille equation and the wave speed equation, from first principles are also provided. Example applications to experimental data throughout illustrate physiological relevance, whilst problem sets at the end of each chapter provide practice and test reader comprehension. This book is ideal for biomedical engineering and biophysics graduate students and researchers wishing to understand

This book provides an integrated treatment of the theory of nonnegative matrices (matrices with only positive numbers or zero as entries) and some related classes of positive matrices, concentrating on connections with game theory, combinatorics, inequalities, optimisation and mathematical economics. The wide variety of applications, which include price fixing, scheduling and the fair division problem, have been carefully chosen both for their elegant mathematical content and for their accessibility to students with minimal preparation. Many results in matrix theory are also presented. The treatment is rigorous and almost all results are proved completely. These results and applications will be of great interest to researchers in linear programming, statistics and operations research. The minimal prerequisites also make the book accessible to first-year graduate students.

This book focuses specifically on bin and bulk parameterizations for the prediction of cloud and precipitation at various scales - the cloud scale, mesoscale, synoptic scale, and the global climate scale. It provides a background to the fundamental principles of parameterization physics, including processes involved in the production of clouds, ice particles, liquid water, snow aggregate, graupel and hail. It presents full derivations of the parameterizations, allowing readers to build parameterization packages, with varying levels of complexity based on information in the book. Architectures for a range of dynamical models are given, in which parameterizations form a significant tool for investigating large non-linear numerical systems. Model codes are available online at www.cambridge.org/9780521883382. Written for researchers and advanced students of cloud and precipitation microphysics, this book is also a valuable reference for all atmospheric scientists involved in models of nume

John Anderson and Colin Ewen, two of the most notable exponents of 'dependency phonology', present in this book a detailed account of this integrated model for the representational of segmental and suprasegmental structure in phonology. Dependency phonology departs from traditional 'linear' models of phonology, and the more recent non-linear models of autosegmental and metrical phonology, in several respects. Unlike in these models, suprasegmental structure is derived directly from the segmental representations, and these representations are based on single-valued features, or components (rather than Chomsky and Halle-type binary features), linked by the dependency relation to form suprasegmental structures, with the exact nature of the dependency relations being directly determined by the properties of the segmental structure. Phonology is currently noteworthy for the diversity of views within the discipline, but no linguist or phonetician with a serious interest in phonology can af

In this fully revised and expanded edition of Smooth Tests of Goodness of Fit, the latest powerful techniques for assessing statistical and probabilistic models using this proven class of procedures a

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.

Since the 1970s social scientists and scientists in a variety of fields - psychology, sociology, education, psychiatry, economics and engineering - have been interested in problems that require the statistical analysis of data over time and there has been in effect a conceptual revolution in ways of thinking about pattern and regularity. This book is a comprehensive introduction to all the major time-series techniques, both time-domain and frequency-domain. It includes work on linear models that simplify the solution of univariate and multivariate problems. The author begins with a non-mathematical overview: throughout, he provides easy-to-understand, fully worked examples drawn from real studies in psychology and sociology. Other, less comprehensive, books on time-series analysis require calculus: this presupposes only a standard introductory statistics course covering analysis of variance and regression. The chapters are short, designed to build concepts (and the reader's confidence)

The BUGS (Bayesian inference Using Gibbs Sampling) project is concerned with free, flexible software for the Bayesian analysis of complex statistical models using Markov Chain Monte Carlo (MCMC) meth

Analytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures. The theory has emerged over recent decades as essential both for the analysis of algorithms and for the study of scientific models in many disciplines, including probability theory, statistical physics, computational biology, and information theory. With a careful combination of symbolic enumeration methods and complex analysis, drawing heavily on generating functions, results of sweeping generality emerge that can be applied in particular to fundamental structures such as permutations, sequences, strings, walks, paths, trees, graphs and maps. This account is the definitive treatment of the topic. The authors give full coverage of the underlying mathematics and a thorough treatment of both classical and modern applications of the theory. The text is complemented with exercises, examples, appendices and notes to aid understanding. The book can be used for an advanc

This book provides an account of developments and applications of social accounts. It concentrates particularly on the methods of social accounting that Richard Stone, Nobel Laureate in Economics, developed and applied during his long and distinguished career. The contributors to the volume examine applications of social accounts in economics and demography, addressing issues of new formulations and specifications at the national and regional levels. Economic structure and issues of structural change are investigated within the context of social accounts matrices, and Linear Expenditure Systems are used to model population change and household consumption. The importance of social accounts matrices (SAM) in generating Computable General Equilibrium (CGE) models and the enormous potential that both SAM and CGE models have for policy analysis are stressed.

Do you want to recognize the most suitable models for analysis of statistical data sets? This book provides a hands-on practical guide to using the most suitable models for analysis of statistical da

The core methods in today's econometric toolkit are linear regression for statistical control, instrumental variables methods for the analysis of natural experiments, and differences-in-differences m

Bringing together the key ideas from nonequilibrium statistical mechanics and powerful methodology from quantum field theory, this book captures the essence of nonequilibrium quantum field theory. Beginning with the foundational aspects of the theory, the book presents important concepts and useful techniques, discusses issues of basic interest, and shows how thermal field, linear response, kinetic theories and hydrodynamics emerge. It also illustrates how these concepts and methodology are applied to current research topics including nonequilibrium phase transitions, thermalization in relativistic heavy ion collisions, the nonequilibrium dynamics of Bose-Einstein condensation, and the generation of structures from quantum fluctuations in the early Universe. Divided into five parts, with each part addressing a particular stage in the conceptual and technical development of the subject, this self-contained book is a valuable reference for graduate students and researchers in particle p

This is the first book on applied econometrics using the R system for statistical computing and graphics. It presents hands-on examples for a wide range of econometric models, from classical linear re

Although many books currently available describe statistical models and methods for analyzing longitudinal data, they do not highlight connections between various research threads in the statistical l

The original research papers collected in this volume continue the development of discrete choice analysis, of related structural models for analysis of choice behavior, and of the statistical theory

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.

The book provides an up-to-date survey of statistical and econometric techniques for the analysis of count data, with a focus on conditional distribution models. The book starts with a presentation of

This book is concerned with the theory of unbounded derivations in C*-algebras, a subject whose study was motivated by questions in quantum physics and statistical mechanics, and to which the author has made a considerable contribution. This is an active area of research, and one of the most ambitious aims of the theory is to develop quantum statistical mechanics within the framework of the C*-theory. The presentation, which is based on lectures given in Newcastle upon Tyne and Copenhagen, concentrates on topics involving quantum statistical mechanics and differentiations on manifolds. One of the goals is to formulate the absence theorem of phase transitions in its most general form within the C* setting. For the first time, he globally constructs, within that setting, derivations for a fairly wide class of interacting models, and presents a new axiomatic treatment of the construction of time evolutions and KMS states.

This title provides the fundamental bases for developing turbulence models on rational grounds. The main different methods of approach are considered, ranging from statistical modelling at various deg

Floods of immigration and rapid industrialization and urbanization in America at the turn of the century set in motion the transformation of many long-established institutions. This book examines specific ways in which cultural changes affected the structure of the religious establishment. Statistical models are applied to United States Census data from 1890 and 1906 on city and church populations, revealing connections between the growth of cities, the increase in literacy, and the formation of ethnic subcommunities that led to a new level of religious diversity. The author analyses evidence of growing competition among churches and of a level of individual commitment to congregations, demonstrating that the patterns of religious community established at the turn of the century provided the basis for the current denominational system. The author further analyses the relationship of religious diversity to urban secularization, as well as its role as a catalyst to sectarian conflict. In

With a focus on analyzing and modeling linear dynamic systems using statistical methods, Time Series Analysis formulates various linear models, discusses their theoretical characteristics, and explore

This book/CD bundle of the greatly expanded third edition of Numerical Recipes now has wider coverage than ever before, many new, expanded and updated sections, and two completely new chapters. Co-authored by four leading scientists from academia and industry, Numerical Recipes starts with basic mathematics and computer science and proceeds to complete, working routines. The informal, easy-to-read style that made earlier editions so popular is kept throughout. Highlights of the new material include: a new chapter on classification and inference, Gaussian mixture models, HMMs, hierarchical clustering, and SVMs; a new chapter on computational geometry, covering KD trees, quad- and octrees, Delaunay triangulation, and algorithms for lines, polygons, triangles, and spheres; interior point methods for linear programming; MCMC; an expanded treatment of ODEs with completely new routines; and many new statistical distributions. For support or further licence information please visit www.nr.com

Inferring the precise locations and splicing patterns of genes in DNA is a difficult but important task, with broad applications to biomedicine. The mathematical and statistical techniques that have been applied to this problem are surveyed and organized into a logical framework based on the theory of parsing. Both established approaches and methods at the forefront of current research are discussed. Numerous case studies of existing software systems are provided, in addition to detailed examples that work through the actual implementation of effective gene-predictors using hidden Markov models and other machine-learning techniques. Background material on probability theory, discrete mathematics, computer science, and molecular biology is provided, making the book accessible to students and researchers from across the life and computational sciences. This book is ideal for use in a first course in bioinformatics at graduate or advanced undergraduate level, and for anyone wanting to kee

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

Modern statistical methods use complex, sophisticated models that can lead to intractable computations. Saddlepoint approximations can be the answer. Written from the user's point of view, this book explains in clear language how such approximate probability computations are made, taking readers from the very beginnings to current applications. The core material is presented in chapters 1-6 at an elementary mathematical level. Chapters 7-9 then give a highly readable account of higher-order asymptotic inference. Later chapters address areas where saddlepoint methods have had substantial impact: multivariate testing, stochastic systems and applied probability, bootstrap implementation in the transform domain, and Bayesian computation and inference. No previous background in the area is required. Data examples from real applications demonstrate the practical value of the methods. Ideal for graduate students and researchers in statistics, biostatistics, electrical engineering, econometric

Inferring the precise locations and splicing patterns of genes in DNA is a difficult but important task, with broad applications to biomedicine. The mathematical and statistical techniques that have been applied to this problem are surveyed and organized into a logical framework based on the theory of parsing. Both established approaches and methods at the forefront of current research are discussed. Numerous case studies of existing software systems are provided, in addition to detailed examples that work through the actual implementation of effective gene-predictors using hidden Markov models and other machine-learning techniques. Background material on probability theory, discrete mathematics, computer science, and molecular biology is provided, making the book accessible to students and researchers from across the life and computational sciences. This book is ideal for use in a first course in bioinformatics at graduate or advanced undergraduate level, and for anyone wanting to kee

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

Presents the main statistical tools of econometrics, focusing specifically on modern econometric methodology. The authors unify the approach by using a small number of estimation techniques, mainly generalized method of moments (GMM) estimation and kernel smoothing. The choice of GMM is explained by its relevance in structural econometrics and its preeminent position in econometrics overall. Split into four parts, Part I explains general methods. Part II studies statistical models that are best suited for microeconomic data. Part III deals with dynamic models that are designed for macroeconomic and financial applications. In Part IV the authors synthesize a set of problems that are specific to statistical methods in structural econometrics, namely identification and over-identification, simultaneity, and unobservability. Many theoretical examples illustrate the discussion and can be treated as application exercises. Nobel Laureate James A. Heckman offers a foreword to the work.

Presents the main statistical tools of econometrics, focusing specifically on modern econometric methodology. The authors unify the approach by using a small number of estimation techniques, mainly generalized method of moments (GMM) estimation and kernel smoothing. The choice of GMM is explained by its relevance in structural econometrics and its preeminent position in econometrics overall. Split into four parts, Part I explains general methods. Part II studies statistical models that are best suited for microeconomic data. Part III deals with dynamic models that are designed for macroeconomic and financial applications. In Part IV the authors synthesize a set of problems that are specific to statistical methods in structural econometrics, namely identification and over-identification, simultaneity, and unobservability. Many theoretical examples illustrate the discussion and can be treated as application exercises. Nobel Laureate James A. Heckman offers a foreword to the work.

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.