Matrix Tricks for Linear Statistical Models

Engineers and applied geophysicists routinely encounter interpolation and estimation problems when analysing data from field observations. Introduction to Geostatistics presents practical techniques for the estimation of spatial functions from sparse data. The author's unique approach is a synthesis of classic and geostatistical methods with a focus on the most practical linear minimum-variance estimation methods, and includes suggestions on how to test and extend the applicability of such methods. The author includes many useful methods (often not covered in other geostatistics books) such as estimating variogram parameters, evaluating the need for a variable mean, parameter estimation and model testing in complex cases (e.g. anisotropy, variable mean, and multiple variables), and using information from deterministic mathematical models. Well illustrated with exercises and worked examples taken from hydrogeology, Introduction to Geostatistics assumes no background in statistics and

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.

The quantum inverse scattering method is a means of finding exact solutions of two-dimensional models in quantum field theory and statistical physics (such as the sine-Gordon equation or the quantum non-linear Schrödinger equation). These models are the subject of much attention amongst physicists and mathematicians. The present work is an introduction to this important and exciting area. It consists of four parts. The first deals with the Bethe ansatz and calculation of physical quantities. The authors then tackle the theory of the quantum inverse scattering method before applying it in the second half of the book to the calculation of correlation functions. This is one of the most important applications of the method and the authors have made significant contributions to the area. Here they describe some of the most recent and general approaches and include some new results. The book will be essential reading for all mathematical physicists working in field theory and statistical phy

This book examines the consequences of misspecifications ranging from the fundamental to the nonexistent for the interpretation of likelihood-based methods of statistical estimation and interference. Professor White first explores the underlying motivation for maximum-likelihood estimation, treats the interpretation of the maximum-likelihood estimator (MLE) for misspecified probability models, and gives the conditions under which parameters of interest can be consistently estimated despite misspecification, and the consequences of misspecification, for hypothesis testing in estimating the asymptotic covariance matrix of the parameters. Although the theory presented in the book is motivated by econometric problems, its applicability is by no means restricted to economics. Subject to defined limitations, the theory applies to any scientific context in which statistical analysis is conducted using approximate models.

This book deals primarily with the numerical solution of linear systems of equations by iterative methods. The first part of the book is intended to serve as a textbook for a numerical linear algebra course. The material assumes the reader has a basic knowledge of linear algebra, such as set theory and matrix algebra, however it is demanding for students who are not afraid of theory. To assist the reader, the more difficult passages have been marked, the definitions for each chapter are collected at the beginning of the chapter, and numerous exercises are included throughout the text. The second part of the book serves as a monograph introducing recent results in the iterative solution of linear systems, mainly using preconditioned conjugate gradient methods. This book should be a valuable resource for students and researchers alike wishing to learn more about iterative methods.

This book provides a distinctive and rich conception of methodology within international studies. From a rereading of the works of leading Western thinkers about international studies, Hayward Alker rediscovers a 'neo-Classical' conception of international relations which is both humanistic and scientific. He draws on the work of classical authors such as Aristotle and Thucydides; modern writers like Machiavelli, Vico, Marx, Weber, Deutsch and Bull; and post-modern writers like Havel, Connolly and Toulmin. The central challenge addressed is how to integrate 'positivist' or 'falsificationist' research styles within humanistic or interpretive ones. The author argues that appropriate, philosophically informed reformulations of conventional statistical and game-theoretic analyses are possible, and describes a number of humanistic methodologies for international relations, including argumentation analysis, narrative modeling, computational models of political understanding and reconstructiv

This book provides a distinctive and rich conception of methodology within international studies. From a rereading of the works of leading Western thinkers about international studies, Hayward Alker rediscovers a 'neo-Classical' conception of international relations which is both humanistic and scientific. He draws on the work of classical authors such as Aristotle and Thucydides; modern writers like Machiavelli, Vico, Marx, Weber, Deutsch and Bull; and post-modern writers like Havel, Connolly and Toulmin. The central challenge addressed is how to integrate 'positivist' or 'falsificationist' research styles within humanistic or interpretive ones. The author argues that appropriate, philosophically informed reformulations of conventional statistical and game-theoretic analyses are possible, and describes a number of humanistic methodologies for international relations, including argumentation analysis, narrative modeling, computational models of political understanding and reconstructiv

This is the first volume in a major two-volume set of advanced texts in econometrics. It is essentially a text in statistics which is adapted to deal with economic phenomena. Christian Gourieroux and Alain Monfort have written a text which synthesises a great deal of material scattered across a variety of books and journals. They present both the basic and the more sophisticated statistical models which are crucial to an understanding of econometric models, and have taken care to employ mathematical tools with which a majority of students with a basic course in econometrics will be familiar. One of the most attractive features of the books is the liberal use throughout of real-world economic examples. They are also distinctive for their emphasis on promoting an intuitive understanding of the models and results at the expense of overly technical discussions.

This is the first volume in a major two-volume set of advanced texts in econometrics. It is essentially a text in statistics which is adapted to deal with economic phenomena. Christian Gourieroux and Alain Monfort have written a text which synthesises a great deal of material scattered across a variety of books and journals. They present both the basic and the more sophisticated statistical models which are crucial to an understanding of econometric models, and have taken care to employ mathematical tools with which a majority of students with a basic course in econometrics will be familiar. One of the most attractive features of the books is the liberal use throughout of real-world economic examples. They are also distinctive for their emphasis on promoting an intuitive understanding of the models and results at the expense of overly technical discussions.

There is a growing need for appropriate models which address the management of land and water resources and ecosystems at large space and time scales. Theories of non-linear hydrological processes mus

Stochastic partial differential equations can be used in many areas of science to model complex systems that evolve over time. Their analysis is currently an area of much research interest. This book consists of papers given at the ICMS Edinburgh meeting held in 1994 on this topic, and it brings together some of the world's best known authorities on stochastic partial differential equations. Subjects covered include the stochastic Navier–Stokes equation, critical branching systems, population models, statistical dynamics, and ergodic properties of Markov semigroups. For all workers on stochastic partial differential equations this book will have much to offer.

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.

This book examines the consequences of misspecifications ranging from the fundamental to the nonexistent for the interpretation of likelihood-based methods of statistical estimation and interference. Professor White first explores the underlying motivation for maximum-likelihood estimation, treats the interpretation of the maximum-likelihood estimator (MLE) for misspecified probability models, and gives the conditions under which parameters of interest can be consistently estimated despite misspecification, and the consequences of misspecification, for hypothesis testing in estimating the asymptotic covariance matrix of the parameters. Although the theory presented in the book is motivated by econometric problems, its applicability is by no means restricted to economics. Subject to defined limitations, the theory applies to any scientific context in which statistical analysis is conducted using approximate models.

A graduate or undergraduate textbook for students in any field that uses computer models and simulation. Knowledge of differential equations, linear algebra, and matrix analysis, and some programming

This is the first-ever textbook on the Yang-Baxter equation. A key nonlinear equation for solving two important models in many-body statistical theory - the many-body problem in one dimension with rep

This is a substantial revision of a much-quoted monograph, first published in 1974. The structure is unchanged, but the text has been clarified and the notation brought into line with current practice. A large number of 'Additional Results' are included at the end of each chapter, thereby covering most of the major advances in the last twenty years. Professor Biggs' basic aim remains to express properties of graphs in algebraic terms, then to deduce theorems about them. In the first part, he tackles the applications of linear algebra and matrix theory to the study of graphs; algebraic constructions such as adjacency matrix and the incidence matrix and their applications are discussed in depth. There follows an extensive account of the theory of chromatic polynomials, a subject which has strong links with the 'interaction models' studied in theoretical physics, and the theory of knots. The last part deals with symmetry and regularity properties. Here there are important connections with

This book presents statistical methods for analysis of the duration of events. The primary focus is on models for single-spell data, events in which individual agents are observed for a single duration. Some attention is also given to multiple-spell data. The first part of the book covers model specification, including both structural and reduced form models and models with and without neglected heterogeneity. The book next deals with likelihood based inference about such models, with sections on full and semiparametric specification. A final section treats graphical and numerical methods of specification testing. This is the first published exposition of current econometric methods for the study of duration data.

This book provides students and research workers in the biological, medical and social sciences with the statistical background needed to collect and analyse data in an intelligent and critical manner. Key examples and case studies are used to illustrate commonly encountered research problems and to explain how they may be solved or even avoided altogether. Professor Manly also presents a clear understanding of the opportunities and limitations of different research designs, as well as an introduction to some new methods of analysis that are proving increasingly popular. Topics covered include the differences between observational and experimental studies; the design of sample surveys; multiple regression and its generalizations to log-linear and logistic models; experimental and quasi-experimental designs; interrupted time series; computer intensive methods of statistical inference; and the ethical considerations of research. In the final chapter, there is a useful discussion of how t

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 collection of papers delivered at the Fifth International Symposium in Economic Theory and Econometrics in 1988 is devoted to the estimation and testing of models that impose relatively weak restrictions on the stochastic behaviour of data. Particularly in highly non-linear models, empirical results are very sensitive to the choice of the parametric form of the distribution of the observable variables, and often nonparametric and semiparametric models are a preferable alternative. Methods and applications that do not require string parametric assumptions for their validity, that are based on kernels and on series expansions, and methods for independent and dependent observations are investigated and developed in these essays by renowned econometricians.

This collection of papers delivered at the Fifth International Symposium in Economic Theory and Econometrics in 1988 is devoted to the estimation and testing of models that impose relatively weak restrictions on the stochastic behaviour of data. Particularly in highly non-linear models, empirical results are very sensitive to the choice of the parametric form of the distribution of the observable variables, and often nonparametric and semiparametric models are a preferable alternative. Methods and applications that do not require string parametric assumptions for their validity, that are based on kernels and on series expansions, and methods for independent and dependent observations are investigated and developed in these essays by renowned econometricians.

Configural Frequency Analysis (CFA) is a method for analysis of groups of individuals in cross-classifications. Individuals belong to a type if their particular pattern of characteristics occurs more often than expected, and to an antityte if their particular pattern of characteristics occurs less often than expected. The author's original contribution is his linking of CFA to log-linear modeling and the General Linear Model, enabling the reader to relate CFA to a well-known statistical background. It is shown that CFA and log-linear modeling are methods that complement each other. Introduction to Configural Frequency Analysis covers the latest developments in CFA, and it will be easy to read even for those with only an elementary statistics course as a background.

The advent of electronic computing permits the empirical analysis of economic models of far greater subtlety and rigour than before, when many interesting ideas were not followed up because the calculations involved made this impracticable. The estimation and testing of these more intricate models is usually based on the method of Maximum Likelihood, which is a well-established branch of mathematical statistics. Its use in econometrics has led to the development of a number of special techniques; the specific conditions of econometric research moreover demand certain changes in the interpretation of the basic argument. This book is a self-contained introduction to this field. It consists of three parts. The first deals with general features of Maximum Likelihood methods; the second with linear and nonlinear regression; and the third with discrete choice and related micro-economic models. Readers should already be familiar with elementary statistical theory, with applied econometric res

Analysis of Ordinal Categorical Data Alan Agresti Statistical Science Now has its first coordinated manual of methods for analyzing ordered categorical data. This book discusses specialized models tha

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

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.

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

Structural Sensitivity in Econometric Models Edwin Kuh, John W. Neese and Peter Hollinger Provides a pathbreaking assessment of the worth of linear dynamic systems methods for probing the behavior of

For the second edition of this very successful text, Professor Binmore has written two chapters on analysis in vector spaces. The discussion extends to the notion of the derivative of a vector function as a matrix and the use of second derivatives in classifying stationary points. Some necessary concepts from linear algebra are included where appropriate. The first edition contained numerous worked examples and an ample collection of exercises for all of which solutions were provided at the end of the book. The second edition retains this feature but in addition offers a set of problems for which no solutions are given. Teachers may find this a helpful innovation.

The two parts of this book treat probability and statistics as mathematical disciplines and with the same degree of rigour as is adopted for other branches of applied mathematics at the level of a British honours degree. They contain the minimum information about these subjects that any honours graduate in mathematics ought to know. They are written primarily for general mathematicians, rather than for statistical specialists or for natural scientists who need to use statistics in their work. No previous knowledge of probability or statistics is assumed, though familiarity with calculus and linear algebra is required. The first volume takes the theory of probability sufficiently far to be able to discuss the simpler random processes, for example, queueing theory and random walks. The second volume deals with statistics, the theory of making valid inferences from experimental data, and includes an account of the methods of least squares and maximum likelihood; it uses the results of the

The two parts of this book treat probability and statistics as mathematical disciplines and with the same degree of rigour as is adopted for other branches of applied mathematics at the level of a British honours degree. They contain the minimum information about these subjects that any honours graduate in mathematics ought to know. They are written primarily for general mathematicians, rather than for statistical specialists or for natural scientists who need to use statistics in their work. No previous knowledge of probability or statistics is assumed, though familiarity with calculus and linear algebra is required. The first volume takes the theory of probability sufficiently far to be able to discuss the simpler random processes, for example, queueing theory and random walks. The second volume deals with statistics, the theory of making valid inferences from experimental data, and includes an account of the methods of least squares and maximum likelihood; it uses the results of the

Most biologists use nonlinear regression more than any other statistical technique, but there are very few places to learn about curve-fitting. This book, by the author of the very successfulIntuitive

This book represents an entirely fresh approach for introducing to students the mathematical and statistical concepts and tools that form the backbone for the study of the theory and applications of l

Mathematical elegance is a constant theme in this treatment of linear programming and matrix games. Condensed tableau, minimal in size and notation, are employed for the simplex algorithm. In the cont

Road Traffic Modelling and Management: Using Statistical Monitoring and Deep Learning provides a framework for understanding and enhancing road traffic monitoring and management. It examines both the commonly used traffic analysis methodologies as well the emerging ones that use deep learning methods. The book also shows how to understand statistical models and machine learning algorithms, and how to apply them to traffic modelling, estimation, forecasting and traffic congestion monitoring. Providing both a theoretical framework along with practical technical solutions, Road Traffic Modelling and Management: Using Statistical Monitoring and Deep Learning is for researchers and practitioners who want to improve the performance of intelligent transportation systems.

This book collects and unifies statistical models and methods that have been proposed for analyzing interval-censored failure time data. It provides the first comprehensive coverage of the topic of in

In this monograph we have considered a class of autoregressive models whose coefficients are random. The models have special appeal among the non-linear models so far considered in the statistical lit

The research reported in this book fulfills both a general and a specific purpose. Linear programming models are developed in order to improve the process of planning for economic development, both sh

OpenFOAM software and its growing popularity is attributed to the scope of customization for specific applications and large scale parallel simulations. This open source software is widely used in aerospace community and its popularity is increasing at a rapid pace. Introduction to OpenFOAM for Aeronautical Engineers covers aerospace CFD which includes turbulence modelling, external aerodynamics, compressible flows, sprays and combustion from the OpenFOAM usage perspective. The book provides adequate examples covering most of the aspects of CFD code and enables readers to carry out their own modifications. Additionally, modification of existing solvers and utilities to implement new models as well as tips and tricks related to solvers used in aeronautical applications are included. Lastly, a short introduction to Linux and C++ is provided along with references to other easily available sources. Introduction to OpenFOAM for Aeronautical Engineers is for aerospace researchers, engineers,

Nanomaterials possess special mechanical, electrical, and electronic properties. As a result, nanomaterials play a significant role in various nanoelectromechanical systems. Some of these materials include nanoparticles, nanowires, nanotubes, nanotube resonators, and nanoactuators. These structures are broadly utilized in civil, mechanical, and aerospace engineering. The dynamic analysis of nanostructures is important, because one must have knowledge about the mechanical behaviours to get an accurate prediction of dynamic characteristics. Conducting experiments at the nanoscale size is both complicated and expensive. Therefore, the development of appropriate mathematical models for the study of the dynamic behaviour of nanostructures is important. These models/problems are governed by linear/nonlinear differential equations which are not always possible to solve analytically. This deficiency compels us to search for numerical and computational methods. This book provides a detailed exp