Matrix Tricks for Linear Statistical Models

This book provides a balanced, modern introduction to Bayesian and frequentist methods for regression analysis. The author discusses Frequentist and Bayesian Inferences; Linear Models; Binary Data Mod

Unlike uncertain dynamical systems in physical sciences where models for prediction are somewhat given to us by physical laws, uncertain dynamical systems in economics need statistical models. In this

A classic in its own right, this book continues to provide an introduction to modern generalized linear models for categorical variables. The text emphasizes methods that are most commonly used in pra

Group inverses for singular M-matrices are useful tools not only in matrix analysis, but also in the analysis of stochastic processes, graph theory, electrical networks, and demographic models. Group

As one of the most comprehensive machine learning texts around, this book does justice to the field's incredible richness, but without losing sight of the unifying principles. Peter Flach's clear, example-based approach begins by discussing how a spam filter works, which gives an immediate introduction to machine learning in action, with a minimum of technical fuss. Flach provides case studies of increasing complexity and variety with well-chosen examples and illustrations throughout. He covers a wide range of logical, geometric and statistical models and state-of-the-art topics such as matrix factorisation and ROC analysis. Particular attention is paid to the central role played by features. The use of established terminology is balanced with the introduction of new and useful concepts, and summaries of relevant background material are provided with pointers for revision if necessary. These features ensure Machine Learning will set a new standard as an introductory textbook.

As one of the most comprehensive machine learning texts around, this book does justice to the field's incredible richness, but without losing sight of the unifying principles. Peter Flach's clear, example-based approach begins by discussing how a spam filter works, which gives an immediate introduction to machine learning in action, with a minimum of technical fuss. Flach provides case studies of increasing complexity and variety with well-chosen examples and illustrations throughout. He covers a wide range of logical, geometric and statistical models and state-of-the-art topics such as matrix factorisation and ROC analysis. Particular attention is paid to the central role played by features. The use of established terminology is balanced with the introduction of new and useful concepts, and summaries of relevant background material are provided with pointers for revision if necessary. These features ensure Machine Learning will set a new standard as an introductory textbook.

Many of the commonly used methods for modeling and fitting psychophysical data are special cases of statistical procedures of great power and generality, notably the Generalized Linear Model (GLM). Th

By considering cross-sectional and longitudinal aspects, linear and non-linear models, point and change data, different time periods, micro- and macro-level interaction, and data for individuals with

The traditional view of the relationship between business and the arts is very much a one-way affair: organisations may endorse, fund or publicise the arts but the arts have nothing to offer from a business perspective. The Value of Arts for Business challenges this view by showing how the arts, in the form of Arts-based Initiatives (ABIs), can be used to enhance value-creation capacity and boost business performance. The book introduces and explains three models that show how organisations can successfully implement and manage ABIs. Firstly, the Arts Value Matrix enables managers to see how organisational value-drivers are affected by ABIs. Secondly, the Arts Benefits Constellation shows how to assess the benefits of using ABIs. Finally, the Arts Value Map shows how ABIs can be integrated and aligned with organisational strategy and operations. These models lay the foundations for a new research area exploring the links between arts and business.

Knowledge of risk models and the assessment of risk is a fundamental part of the training of actuaries and all who are involved in financial, pensions and insurance mathematics. This book provides students and others with a firm foundation in a wide range of statistical and probabilistic methods for the modelling of risk, including short-term risk modelling, model-based pricing, risk-sharing, ruin theory and credibility. It covers much of the international syllabuses for professional actuarial examinations in risk models, but goes into further depth, with worked examples, exercises and detailed case studies. The authors also use the statistical package R to demonstrate how simple code and functions can be used profitably in an actuarial context. The authors' engaging and pragmatic approach, balancing rigour and intuition and developed over many years of teaching the subject, makes this book ideal for self-study or for students taking courses in risk modelling.

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,

Focusing on what actuaries need in practice, this introductory account provides readers with essential tools for handling complex problems and explains how simulation models can be created, used and re-used (with modifications) in related situations. The book begins by outlining the basic tools of modelling and simulation, including a discussion of the Monte Carlo method and its use. Part II deals with general insurance and Part III with life insurance and financial risk. Algorithms that can be implemented on any programming platform are spread throughout and a program library written in R is included. Numerous figures and experiments with R-code illustrate the text. The author's non-technical approach is ideal for graduate students, the only prerequisites being introductory courses in calculus and linear algebra, probability and statistics. The book will also be of value to actuaries and other analysts in the industry looking to update their skills.

Understanding damage and failure of composite materials is critical for reliable and cost-effective engineering design. Bringing together materials mechanics and modeling, this book provides a complete guide to damage, fatigue and failure of composite materials. Early chapters focus on the underlying principles governing composite damage, reviewing basic equations and mechanics theory, before describing mechanisms of damage such as cracking, breakage and buckling. In subsequent chapters, the physical mechanisms underlying the formation and progression of damage under mechanical loads are described with ample experimental data, and micro- and macro-level damage models are combined. Finally, fatigue of composite materials is discussed using fatigue-life diagrams. While there is a special emphasis on polymer matrix composites, metal and ceramic matrix composites are also described. Outlining methods for more reliable design of composite structures, this is a valuable resource for engineer

Arising from courses taught by the authors, this largely self-contained treatment is ideal for mathematicians who are interested in applications or for students from applied fields who want to understand the mathematics behind their subject. Early chapters cover Fourier analysis, functional analysis, probability and linear algebra, all of which have been chosen to prepare the reader for the applications to come. The book includes rigorous proofs of core results in compressive sensing and wavelet convergence. Fundamental is the treatment of the linear system y=Φx in both finite and infinite dimensions. There are three possibilities: the system is determined, overdetermined or underdetermined, each with different aspects. The authors assume only basic familiarity with advanced calculus, linear algebra and matrix theory and modest familiarity with signal processing, so the book is accessible to students from the advanced undergraduate level. Many exercises are also included.

Arising from courses taught by the authors, this largely self-contained treatment is ideal for mathematicians who are interested in applications or for students from applied fields who want to understand the mathematics behind their subject. Early chapters cover Fourier analysis, functional analysis, probability and linear algebra, all of which have been chosen to prepare the reader for the applications to come. The book includes rigorous proofs of core results in compressive sensing and wavelet convergence. Fundamental is the treatment of the linear system y=Φx in both finite and infinite dimensions. There are three possibilities: the system is determined, overdetermined or underdetermined, each with different aspects. The authors assume only basic familiarity with advanced calculus, linear algebra and matrix theory and modest familiarity with signal processing, so the book is accessible to students from the advanced undergraduate level. Many exercises are also included.

Machine learning methods extract value from vast data sets quickly and with modest resources. They are established tools in a wide range of industrial applications, including search engines, DNA sequencing, stock market analysis, and robot locomotion, and their use is spreading rapidly. People who know the methods have their choice of rewarding jobs. This hands-on text opens these opportunities to computer science students with modest mathematical backgrounds. It is designed for final-year undergraduates and master's students with limited background in linear algebra and calculus. Comprehensive and coherent, it develops everything from basic reasoning to advanced techniques within the framework of graphical models. Students learn more than a menu of techniques, they develop analytical and problem-solving skills that equip them for the real world. Numerous examples and exercises, both computer based and theoretical, are included in every chapter. Resources for students and instructors,

This second edition presents the theory of continuum mechanics using computational methods. The text covers a broad range of topics including general problems of large rotation and large deformations and the development and limitations of finite element formulations in solving such problems. Dr Shabana introduces theories on motion kinematics, strain, forces and stresses and goes on to discuss linear and nonlinear constitutive equations, including viscoelastic and plastic constitutive models. General nonlinear continuum mechanics theory is used to develop small and large finite element formulations which correctly describe rigid body motion for use in engineering applications. This second edition features a new chapter that focuses on computational geometry and finite element analysis. This book is ideal for graduate and undergraduate students, professionals and researchers who are interested in continuum mechanics.

This book is intended to provide the reader with a firm conceptual and empirical understanding of basic information-theoretic econometric models and methods. Because most data are observational, practitioners work with indirect noisy observations and ill-posed econometric models in the form of stochastic inverse problems. Consequently, traditional econometric methods in many cases are not applicable for answering many of the quantitative questions that analysts wish to ask. After initial chapters deal with parametric and semiparametric linear probability models, the focus turns to solving nonparametric stochastic inverse problems. In succeeding chapters, a family of power divergence measure-likelihood functions are introduced for a range of traditional and nontraditional econometric-model problems. Finally, within either an empirical maximum likelihood or loss context, Ron C. Mittelhammer and George G. Judge suggest a basis for choosing a member of the divergence family.

This book is intended to provide the reader with a firm conceptual and empirical understanding of basic information-theoretic econometric models and methods. Because most data are observational, practitioners work with indirect noisy observations and ill-posed econometric models in the form of stochastic inverse problems. Consequently, traditional econometric methods in many cases are not applicable for answering many of the quantitative questions that analysts wish to ask. After initial chapters deal with parametric and semiparametric linear probability models, the focus turns to solving nonparametric stochastic inverse problems. In succeeding chapters, a family of power divergence measure-likelihood functions are introduced for a range of traditional and nontraditional econometric-model problems. Finally, within either an empirical maximum likelihood or loss context, Ron C. Mittelhammer and George G. Judge suggest a basis for choosing a member of the divergence family.

There is a huge amount of literature on statistical models for the prediction of survival after diagnosis of a wide range of diseases like cancer, cardiovascular disease, and chronic kidney disease. C

Blending theoretical results with practical applications, this book provides an introduction to random matrix theory and shows how it can be used to tackle a variety of problems in wireless communications. The Stieltjes transform method, free probability theory, combinatoric approaches, deterministic equivalents and spectral analysis methods for statistical inference are all covered from a unique engineering perspective. Detailed mathematical derivations are presented throughout, with thorough explanation of the key results and all fundamental lemmas required for the reader to derive similar calculus on their own. These core theoretical concepts are then applied to a wide range of real-world problems in signal processing and wireless communications, including performance analysis of CDMA, MIMO and multi-cell networks, as well as signal detection and estimation in cognitive radio networks. The rigorous yet intuitive style helps demonstrate to students and researchers alike how to choose

This detailed introduction to distribution theory uses no measure theory, making it suitable for students in statistics and econometrics as well as for researchers who use statistical methods. Good backgrounds in calculus and linear algebra are important and a course in elementary mathematical analysis is useful, but not required. An appendix gives a detailed summary of the mathematical definitions and results that are used in the book. Topics covered range from the basic distribution and density functions, expectation, conditioning, characteristic functions, cumulants, convergence in distribution and the central limit theorem to more advanced concepts such as exchangeability, models with a group structure, asymptotic approximations to integrals, orthogonal polynomials and saddlepoint approximations. The emphasis is on topics useful in understanding statistical methodology; thus, parametric statistical models and the distribution theory associated with the normal distribution are cover

This new book provides a unified, in-depth, readable introduction to the multipredictor regression methods most widely used in biostatistics: linear models for continuous outcomes, logistic models for

In this book, the authors treat macroeconomic models as composed of large numbers of micro-units or agents of several types and explicitly discuss stochastic dynamic and combinatorial aspects of interactions among them. In mainstream macroeconomics sound microfoundations for macroeconomics have meant incorporating sophisticated intertemporal optimization by representative agents into models. Optimal growth theory, once meant to be normative, is now taught as a descriptive theory in mainstream macroeconomic courses. In neoclassical equilibria flexible prices led the economy to the state of full employment and marginal productivities are all equated. Professors Aoki and Yoshikawa contrariwise show that such equilibria are not possible in economies with a large number of agents of heterogeneous types. They employ a set of statistical dynamical tools via continuous-time Markov chains and statistical distributions of fractions of agents by types available in the new literature of combinator

The traditional view of the relationship between business and the arts is very much a one-way affair: organisations may endorse, fund or publicise the arts but the arts have nothing to offer from a business perspective. The Value of Arts for Business challenges this view by showing how the arts, in the form of Arts-based Initiatives (ABIs), can be used to enhance value-creation capacity and boost business performance. The book introduces and explains three models that show how organisations can successfully implement and manage ABIs. Firstly, the Arts Value Matrix enables managers to see how organisational value-drivers are affected by ABIs. Secondly, the Arts Benefits Constellation shows how to assess the benefits of using ABIs. Finally, the Arts Value Map shows how ABIs can be integrated and aligned with organisational strategy and operations. These models lay the foundations for a new research area exploring the links between arts and business.

Attempts by ecologists to establish models for predicting the growth of a population or the fluctuations of a natural resource can be confounded by environmental heterogeneity. Spatio-Temporal Heterogeneity explores a range of available statistical methods to help ecologists in the attempt to unravel complexities, demonstrating how to place these changes into an understandable statistical framework. It addresses several key questions, including how to interpret the parameters of statistical models in relation to the biological and environmental realities, how to design a study to collect the best sample data and how to avoid pitfalls in modelling, design, statistical assessment and interpretation. Dutilleul uses a variety of examples to facilitate understanding, from plant ecology, earth and atmospheric sciences, animal biology, forestry and limnology. The accompanying CD-ROM contains MATLAB and SAS codes to aid analyses.

Attempts by ecologists to establish models for predicting the growth of a population or the fluctuations of a natural resource can be confounded by environmental heterogeneity. Spatio-Temporal Heterogeneity explores a range of available statistical methods to help ecologists in the attempt to unravel complexities, demonstrating how to place these changes into an understandable statistical framework. It addresses several key questions, including how to interpret the parameters of statistical models in relation to the biological and environmental realities, how to design a study to collect the best sample data and how to avoid pitfalls in modelling, design, statistical assessment and interpretation. Dutilleul uses a variety of examples to facilitate understanding, from plant ecology, earth and atmospheric sciences, animal biology, forestry and limnology. The accompanying CD-ROM contains MATLAB and SAS codes to aid analyses.

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

Describing and evaluating the basic principles and methods of subsurface sensing and imaging, Introduction to Subsurface Imaging is a clear and comprehensive treatment that links theory to a wide range of real-world applications in medicine, biology, security and geophysical/environmental exploration. It integrates the different sensing techniques (acoustic, electric, electromagnetic, optical, x-ray or particle beams) by unifying the underlying physical and mathematical similarities, and computational and algorithmic methods. Time-domain, spectral and multisensor methods are also covered, whilst all the necessary mathematical, statistical and linear systems tools are given in useful appendices to make the book self-contained. Featuring a logical blend of theory and applications, a wealth of color illustrations, homework problems and numerous case studies, this is suitable for use as both a course text and as a professional reference.

Simplex geometry is a topic generalizing geometry of the triangle and tetrahedron. The appropriate tool for its study is matrix theory, but applications usually involve solving huge systems of linear equations or eigenvalue problems, and geometry can help in visualizing the behaviour of the problem. In many cases, solving such systems may depend more on the distribution of non-zero coefficients than on their values, so graph theory is also useful. The author has discovered a method that in many (symmetric) cases helps to split huge systems into smaller parts. Many readers will welcome this book, from undergraduates to specialists in mathematics, as well as non-specialists who only use mathematics occasionally, and anyone who enjoys geometric theorems. It acquaints the reader with basic matrix theory, graph theory and elementary Euclidean geometry so that they too can appreciate the underlying connections between these various areas of mathematics and computer science.

Extended abstracts for 11 papers look at data sources for GeoChange research, sensing change, spatial and temporal change and scale, and combining statistical and ontological models. GeoChange may be

The search for symmetry is part of the fundamental scientific paradigm in mathematics and physics. Can this be valid also for economics? This book represents an attempt to explore this possibility. The behavior of price-taking producers, monopolists, monopsonists, sectoral market equilibria, behavior under risk and uncertainty, and two-person zero- and non-zero-sum games are analyzed and discussed under the unifying structure called the linear complementarity problem. Furthermore, the equilibrium problem allows for the relaxation of often-stated but unnecessary assumptions. This unifying approach offers the advantage of a better understanding of the structure of economic models. It also introduces the simplest and most elegant algorithm for solving a wide class of problems.

The search for symmetry is part of the fundamental scientific paradigm in mathematics and physics. Can this be valid also for economics? This book represents an attempt to explore this possibility. The behavior of price-taking producers, monopolists, monopsonists, sectoral market equilibria, behavior under risk and uncertainty, and two-person zero- and non-zero-sum games are analyzed and discussed under the unifying structure called the linear complementarity problem. Furthermore, the equilibrium problem allows for the relaxation of often-stated but unnecessary assumptions. This unifying approach offers the advantage of a better understanding of the structure of economic models. It also introduces the simplest and most elegant algorithm for solving a wide class of problems.

Econophysics applies the methodology of physics to the study of economics. However, whilst physicists have good understanding of statistical physics, they may be unfamiliar with recent advances in statistical conjectures, including Bayesian and predictive methods. Equally, economists with knowledge of probabilities do not have a background in statistical physics and agent-based models. Proposing a unified view for a dynamic probabilistic approach, this book is useful for advanced undergraduate and graduate students as well as researchers in physics, economics and finance. The book takes a finitary approach to the subject, discussing the essentials of applied probability, and covering finite Markov chain theory and its applications to real systems. Each chapter ends with a summary, suggestions for further reading, and exercises with solutions at the end of the book.

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

This book provides a thorough analysis of internal rating systems. Two case studies are devoted to building and validating statistical-based models for borrowers’ ratings, using SPSS-PASW and SA

Prospect Theory: For Risk and Ambiguity, provides a comprehensive and accessible textbook treatment of the way decisions are made both when we have the statistical probabilities associated with uncertain future events (risk) and when we lack them (ambiguity). The book presents models, primarily prospect theory, that are both tractable and psychologically realistic. A method of presentation is chosen that makes the empirical meaning of each theoretical model completely transparent. Prospect theory has many applications in a wide variety of disciplines. The material in the book has been carefully organized to allow readers to select pathways through the book relevant to their own interests. With numerous exercises and worked examples, the book is ideally suited to the needs of students taking courses in decision theory in economics, mathematics, finance, psychology, management science, health, computer science, Bayesian statistics, and engineering.

Prospect Theory: For Risk and Ambiguity, provides a comprehensive and accessible textbook treatment of the way decisions are made both when we have the statistical probabilities associated with uncertain future events (risk) and when we lack them (ambiguity). The book presents models, primarily prospect theory, that are both tractable and psychologically realistic. A method of presentation is chosen that makes the empirical meaning of each theoretical model completely transparent. Prospect theory has many applications in a wide variety of disciplines. The material in the book has been carefully organized to allow readers to select pathways through the book relevant to their own interests. With numerous exercises and worked examples, the book is ideally suited to the needs of students taking courses in decision theory in economics, mathematics, finance, psychology, management science, health, computer science, Bayesian statistics, and engineering.

This monograph provides an empirical analysis of the enlistment, attrition, and reenlistment effects of bonuses, applying statistical models that control for such other factors as recruiting resources

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.