Matrix-analytic Methods in Stochastic Models

Doubt over the trustworthiness of published empirical results is not unwarranted and is often a result of statistical mis-specification: invalid probabilistic assumptions imposed on data. Now in its second edition, this bestselling textbook offers a comprehensive course in empirical research methods, teaching the probabilistic and statistical foundations that enable the specification and validation of statistical models, providing the basis for an informed implementation of statistical procedure to secure the trustworthiness of evidence. Each chapter has been thoroughly updated, accounting for developments in the field and the author's own research. The comprehensive scope of the textbook has been expanded by the addition of a new chapter on the Linear Regression and related statistical models. This new edition is now more accessible to students of disciplines beyond economics and includes more pedagogical features, with an increased number of examples as well as review questions and e

Variational Bayesian learning is one of the most popular methods in machine learning. Designed for researchers and graduate students in machine learning, this book summarizes recent developments in the non-asymptotic and asymptotic theory of variational Bayesian learning and suggests how this theory can be applied in practice. The authors begin by developing a basic framework with a focus on conjugacy, which enables the reader to derive tractable algorithms. Next, it summarizes non-asymptotic theory, which, although limited in application to bilinear models, precisely describes the behavior of the variational Bayesian solution and reveals its sparsity inducing mechanism. Finally, the text summarizes asymptotic theory, which reveals phase transition phenomena depending on the prior setting, thus providing suggestions on how to set hyperparameters for particular purposes. Detailed derivations allow readers to follow along without prior knowledge of the mathematical techniques specific to

Major figures of twentieth-century philosophy were enthralled by the revolution in formal logic, and many of their arguments are based on novel mathematical discoveries. Hilary Putnam claimed that the Löwenheim-Skølem theorem refutes the existence of an objective, observer-independent world; Bas van Fraassen claimed that arguments against empiricism in philosophy of science are ineffective against a semantic approach to scientific theories; W. V. O. Quine claimed that the distinction between analytic and synthetic truths is trivialized by the fact that any theory can be reduced to one in which all truths are analytic. This book dissects these and other arguments through in-depth investigation of the mathematical facts undergirding them. It presents a systematic, mathematically rigorous account of the key notions arising from such debates, including theory, equivalence, translation, reduction, and model. The result is a far-reaching reconceptualization of the role of formal methods in a

Major figures of twentieth-century philosophy were enthralled by the revolution in formal logic, and many of their arguments are based on novel mathematical discoveries. Hilary Putnam claimed that the Löwenheim-Skølem theorem refutes the existence of an objective, observer-independent world; Bas van Fraassen claimed that arguments against empiricism in philosophy of science are ineffective against a semantic approach to scientific theories; W. V. O. Quine claimed that the distinction between analytic and synthetic truths is trivialized by the fact that any theory can be reduced to one in which all truths are analytic. This book dissects these and other arguments through in-depth investigation of the mathematical facts undergirding them. It presents a systematic, mathematically rigorous account of the key notions arising from such debates, including theory, equivalence, translation, reduction, and model. The result is a far-reaching reconceptualization of the role of formal methods in a

Empirical translation studies is a rapidly evolving research area. This volume, written by world-leading researchers, demonstrates the integration of two new research paradigms: socially-oriented and data driven approaches to empirical translation studies. These two models expand current translation studies and stimulate reader debates around how development of quantitative research methods and integration with advances in translation technologies would significantly increase the research capacities of translation studies. Highly engaging, the volume pioneers the development of socially-oriented innovative research methods to enhance the current research capacities of theoretical (descriptive) translation studies in order to tackle real-life research issues, such as environmental protection and multicultural health promotion. Illustrative case studies are used, bringing insight into advanced research methodologies of designing, developing and analysing large scale digital databases for

The methods and techniques presented in this book are focused on spatial data and its use in monitoring agricultural resources, farm management, and regional markets. Spatial econometrics models are i

The seismic ambient field allows us to study interactions between the atmosphere, the oceans and the solid Earth. The theoretical understanding of seismic ambient noise has improved substantially in the last decades, and the number of its applications has increased dramatically. With chapters written by eminent scientists from the field, this book covers a range of topics including ambient noise observations, generation models of their physical origins, numerical modelling and processing methods. The later chapters focus on applications in imaging and monitoring the internal structure of the Earth, including interferometry for time-dependant imaging and tomography. This volume thus provides a comprehensive overview of this cutting-edge discipline for graduate students studying geophysics and for scientists working in seismology and other imaging sciences.

This practical book is designed for applied researchers who want to use mixed models with their data. It discusses the basic principles of mixed model analysis, including two-level and three-level structures, and covers continuous outcome variables, dichotomous outcome variables, and categorical and survival outcome variables. Emphasizing interpretation of results, the book develops the most important applications of mixed models, such as the study of group differences, longitudinal data analysis, multivariate mixed model analysis, IPD meta-analysis, and mixed model predictions. All examples are analyzed with STATA, and an extensive overview and comparison of alternative software packages is provided. All datasets used in the book are available for download, so readers can re-analyze the examples to gain a strong understanding of the methods. Although most examples are taken from epidemiological and clinical studies, this book is also highly recommended for researchers working in other

Gain an in-depth understanding of converter-interfaced energy storage systems with this unique text, covering modelling, dynamic behaviour, control, and stability analysis. Providing comprehensive coverage, it demonstrates the technical and economic aspects of energy storage systems, and provides a thorough overview of energy storage technologies. Several different modelling techniques are presented, including power system models, voltage-sourced converter models, and energy storage system models. Using a novel stochastic control approach developed by the authors, you will learn about the impact of energy storage on the dynamic interaction of microgrids with distribution and transmission systems. Compare the numerous real-world simulation data and numerical examples provided with your own models and control strategies. Accompanied online by a wealth of numerical examples and supporting data, this is the ideal text for graduate students, researchers, and industry professionals working i

This book represents the first comprehensive examination of templatic constructions - namely, linguistic structures involving unexpected linear stipulation - in both morphology and syntax from a typological perspective. It provides a state-of-the-art overview of the previous literature, develops a new typology for categorizing templatic constructions across grammatical domains, and examines their cross-linguistic variation by employing cutting-edge computational methods. It will be of interest to descriptive linguists seeking to gain a better sense of the diversity of the world's templatic constructions, theoretical linguists developing restrictive models of possible templates, and typologists interested in the attested range of patterns of linear stipulation and the application of new kinds of multivariate methods to cross-linguistic data. The new typological framework is illustrated in detail via a number of case studies involving languages of Africa, Europe, Asia, and the Americas,

This book is a comprehensive account of the most recent developments in modern ophthalmic optics. It makes use of the powerful matrix formalism to describe curvature and power, providing a unified view of the optical and geometrical properties of lenses. This unified approach is applicable to the design and properties of not only spectacle lenses, but also contact and intraocular lenses (IOL). The newest developments in lens design, manufacturing and testing are discussed, with an emphasis on the description of free-form technology, which has surpassed traditional manufacturing methods and allows digital lenses to be specifically designed with the unique requirements of the user. Other important topics which are covered include modern lens materials, up-to-date lens measuring techniques, contact and intraocular lenses, progressive power lenses, low vision aids, ocular protection and coatings. Providing a broad overview of recent developments in the field, it is ideal for researchers, m

The Earth and environmental sciences are becoming progressively more quantitative due to the increased use of mathematical models and new data analysis techniques. This accessible introduction presents an overview of the mathematical methods essential for understanding Earth processes, providing an invaluable resource for students and early career researchers who may have missed (or forgotten) the mathematics they need to succeed as scientists. Topics build gently from basic methods such as calculus to more advanced techniques including linear algebra and differential equations. The practical applications of the mathematical methods to a variety of topics are discussed, ranging from atmospheric science and oceanography to biogeochemistry and geophysics. Including over 530 exercises and end-of-chapter problems, as well as additional computer codes in Python and MATLAB®, this book supports readers in applying appropriate analytical or computational methods to solving real research questi

This book combines a comprehensive state-of-the-art analysis of bifurcations of discrete-time dynamical systems with concrete instruction on implementations (and example applications) in the free MATLAB® software MatContM developed by the authors. While self-contained and suitable for independent study, the book is also written with users in mind and is an invaluable reference for practitioners. Part I focuses on theory, providing a systematic presentation of bifurcations of fixed points and cycles of finite-dimensional maps, up to and including cases with two control parameters. Several complementary methods, including Lyapunov exponents, invariant manifolds and homoclinic structures, and parts of chaos theory, are presented. Part II introduces MatContM through step-by-step tutorials on how to use the general numerical methods described in Part I for simple dynamical models defined by one- and two-dimensional maps. Further examples in Part III show how MatContM can be used to analyze

This practical book is designed for applied researchers who want to use mixed models with their data. It discusses the basic principles of mixed model analysis, including two-level and three-level structures, and covers continuous outcome variables, dichotomous outcome variables, and categorical and survival outcome variables. Emphasizing interpretation of results, the book develops the most important applications of mixed models, such as the study of group differences, longitudinal data analysis, multivariate mixed model analysis, IPD meta-analysis, and mixed model predictions. All examples are analyzed with STATA, and an extensive overview and comparison of alternative software packages is provided. All datasets used in the book are available for download, so readers can re-analyze the examples to gain a strong understanding of the methods. Although most examples are taken from epidemiological and clinical studies, this book is also highly recommended for researchers working in other

This book presents a quantitative history of constitutional law in the United States and brings together humanistic and social-scientific approaches to studying law. Using theoretical models of adjudication, Tom S. Clark presents a statistical model of law and uses the model to document the historical development of constitutional law. Using sophisticated statistical methods and historical analysis of court decisions, the author documents how social and political forces shape the path of law. Spanning the history of constitutional law since Reconstruction, this book illustrates the way in which the law evolves with American life and argues that a social-scientific approach to the history of law illuminates connections across disparate areas of the law, connected by the social context in which the Constitution has been interpreted.

This hands-on introduction to numerical geodynamic modelling provides a solid grounding in the necessary mathematical theory and techniques, including continuum mechanics and partial differential equations, before introducing key numerical modelling methods and applications. Fully updated, this second edition includes four completely new chapters covering the most recent advances in modelling inertial processes, seismic cycles and fluid-solid interactions, and the development of adaptive mesh refinement algorithms. Many well-documented, state-of-the-art visco-elasto-plastic 2D models are presented, which allow robust modelling of key geodynamic processes. Requiring only minimal prerequisite mathematical training, and featuring over sixty practical exercises and ninety MATLAB® examples, this user-friendly resource encourages experimentation with geodynamic models. It is an ideal introduction for advanced courses and can be used as a self-study aid for graduates seeking to master geodyna

Music therapy as an intervention in medical, educational and many other environments has a rich and diverse history of methods, approaches and models. Consolidating the many components of music therap

Word stress has long presented challenges to phonologists, as they have sought to uncover patterns in its distribution, and devise models to account for its behaviour and formal representation both within single languages and cross-linguistically. In this collection, a team of world-renowned researchers present a variety of viewpoints on the methods and problems involved. Offering fresh perspectives on the topic and its study, this book is specifically concerned with basing theoretical work on broad typological surveys and focuses on the collection, selection and use of data in the analysis of word stress and word rhythm, including their phonetic manifestations. An extensive introduction presents a state-of-the-art review of stress research. The contributors also present StressTyp2, a project in an advanced stage of development, which intends to make publicly available information on word stress in a broad sample of languages and will offer new ways of understanding this key research a

Recent years have witnessed an explosion in the volume and variety of data collected in all scientific disciplines and industrial settings. Such massive data sets present a number of challenges to researchers in statistics and machine learning. This book provides a self-contained introduction to the area of high-dimensional statistics, aimed at the first-year graduate level. It includes chapters that are focused on core methodology and theory - including tail bounds, concentration inequalities, uniform laws and empirical process, and random matrices - as well as chapters devoted to in-depth exploration of particular model classes - including sparse linear models, matrix models with rank constraints, graphical models, and various types of non-parametric models. With hundreds of worked examples and exercises, this text is intended both for courses and for self-study by graduate students and researchers in statistics, machine learning, and related fields who must understand, apply, and ad

Meaningful use of advanced Bayesian methods requires a good understanding of the fundamentals. This engaging book explains the ideas that underpin the construction and analysis of Bayesian models, with particular focus on computational methods and schemes. The unique features of the text are the extensive discussion of available software packages combined with a brief but complete and mathematically rigorous introduction to Bayesian inference. The text introduces Monte Carlo methods, Markov chain Monte Carlo methods, and Bayesian software, with additional material on model validation and comparison, transdimensional MCMC, and conditionally Gaussian models. The inclusion of problems makes the book suitable as a textbook for a first graduate-level course in Bayesian computation with a focus on Monte Carlo methods. The extensive discussion of Bayesian software - R/R-INLA, OpenBUGS, JAGS, STAN, and BayesX - makes it useful also for researchers and graduate students from beyond statistics.

Meaningful use of advanced Bayesian methods requires a good understanding of the fundamentals. This engaging book explains the ideas that underpin the construction and analysis of Bayesian models, with particular focus on computational methods and schemes. The unique features of the text are the extensive discussion of available software packages combined with a brief but complete and mathematically rigorous introduction to Bayesian inference. The text introduces Monte Carlo methods, Markov chain Monte Carlo methods, and Bayesian software, with additional material on model validation and comparison, transdimensional MCMC, and conditionally Gaussian models. The inclusion of problems makes the book suitable as a textbook for a first graduate-level course in Bayesian computation with a focus on Monte Carlo methods. The extensive discussion of Bayesian software - R/R-INLA, OpenBUGS, JAGS, STAN, and BayesX - makes it useful also for researchers and graduate students from beyond statistics.

This is a thorough exploration of the models and methods of financial econometrics by one of the world's leading financial econometricians and is for students in economics, finance, statistics, mathematics, and engineering who are interested in financial applications. Based on courses taught around the world, the up-to-date content covers developments in econometrics and finance over the last twenty years while ensuring a solid grounding in the fundamental principles of the field. Care has been taken to link theory and application to provide real-world context for students. Worked exercises and empirical examples have also been included to make sure complicated concepts are solidly explained and understood.

This is a thorough exploration of the models and methods of financial econometrics by one of the world's leading financial econometricians and is for students in economics, finance, statistics, mathematics, and engineering who are interested in financial applications. Based on courses taught around the world, the up-to-date content covers developments in econometrics and finance over the last twenty years while ensuring a solid grounding in the fundamental principles of the field. Care has been taken to link theory and application to provide real-world context for students. Worked exercises and empirical examples have also been included to make sure complicated concepts are solidly explained and understood.

Loss Models contains a wealth of examples that highlight the real-world applications of the concepts presented, and puts the emphasis on calculations and spreadsheet implementation. With a focus on the loss process, the book reviews the essential quantitative techniques such as random variables, basic distributional quantities, and the recursive method, and discusses techniques for classifying and creating distributions. Parametric, non-parametric, and Bayesian estimation methods are thoroughly covered. In addition, the authors offer practical advice for choosing an appropriate model. This important text:•Presents a revised and updated edition of the classic guide for actuaries that aligns with newly introduced Exams STAM and LTAM•Contains a wealth of exercises taken from previous exams•Includes fresh and additional content related to the material required by the Society of Actuaries (SOA) and the Canadian Institute of Actuaries (CIA)•Offers a solutions manual available for further ins

This book addresses essential questions about housing by building theoretical models based on various real world problems in Japan and testing these models using econometric methods. Almost all relate

This book presents a quantitative history of constitutional law in the United States and brings together humanistic and social-scientific approaches to studying law. Using theoretical models of adjudication, Tom S. Clark presents a statistical model of law and uses the model to document the historical development of constitutional law. Using sophisticated statistical methods and historical analysis of court decisions, the author documents how social and political forces shape the path of law. Spanning the history of constitutional law since Reconstruction, this book illustrates the way in which the law evolves with American life and argues that a social-scientific approach to the history of law illuminates connections across disparate areas of the law, connected by the social context in which the Constitution has been interpreted.

By the award-winning former president of the Linguistic Society of America, this collection of some of John Russell Rickford's pioneering works shows how linguists in sociolinguistics and creole studies can benefit from utilizing data, theories and methods from each other, as they more frequently did in the 1960s and 1970s, when both subfields, in their modern forms at least, were getting started. The volume addresses fundamental sociolinguistic topics such as social class, style, fieldwork, speech community, sociolinguistic competence and language attitudes with data from Guyanese and other Caribbean creoles. Recurrent concepts are also considered including language versatility, variation and change, vernacular use, school success and criminal justice in African America and the Caribbean, using models, case studies and methodologies from sociolinguistics. Theoretical and applied scholars, students apprehensive about sociolinguistic fieldwork, and those considering dynamic methods like

Gain insights into image-processing methodologies and algorithms, using machine learning and neural networks in Python. This book begins with the environment setup, understanding basic image-processing terminology, and exploring Python concepts that will be useful for implementing the algorithms discussed in the book. You will then cover all the core image processing algorithms in detail before moving onto the biggest computer vision library: OpenCV. You’ll see the OpenCV algorithms and how to use them for image processing. The next section looks at advanced machine learning and deep learning methods for image processing and classification. You’ll work with concepts such as pulse coupled neural networks, AdaBoost, XG boost, and convolutional neural networks for image-specific applications. Later you’ll explore how models are made in real time and then deployed using various DevOps tools. All the concepts in Practical Machine Learning and Image Processing are explained using r

This pioneering, course-tested text is the first to combine communications theory with the physics of optical communications. Comprehensive and rigorous, it brings together an in-depth treatment of the physical characteristics of the guided lightwave channel with the study of modern methods of algorithmic-based communication in time and space. The many different levels at which a lightwave communication signal can be described are integrated to provide a unified explanation of how a commonplace bit stream is transformed into a physical lightwave, how that lightwave travels through an optical fiber, and how it is then transformed back into the bit stream. Background fundamentals such as linear systems and electromagnetics are explained in relation to modern topics such as channel models, encoding, modulation and interference, and end-of-chapter problems are provided throughout. This is an essential text for students taking courses on optical communications, as well as researchers and pr

The text covers important algorithm design techniques, such as greedy algorithms, dynamic programming, and divide-and-conquer, and gives applications to contemporary problems. Techniques including Fast Fourier transform, KMP algorithm for string matching, CYK algorithm for context free parsing and gradient descent for convex function minimization are discussed in detail. The book's emphasis is on computational models and their effect on algorithm design. It gives insights into algorithm design techniques in parallel, streaming and memory hierarchy computational models. The book also emphasizes the role of randomization in algorithm design, and gives numerous applications ranging from data-structures such as skip-lists to dimensionality reduction methods.

The text covers important algorithm design techniques, such as greedy algorithms, dynamic programming, and divide-and-conquer, and gives applications to contemporary problems. Techniques including Fast Fourier transform, KMP algorithm for string matching, CYK algorithm for context free parsing and gradient descent for convex function minimization are discussed in detail. The book's emphasis is on computational models and their effect on algorithm design. It gives insights into algorithm design techniques in parallel, streaming and memory hierarchy computational models. The book also emphasizes the role of randomization in algorithm design, and gives numerous applications ranging from data-structures such as skip-lists to dimensionality reduction methods.

For courses in Introductory Statistics. Encourages statistical thinking using technology, innovative methods, and a sense of humor Inspired by the 2016 GAISE Report revision, Stats: Data and Models, 5th Edition by De Veaux/Velleman/Bock uses innovative strategies to help students think critically about data — while maintaining the book’s core concepts, coverage, and most importantly, readability.By using technology and simulations to demonstrate variability at critical points throughout the course, the authors make it easier for instructors to teach and for students to understand more complicated statistical concepts later in the course (such as the Central Limit Theorem). In addition, students get more exposure to large data sets and multivariate thinking, which better prepares them to be critical consumers of statistics in the 21st century. The 5th Edition’s approach to teaching Stats: Data and Models is revolutionary, yet it retains the book's lively tone

Richly illustrated throughout with actual tissue images, this innovative book shows that the soft-hard tissue junction is best understood in a biomechanical context. The authors describe their pioneering experimental methods, providing an essential structure-function framework for computational modelling, and thereby encouraging the development of more realistic, predictive models of this important tissue junction. Covering the three main musculoskeletal junctions of cartilage-bone, disc-vertebra, and ligament/tendon-bone, the relevant soft tissues are examined with respect to both their own inherent structure and their mode of integration with the hard tissue. The soft-hard tissue interface is explored with a focus on structural damage resulting from overloading, and its associated pathologies. Adopting a multiscale approach, ranging in structural resolution from the macro to fibril levels, this is a must-have guide to the field and an ideal resource for researchers seeking new and cr

Geodynamics is the study of the deformation and flow of the solid Earth and other planetary interiors. Focusing on the Earth's mantle, this book provides a comprehensive, mathematically advanced treatment of the continuum mechanics of mantle processes and the craft of formulating geodynamical models to approximate them. Topics covered include slow viscous flow, elasticity and viscoelasticity, boundary-layer theory, long-wave theories including lubrication theory and shell theory, two-phase flow, and hydrodynamic stability and thermal convection. A unifying theme is the utility of powerful general methods (dimensional analysis, scaling analysis, and asymptotic analysis) that can be applied in many specific contexts. Featuring abundant exercises with worked solutions for graduate students and researchers, this book will make a useful resource for Earth scientists and applied mathematicians with an interest in mantle dynamics and geodynamics more broadly.

Understand the benefits of robust statistics for signal processing with this authoritative yet accessible text. The first ever book on the subject, it provides a comprehensive overview of the field, moving from fundamental theory through to important new results and recent advances. Topics covered include advanced robust methods for complex-valued data, robust covariance estimation, penalized regression models, dependent data, robust bootstrap, and tensors. Robustness issues are illustrated throughout using real-world examples and key algorithms are included in a MATLAB Robust Signal Processing Toolbox accompanying the book online, allowing the methods discussed to be easily applied and adapted to multiple practical situations. This unique resource provides a powerful tool for researchers and practitioners working in the field of signal processing.

Why in the early 1970s does The Times reject the idea of a national lottery, as rewarding luck not merit and effort, but warmly welcome one by the 1990s? Why in the 1970s do the Daily Mail's TV reviews address serious contemporary themes such as class- and race-relations, whereas forty years later they are largely concerned with celebrities, talent shows, and nostalgia? Why does the Conservative Chancellor in the 2010s mention 'Britain' so very often, when the Conservative Chancellor in the 1970s scarcely does at all? Covering news stories spanning fort-five years, Michael Toolan explores how wealth inequality has been presented in centre-right British newspapers, focusing on changes in the representation may have helped present-day inequality seem justifiable. Toolan employs corpus linguistic and critical discourse analytic methods to identify changing lexis and verbal patterns and gaps, all of which contribute to the way wealth inequality was represented in each of the decades from t

This conference proceedings volume presents advanced methods in time series estimation models that are applicable various areas of applied economic research such as international economics, macroecono

This book introduces double-prism multi-mode scanning theory and technology, focusing on double Risley-prism, multi-mode scanning models, methods and key techniques applied in multi-mode optical scann

The Euler and Navier–Stokes equations are the fundamental mathematical models of fluid mechanics, and their study remains central in the modern theory of partial differential equations. This volume of articles, derived from the workshop 'PDEs in Fluid Mechanics' held at the University of Warwick in 2016, serves to consolidate, survey and further advance research in this area. It contains reviews of recent progress and classical results, as well as cutting-edge research articles. Topics include Onsager's conjecture for energy conservation in the Euler equations, weak-strong uniqueness in fluid models and several chapters address the Navier–Stokes equations directly; in particular, a retelling of Leray's formative 1934 paper in modern mathematical language. The book also covers more general PDE methods with applications in fluid mechanics and beyond. This collection will serve as a helpful overview of current research for graduate students new to the area and for more established researc

Stochastic differential equations are differential equations whose solutions are stochastic processes. They exhibit appealing mathematical properties that are useful in modeling uncertainties and noisy phenomena in many disciplines. This book is motivated by applications of stochastic differential equations in target tracking and medical technology and, in particular, their use in methodologies such as filtering, smoothing, parameter estimation, and machine learning. It builds an intuitive hands-on understanding of what stochastic differential equations are all about, but also covers the essentials of Itô calculus, the central theorems in the field, and such approximation schemes as stochastic Runge–Kutta. Greater emphasis is given to solution methods than to analysis of theoretical properties of the equations. The book's practical approach assumes only prior understanding of ordinary differential equations. The numerous worked examples and end-of-chapter exercises include application-