Matrix-analytic Methods in Stochastic Models

This volume provides a practical introduction to the method of maximum likelihood as used in social science research. Ward and Ahlquist focus on applied computation in R and use real social science data from actual, published research. Unique among books at this level, it develops simulation-based tools for model evaluation and selection alongside statistical inference. The book covers standard models for categorical data as well as counts, duration data, and strategies for dealing with data missingness. By working through examples, math, and code, the authors build an understanding about the contexts in which maximum likelihood methods are useful and develop skills in translating mathematical statements into executable computer code. Readers will not only be taught to use likelihood-based tools and generate meaningful interpretations, but they will also acquire a solid foundation for continued study of more advanced statistical techniques.

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

This book presents the latest developments in optimization and optimal control models; exact, approximate and hybrid methods; and their applications in lean and green supply chains. It examines supply

This volume provides methods to study bone morphogenetic proteins (BMPs) and BMP modulators in cell culture, in both invertebrate and vertebrate animal models, and for therapeutic applications. Chapte

This volume provides a practical introduction to the method of maximum likelihood as used in social science research. Ward and Ahlquist focus on applied computation in R and use real social science data from actual, published research. Unique among books at this level, it develops simulation-based tools for model evaluation and selection alongside statistical inference. The book covers standard models for categorical data as well as counts, duration data, and strategies for dealing with data missingness. By working through examples, math, and code, the authors build an understanding about the contexts in which maximum likelihood methods are useful and develop skills in translating mathematical statements into executable computer code. Readers will not only be taught to use likelihood-based tools and generate meaningful interpretations, but they will also acquire a solid foundation for continued study of more advanced statistical techniques.

Optimization methods play a central role in financial modeling. This textbook is devoted to explaining how state-of-the-art optimization theory, algorithms, and software can be used to efficiently solve problems in computational finance. It discusses some classical mean–variance portfolio optimization models as well as more modern developments such as models for optimal trade execution and dynamic portfolio allocation with transaction costs and taxes. Chapters discussing the theory and efficient solution methods for the main classes of optimization problems alternate with chapters discussing their use in the modeling and solution of central problems in mathematical finance. This book will be interesting and useful for students, academics, and practitioners with a background in mathematics, operations research, or financial engineering. The second edition includes new examples and exercises as well as a more detailed discussion of mean–variance optimization, multi-period models, and add

This book offers an up-to-date, comprehensive coverage of stochastic dominance and its related concepts in a unified framework. A method for ordering probability distributions, stochastic dominance has grown in importance recently as a way to measure comparisons in welfare economics, inequality studies, health economics, insurance wages, and trade patterns. Whang pays particular attention to inferential methods and applications, citing and summarizing various empirical studies in order to relate the econometric methods with real applications and using computer codes to enable the practical implementation of these methods. Intuitive explanations throughout the book ensure that readers understand the basic technical tools of stochastic dominance.

For three centuries, a mixture of religion, violence, and economic conditions created a fertile matrix in Western Europe that racialized an entire diasporic population who lived in the urban centers of the Latin West: Jews. This Element explores how religion and violence, visited on Jewish bodies and Jewish lives, coalesced to create the first racial state in the history of the West. It is an example of how the methods and conceptual frames of postcolonial and race studies, when applied to the study of religion, can be productive of scholarship that rewrites the foundational history of the past.

It is difficult to imagine forces in the modern world as potent as nationalism and religion. Both provide people with a source of meaning, each has motivated individuals to carry out extraordinary acts of heroism and cruelty, and both serve as the foundation for communal and personal identity. While the subject has received both scholarly and popular attention, this distinctive book is the first comparative study to examine the origins and development of three distinct models: religious nationalism, secular nationalism, and civil-religious nationalism. Using multiple methods, the authors develop a new theoretical framework that can be applied across diverse countries and religious traditions to understand the emergence, development, and stability of different church-state arrangements over time. The work combines public opinion, constitutional, and content analysis of the United States, Israel, India, Greece, Uruguay, and Malaysia, weaving together historical and contemporary illustrat

It is difficult to imagine forces in the modern world as potent as nationalism and religion. Both provide people with a source of meaning, each has motivated individuals to carry out extraordinary acts of heroism and cruelty, and both serve as the foundation for communal and personal identity. While the subject has received both scholarly and popular attention, this distinctive book is the first comparative study to examine the origins and development of three distinct models: religious nationalism, secular nationalism, and civil-religious nationalism. Using multiple methods, the authors develop a new theoretical framework that can be applied across diverse countries and religious traditions to understand the emergence, development, and stability of different church-state arrangements over time. The work combines public opinion, constitutional, and content analysis of the United States, Israel, India, Greece, Uruguay, and Malaysia, weaving together historical and contemporary illustrat

Working with Dynamic Crop Models: Methods, Tools and Examples for Agriculture and Environment, 3e, is a complete guide to working with dynamic system models, with emphasis on models in agronomy and en

High-dimensional probability offers insight into the behavior of random vectors, random matrices, random subspaces, and objects used to quantify uncertainty in high dimensions. Drawing on ideas from probability, analysis, and geometry, it lends itself to applications in mathematics, statistics, theoretical computer science, signal processing, optimization, and more. It is the first to integrate theory, key tools, and modern applications of high-dimensional probability. Concentration inequalities form the core, and it covers both classical results such as Hoeffding's and Chernoff's inequalities and modern developments such as the matrix Bernstein's inequality. It then introduces the powerful methods based on stochastic processes, including such tools as Slepian's, Sudakov's, and Dudley's inequalities, as well as generic chaining and bounds based on VC dimension. A broad range of illustrations is embedded throughout, including classical and modern results for covariance estimation, clust

Born of a belief that economic insights should not require much mathematical sophistication, this book proposes novel and parsimonious methods to incorporate ignorance and uncertainty into economic modeling, without complex mathematics. Economics has made great strides over the past several decades in modeling agents' decisions when they are incompletely informed, but many economists believe that there are aspects of these models that are less than satisfactory. Among the concerns are that ignorance is not captured well in most models, that agents' presumed cognitive ability is implausible, and that derived optimal behavior is sometimes driven by the fine details of the model rather than the underlying economics. Compte and Postlewaite lay out a tractable way to address these concerns, and to incorporate plausible limitations on agents' sophistication. A central aspect of the proposed methodology is to restrict the strategies assumed available to agents.

Social scientists who study religion generally believe that social networks play a central role in religious life. However, most studies draw on measures that are relatively poor proxies for capturing the effects of social networks. This book illustrates how researchers can draw on formal social network analysis methods to explore the interplay of networks and religion. The book's introductory chapters provide overviews of the social scientific study of religion and social network analysis. The remaining chapters explore a variety of topics current in the social scientific study of religion, as well as introducing a variety of social network theories and methods, such as balance theory, ego-network analysis, exponential random graph models, and stochastic actor-oriented models. By embedding social network analysis within a social scientific study of religion framework, Networks and Religion offers an array of approaches for studying the role that social networks play in religious belie

Born of a belief that economic insights should not require much mathematical sophistication, this book proposes novel and parsimonious methods to incorporate ignorance and uncertainty into economic modeling, without complex mathematics. Economics has made great strides over the past several decades in modeling agents' decisions when they are incompletely informed, but many economists believe that there are aspects of these models that are less than satisfactory. Among the concerns are that ignorance is not captured well in most models, that agents' presumed cognitive ability is implausible, and that derived optimal behavior is sometimes driven by the fine details of the model rather than the underlying economics. Compte and Postlewaite lay out a tractable way to address these concerns, and to incorporate plausible limitations on agents' sophistication. A central aspect of the proposed methodology is to restrict the strategies assumed available to agents.

Demystifying Numerical Models: Step-by Step Modeling of Engineering Systems is the perfect guide on the analytic concepts of engineering components and systems. In simplified terms, the book focuses o

These proceedings provide methods, techniques, different mathematical tools and recent results in the study of formal and analytic solutions to Diff. (differential, partial differential, difference, q

Written by the leading expert in the field, this text reviews the major new developments in envelope models and methods An Introduction to Envelopes provides an overview of the theory and method

This book presents the latest developments and breakthroughs in fuzzy theory and performance prediction of queuing and reliability models by using the stochastic modeling and optimization theory. The

This book highlights a range of new approaches and concepts in the field of software engineering. Based on systematic methods, graphical and formal models, the approaches are designed for solving prac

Social scientists who study religion generally believe that social networks play a central role in religious life. However, most studies draw on measures that are relatively poor proxies for capturing the effects of social networks. This book illustrates how researchers can draw on formal social network analysis methods to explore the interplay of networks and religion. The book's introductory chapters provide overviews of the social scientific study of religion and social network analysis. The remaining chapters explore a variety of topics current in the social scientific study of religion, as well as introducing a variety of social network theories and methods, such as balance theory, ego-network analysis, exponential random graph models, and stochastic actor-oriented models. By embedding social network analysis within a social scientific study of religion framework, Networks and Religion offers an array of approaches for studying the role that social networks play in religious belie

Modern scientific computational methods are undergoing a transformative change; big data and statistical learning methods now have the potential to outperform the classical first-principles modeling paradigm. This book bridges this transition, connecting the theory of probability, stochastic processes, functional analysis, numerical analysis, and differential geometry. It describes two classes of computational methods to leverage data for modeling dynamical systems. The first is concerned with data fitting algorithms to estimate parameters in parametric models that are postulated on the basis of physical or dynamical laws. The second is on operator estimation, which uses the data to nonparametrically approximate the operator generated by the transition function of the underlying dynamical systems. This self-contained book is suitable for graduate studies in applied mathematics, statistics, and engineering. Carefully chosen elementary examples with supplementary MATLAB® codes and append

This volume explores the various methods used to study tertiary lymphoid structures (TLS) in pathological situations. Pre-clinical models are also discussed in detail to show how TLS structure, develo

Discover the nonlinear methods and tools needed to design real-world microwave circuits with this tutorial guide. Balancing theoretical background with practical tools and applications, it covers everything from the basic properties of nonlinear systems such as gain compression, intermodulation and harmonic distortion, to nonlinear circuit analysis and simulation algorithms, and state-of-the-art equivalent circuit and behavioral modeling techniques. Model formulations discussed in detail include time-domain transistor compact models and frequency-domain linear and nonlinear scattering models. Learn how to apply these tools to designing real circuits with the help of a power amplifier design example, which covers all stages from active device model extraction and the selection of bias and terminations, through to performance verification. Realistic examples, illustrative insights and clearly conveyed mathematical formalism make this an essential learning aid for both professionals worki

This engaging study focuses on the role of assemblies in later Anglo-Saxon politics, challenging and nuancing existing models of the late Anglo-Saxon state. Its ten chapters investigate both traditional constitutional aspects of assemblies - who attended these events, where and when they met, and what business they conducted - and the symbolic and representational nature of these gatherings. Levi Roach takes into account important recent work on continental rulership, and argues that assemblies were not a check on kingship in these years, but rather an essential feature of it. In particular, the author highlights the role of symbolic communication at assemblies, arguing that ritual and demonstration were as important in English politics as they were elsewhere in Europe. Far from being exceptional, the methods of rulership employed by English kings look very much like those witnessed elsewhere on the continent, where assemblies and ritual formed an essential part of the political order.

Bayesian methods are being increasingly employed in many different areas of research in the physical sciences. In astrophysics, models are used to make predictions to be compared to observations. These observations offer information that is incomplete and uncertain, so the comparison has to be pursued by following a probabilistic approach. With contributions from leading experts, this volume covers the foundations of Bayesian inference, a description of computational methods, and recent results from their application to areas such as exoplanet detection and characterisation, image reconstruction, and cosmology. It appeals to both young researchers seeking to learn about Bayesian methods as well as to astronomers wishing to incorporate these approaches in their research areas. It provides the next generation of researchers with the tools of modern data analysis that are already becoming standard in current astrophysical research.

This book focuses on applications of social network analysis in predictive policing. Data science is used to identify potential criminal activity by analyzing the relationships between offenders to

Applying the tools and methods of analytic philosophy, analytic feminism is an approach adopted in discussions of sexism, classism and racism. The Bloomsbury Companion to Analytic Feminism presents t

The contributions to EURO-C 2018 review and discuss research advancements in computational modelling of cementitious materials, and assess the applicability and robustness of methods and models f

This is a monograph on the emerging branch of mathematical biophysics combining asymptotic analysis with numerical and stochastic methods to analyze partial differential equations arising in biologica

This book provides new theories, applications and quantitative methods in demography, population studies and statistics. It presents and applies data analysis, statistics and stochastic modeling techn

Models and Methods for Youth and Young Adult Ministry is a rare book on young adult and youth ministry in that it weaves sound theology and solid pastoral practice. It invites pastoral practitioners,

This new textbook will provide state-of-the-art models, concepts and solution methods important in the design, control, operation, and management of service systems. It will cover supply chain managem

Actuaries have access to a wealth of individual data in pension and insurance portfolios, but rarely use its full potential. This book will pave the way, from methods using aggregate counts to modern developments in survival analysis. Based on the fundamental concept of the hazard rate, Part I shows how and why to build statistical models, based on data at the level of the individual persons in a pension scheme or life insurance portfolio. Extensive use is made of the R statistics package. Smooth models, including regression and spline models in one and two dimensions, are covered in depth in Part II. Finally, Part III uses multiple-state models to extend survival models beyond the simple life/death setting, and includes a brief introduction to the modern counting process approach. Practising actuaries will find this book indispensable, and students will find it helpful when preparing for their professional examinations.

Presenting in depth discussions of various statistical models and methods needed for the analysis of medical, biological and biostatistics data, this book emphasizes the analysis of data when normal d

Linear Models and the Relevant Distributions and Matrix Algebra provides in-depth and detailed coverage of the use of linear statistical models as a basis for parametric and predictive inference. It c

Remote Sensing of Landscapes with Spectral Images describes how to process and interpret spectral images using physical models to bridge the gap between the engineering and theoretical sides of remote-sensing and the world that we encounter when we venture outdoors. The emphasis is on the practical use of images rather than on theory and mathematical derivations. Examples are drawn from a variety of landscapes and interpretations are tested against the reality seen on the ground. The reader is led through analysis of real images (using figures and explanations); the examples are chosen to illustrate important aspects of the analytic framework. This textbook will form a valuable reference for graduate students and professionals in a variety of disciplines including ecology, forestry, geology, geography, urban planning, archaeology and civil engineering. It is supplemented by a website hosting digital colour versions of figures in the book as well as ancillary images: www.cambridge.org/

Advances in nonlinear dynamics, especially modern multifractal cascade models, allow us to investigate the weather and climate at unprecedented levels of accuracy. Using new stochastic modeling and data analysis techniques, this book provides an overview of the nonclassical, multifractal statistics. By generalizing the classical turbulence laws, emergent higher-level laws of atmospheric dynamics are obtained and are empirically validated over time-scales of seconds to decades and length-scales of millimetres to the size of the planet. In generalizing the notion of scale, atmospheric complexity is reduced to a manageable scale-invariant hierarchy of processes, thus providing a new perspective for modeling and understanding the atmosphere. This synthesis of state-of-the-art data and nonlinear dynamics is systematically compared with other analyses and global circulation model outputs. This is an important resource for atmospheric science researchers new to multifractal theory and is also

This book is a guide to the use of inverse theory for estimation and conditional simulation of flow and transport parameters in porous media. It describes the theory and practice of estimating properties of underground petroleum reservoirs from measurements of flow in wells, and it explains how to characterize the uncertainty in such estimates. Early chapters present the reader with the necessary background in inverse theory, probability and spatial statistics. The book demonstrates how to calculate sensitivity coefficients and the linearized relationship between models and production data. It also shows how to develop iterative methods for generating estimates and conditional realizations. The text is written for researchers and graduates in petroleum engineering and groundwater hydrology, and can be used as a textbook for advanced courses on inverse theory in petroleum engineering. It includes many worked examples to demonstrate the methodologies and a selection of exercises.

Written by a group of international experts in their field, this book is a review of Lagrangian observation, analysis and assimilation methods in physical and biological oceanography. This multidisciplinary text presents new results on nonlinear analysis of Lagrangian dynamics, the prediction of particle trajectories, and Lagrangian stochastic models. It includes historical information, up-to-date developments, and speculation on future developments in Lagrangian-based observations, analysis, and modeling of physical and biological systems. Containing contributions from experimentalists, theoreticians, and modelers in the fields of physical oceanography, marine biology, mathematics, and meteorology, this book will be of great interest to researchers and graduate students looking for both practical applications and information on the theory of transport and dispersion in physical systems, biological modeling, and data assimilation.