Matrix-analytic Methods in Stochastic Models

Copulas are mathematical objects that fully capture the dependence structure among random variables and hence offer great flexibility in building multivariate stochastic models. Since their introducti

Based on course notes from over twenty years of teaching engineering and physical sciences at Michigan Technological University, Tomas Co's engineering mathematics textbook is rich with examples, applications and exercises. Professor Co uses analytical approaches to solve smaller problems to provide mathematical insight and understanding, and numerical methods for large and complex problems. The book emphasises applying matrices with strong attention to matrix structure and computational issues such as sparsity and efficiency. Chapters on vector calculus and integral theorems are used to build coordinate-free physical models with special emphasis on orthogonal co-ordinates. Chapters on ODEs and PDEs cover both analytical and numerical approaches. Topics on analytical solutions include similarity transform methods, direct formulas for series solutions, bifurcation analysis, Lagrange–Charpit formulas, shocks/rarefaction and others. Topics on numerical methods include stability analysis,

Partial Differential Equations: Topics in Fourier Analysis explains how to use the Fourier transform and heuristic methods to obtain significant insight into the solutions of standard PDE models. It s

This book presents topics in a single source format using unified spectral theory of computing. With developments of DNS and LES, practitioners are rediscovering waves as important in fluid flows, and capturing these numerically is central to high accuracy computing. Analysis of waves and its use in numerical methods in propagating energy at the right velocity (dispersion effects) and with right amplitude (dissipation) are essential. Most industrial codes using Reynolds-averaged Navier–Stokes equations with turbulence models cannot conceive of capturing waves. The new themes covered in this book are: • Correct error propagation analysis • Practical compact schemes and global analysis tool • Aliasing error and its alleviation • Spurious upstream propagating q-waves • Explanation of the Gibbs phenomenon • New 1D and 2D filters for LES/DNS without SGS modelling • Anisotropic skewed wave propagation • Development and analysis of dispersion relation preservation (DRP) schemes • Flow instabi

This book covers a large spectrum of dynamical models in engineering: discrete and continuous time, deterministic and stochastic, state space and input-output systems. It includes proofs, exercises, a

Students in both social and natural sciences often seek regression methods to explain the frequency of events, such as visits to a doctor, auto accidents, or new patents awarded. This book, now in its second edition, provides the most comprehensive and up-to-date account of models and methods to interpret such data. The authors combine theory and practice to make sophisticated methods of analysis accessible to researchers and practitioners working with widely different types of data and software in areas such as applied statistics, econometrics, marketing, operations research, actuarial studies, demography, biostatistics and quantitative social sciences. The new material includes new theoretical topics, an updated and expanded treatment of cross-section models, coverage of bootstrap-based and simulation-based inference, expanded treatment of time series, multivariate and panel data, expanded treatment of endogenous regressors, coverage of quantile count regression, and a new chapter on

Students in both social and natural sciences often seek regression methods to explain the frequency of events, such as visits to a doctor, auto accidents, or new patents awarded. This book, now in its second edition, provides the most comprehensive and up-to-date account of models and methods to interpret such data. The authors combine theory and practice to make sophisticated methods of analysis accessible to researchers and practitioners working with widely different types of data and software in areas such as applied statistics, econometrics, marketing, operations research, actuarial studies, demography, biostatistics and quantitative social sciences. The new material includes new theoretical topics, an updated and expanded treatment of cross-section models, coverage of bootstrap-based and simulation-based inference, expanded treatment of time series, multivariate and panel data, expanded treatment of endogenous regressors, coverage of quantile count regression, and a new chapter on

This book is a major update of novel targets in angiogenesis modulation, including pro- and anti-angiogenesis. There is in-depth coverage of preclinical and clinical methods and models, investigationa

Thorough and informative, this Methods in Molecular Biology? book presents key models used to characterize the tissue-protective actions of cytokines. Offers lists of materials and reagents, step-by-s

The aim of this book is to promote interaction between Engineering, Finance and Insurance, as there are many models and solution methods in common for solving real-life problems in these three topics.

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 modelling and d

Recent decades have brought advances in statistical theory for missing data, which, combined with advances in computing ability, have allowed implementation of a wide array of analyses. In fact, so many methods are available that it can be difficult to ascertain when to use which method. This book focuses on the prevention and treatment of missing data in longitudinal clinical trials. Based on his extensive experience with missing data, the author offers advice on choosing analysis methods and on ways to prevent missing data through appropriate trial design and conduct. He offers a practical guide to key principles and explains analytic methods for the non-statistician using limited statistical notation and jargon. The book's goal is to present a comprehensive strategy for preventing and treating missing data, and to make available the programs used to conduct the analyses of the example dataset.

A comprehensive manual on the efficient modeling and analysis of photonic devices through building numerical codes, this book provides graduate students and researchers with the theoretical background and MATLAB programs necessary for them to start their own numerical experiments. Beginning by summarizing topics in optics and electromagnetism, the book discusses optical planar waveguides, linear optical fiber, the propagation of linear pulses, laser diodes, optical amplifiers, optical receivers, finite-difference time-domain method, beam propagation method and some wavelength division devices, solitons, solar cells and metamaterials. Assuming only a basic knowledge of physics and numerical methods, the book is ideal for engineers, physicists and practising scientists. It concentrates on the operating principles of optical devices, as well as the models and numerical methods used to describe them.

Age-Period-Cohort Analysis: New Models, Methods, and Empirical Applications is based on a decade of the authors’ collaborative work in age-period-cohort (APC) analysis. Within a single, consistent HAP

Recent decades have brought advances in statistical theory for missing data, which, combined with advances in computing ability, have allowed implementation of a wide array of analyses. In fact, so many methods are available that it can be difficult to ascertain when to use which method. This book focuses on the prevention and treatment of missing data in longitudinal clinical trials. Based on his extensive experience with missing data, the author offers advice on choosing analysis methods and on ways to prevent missing data through appropriate trial design and conduct. He offers a practical guide to key principles and explains analytic methods for the non-statistician using limited statistical notation and jargon. The book's goal is to present a comprehensive strategy for preventing and treating missing data, and to make available the programs used to conduct the analyses of the example dataset.

This is a collection of articles on fundamental physical principles and methods, the topics ranging from matrix models, random surfaces, quantum dots and rings, to black holes, cosmology and testing o

This volume provides a modern introduction to stochastic geometry, random fields and spatial statistics at a (post)graduate level. It is focused on asymptotic methods in geometric probability includi

The book shows how the abstract methods of analytic semigroups and evolution equations in Banach spaces can be fruitfully applied to the study of parabolic problems. Particular attention is paid to op

Symmetry and Pattern in Projective Geometry is a self-contained study of projective geometry which compares and contrasts the analytic and axiomatic methods. The analytic approach is based on homogene

In recent decades an increasing number of psych-analytic investigators have tried to fathom the nature and origin of schizophrenia 'from within.' Unlike other psychiatric methods, psycho-analytic inve

An Introduction to Mathematics for Economics introduces quantitative methods to students of economics and finance in a succinct and accessible style. The introductory nature of this textbook means a background in economics is not essential, as it aims to help students appreciate that learning mathematics is relevant to their overall understanding of the subject. Economic and financial applications are explained in detail before students learn how mathematics can be used, enabling students to learn how to put mathematics into practice. Starting with a revision of basic mathematical principles the second half of the book introduces calculus, emphasising economic applications throughout. Appendices on matrix algebra and difference/differential equations are included for the benefit of more advanced students. Other features, including worked examples and exercises, help to underpin the readers' knowledge and learning. Akihito Asano has drawn upon his own extensive teaching experience to cr

Flood inundation models enable us to make hazard predictions for floodplains, mitigating increasing flood fatalities and losses. This book provides an understanding of hydraulic modelling and floodplain dynamics, with a key focus on state-of-the-art remote sensing data, and methods to estimate and communicate uncertainty. Academic researchers in the fields of hydrology, climate change, environmental science and natural hazards, and professionals and policy-makers working in flood risk mitigation, hydraulic engineering and remote sensing will find this an invaluable resource. This volume is the third in a collection of four books on flood disaster management theory and practice within the context of anthropogenic climate change. The others are: Floods in a Changing Climate: Extreme Precipitation by Ramesh Teegavarapu, Floods in a Changing Climate: Hydrological Modeling by P. P. Mujumdar and D. Nagesh Kumar and Floods in a Changing Climate: Risk Management by Slodoban Simonović.

Stochastic Dynamics of Marine Structures is a text for students and a reference for professionals on the basic theory and methods used for stochastic modelling and analysis of marine structures subjected to environmental loads. The first part of the book provides a detailed introduction to the basic dynamic analysis of structures, serving as a foundation for later chapters on stochastic response analysis. This includes an extensive chapter on the finite element method. A careful introduction to stochastic modelling is provided, which includes such concepts as stochastic process, variance spectrum, random environmental processes, response spectrum, response statistics and short- and long-term extreme value models. The second part of the book offers detailed discussion of limit state design approaches, fatigue design methods, the equations of motion for dynamic structures and numerical solution techniques. The final chapter highlights methods for prediction of extreme values from measure

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

This volume of Advances in Econometrics is devoted to dynamic stochastic general equilibrium (DSGE) models. The editors (of Southern Methodist U., the U. of California, and the Federal Reserve Bank of

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

Industrial Assembly is a rapidly changing field with significant importance in production. This book is the first of its kind to combine technology, design, methods, and planning and control models

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.

This book provides a general framework for specifying, estimating and testing time series econometric models. Special emphasis is given to estimation by maximum likelihood, but other methods are also discussed, including quasi-maximum likelihood estimation, generalised method of moments estimation, nonparametric estimation and estimation by simulation. An important advantage of adopting the principle of maximum likelihood as the unifying framework for the book is that many of the estimators and test statistics proposed in econometrics can be derived within a likelihood framework, thereby providing a coherent vehicle for understanding their properties and interrelationships. In contrast to many existing econometric textbooks, which deal mainly with the theoretical properties of estimators and test statistics through a theorem-proof presentation, this book squarely addresses implementation to provide direct conduits between the theory and applied work.

This book provides a general framework for specifying, estimating and testing time series econometric models. Special emphasis is given to estimation by maximum likelihood, but other methods are also discussed, including quasi-maximum likelihood estimation, generalised method of moments estimation, nonparametric estimation and estimation by simulation. An important advantage of adopting the principle of maximum likelihood as the unifying framework for the book is that many of the estimators and test statistics proposed in econometrics can be derived within a likelihood framework, thereby providing a coherent vehicle for understanding their properties and interrelationships. In contrast to many existing econometric textbooks, which deal mainly with the theoretical properties of estimators and test statistics through a theorem-proof presentation, this book squarely addresses implementation to provide direct conduits between the theory and applied work.

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.

Over the past forty years, scientists have developed models of human reasoning based on the principle that human languages and classical logic involve fundamentally different concepts and different methods of interpretation. In The Emergence of Meaning Stephen Crain challenges this view, arguing that a common logical nativism underpins human language and logical reasoning. The approach which Crain takes is twofold. Firstly, he uncovers the underlying meanings of logical expressions and logical principles that appear in typologically different languages - English and Mandarin Chinese - and he demonstrates that these meanings and principles directly correspond to the expressions and structures of classical logic. Secondly he reports the findings of new experimental studies which investigate how children acquire the logical concepts of these languages. A step-by-step introduction to logic and a comprehensive review of the literature on child language acquisition make this work accessible

This textbook explains the basic ideas of subjective probability and shows how subjective probabilities must obey the usual rules of probability to ensure coherency. It defines the likelihood function, prior distributions and posterior distributions. It explains how posterior distributions are the basis for inference and explores their basic properties. Various methods of specifying prior distributions are considered, with special emphasis on subject-matter considerations and exchange ability. The regression model is examined to show how analytical methods may fail in the derivation of marginal posterior distributions. The remainder of the book is concerned with applications of the theory to important models that are used in economics, political science, biostatistics and other applied fields. New to the second edition is a chapter on semiparametric regression and new sections on the ordinal probit, item response, factor analysis, ARCH-GARCH and stochastic volatility models. The new ed

This book tells the story of the search for disequilibrium micro-foundations for macroeconomic theory, from the disequilibrium theories of Patinkin, Clower and Leijonhufvud to recent dynamic stochastic general equilibrium models with imperfect competition. Placing this search against the background of wider developments in macroeconomics, the authors contend that this was never a single research program, but involved economists with very different aims who developed the basic ideas about quantity constraints, spillover effects and coordination failures in different ways. The authors contrast this with the equilibrium, market-clearing approach of Phelps and Lucas, arguing that equilibrium theories simply assumed away the problems that had motivated the disequilibrium literature. Although market-clearing models came to dominate macroeconomics, disequilibrium theories never went away and continue to exert an important influence on the subject. Although this book focuses on one strand in m

Aimed at graduates and researchers, and requiring only a basic knowledge of multi-variable calculus, this introduction to computer-based partial differential equation (PDE) modeling provides readers with the practical methods necessary to develop and use PDE mathematical models in biomedical engineering. Taking an applied approach, rather than using abstract mathematics, the reader is instructed through six biomedical example applications, each example characterized by step-by-step discussions of established numerical methods and implemented in reliable computer routines. Adopting this technique, the reader will understand how PDE models are formulated, implemented and tested. Supported by a set of rigorously tested general purpose PDE routines online, and with enhanced understanding through animations, this book will be ideal for anyone faced with interpreting large experimental data sets that need to be analyzed with PDE models in biomedical engineering.

Generalized network design is a very hot topic of research. The monograph describes in a unified manner a series of mathematical models, methods, propositions, and algorithms developed in the last yea

Table of contents: Stochastic methods in nonlinear structural dynamics.- Stochastic models of uncertainties in computational structural dynamics and structural acoustics.- The tale of stochastic linea

Stochastic resonance has been observed in many forms of systems, and has been hotly debated by scientists for over 30 years. Applications incorporating aspects of stochastic resonance may yet prove revolutionary in fields such as distributed sensor networks, nano-electronics, and biomedical prosthetics. Ideal for researchers in fields ranging from computational neuroscience through to electronic engineering, this book addresses in detail various theoretical aspects of stochastic quantization, in the context of the suprathreshold stochastic resonance effect. Initial chapters review stochastic resonance and outline some of the controversies and debates that have surrounded it. The book then discusses suprathreshold stochastic resonance, and its extension to more general models of stochastic signal quantization. Finally, it considers various constraints and tradeoffs in the performance of stochastic quantizers, before culminating with a chapter in the application of suprathreshold stochas

Stochastic biomathematical models are becoming increasingly important as new light is shed on the role of noise in living systems. In certain biological systems, stochastic effects may even enhance a

Emphasizing a quantitative approach, Supply Chain Engineering: Models and Applications provides state-of-the-art mathematical models, concepts, and solution methods important in the design, control, o