Matrix-analytic Methods in Stochastic Models

An essential textbook for any student or researcher in biology needing to design experiments, sample programs or analyse the resulting data. The text begins with a revision of estimation and hypothesis testing methods, covering both classical and Bayesian philosophies, before advancing to the analysis of linear and generalized linear models. Topics covered include linear and logistic regression, simple and complex ANOVA models (for factorial, nested, block, split-plot and repeated measures and covariance designs), and log-linear models. Multivariate techniques, including classification and ordination, are then introduced. Special emphasis is placed on checking assumptions, exploratory data analysis and presentation of results. The main analyses are illustrated with many examples from published papers and there is an extensive reference list to both the statistical and biological literature. The book is supported by a website that provides all data sets, questions for each chapter and l

Hepatitis C infects 170 million people worldwide, and has been labelled the 'silent epidemic' as a result of its concealed attack on the liver. This multidisciplinary overview covers basic concepts related to the discovery of the virus, development of serological and nucleic acid tests to detect infection, the structure of the virus genome, generation of virus gene products, and proposed replication scheme. It then goes on to introduce the epidemiology, transmission, pathogenesis of infection, the development of hepatocellular carcinoma associated with chronic virus infection, and current strategies for treatment. The book then discusses advances in cell culture systems, animal models of infection, and emerging treatments and vaccine development. Through its coverage of basic science, clinical consequences, and methods of research, this integrated and accessible account will be of immense value to biomedical scientists and clinicians alike, and a useful introduction for all those study

The third edition of this successful textbook is fully updated and includes important recent developments in cosmology. It begins with an introduction to cosmology and general relativity, and goes on to cover the mathematical models of standard cosmology. The physical aspects of cosmology, including primordial nucleosynthesis, the astroparticle physics of inflation, and the current ideas on structure formation are discussed. Alternative models of cosmology are reviewed, including the model of Quasi-Steady State Cosmology, which has recently been proposed as an alternative to Big Bang Cosmology. The final chapters discuss observational cosmology, and debate theory versus observational methods. The book includes 400 problems and numerous worked examples. This introductory textbook describes modern cosmology at a level suitable for advanced undergraduates and graduates who are familiar with mathematical methods and basic theoretical physics. It is intended for use on courses in theoretic

This 2002 book presents the reader with mathematical tools taken from matrix calculus and zero-one matrices and demonstrates how these tools greatly facilitate the application of classical statistical procedures to econometric models. The matrix calculus results are derived from a few basic rules that are generalizations of the rules of ordinary calculus. These results are summarized in a useful table. Well-known zero-one matrices, together with some newer ones, are defined, their mathematical roles explained, and their useful properties presented. The basic building blocks of classical statistics, namely the score vector, the information matrix, and the Cramer-Rao lower bound, are obtained for a sequence of linear econometric models of increasing statistical complexity. From these are obtained interactive interpretations of maximum likelihood estimators, linking them with efficient econometric estimators. Classical test statistics are also derived and compared for hypotheses of intere

Almost every artifact in archaeological analysis originates in or on the ground. While there are elaborate methods for extracting and analyzing artifacts, treatment of the matrix within which they are

This book describes the Bayesian approach to statistics at a level suitable for final year undergraduate and Masters students. It is unusual in presenting Bayesian statistics with a practical flavor and an emphasis on mainstream statistics, showing how to infer scientific, medical, and social conclusions from numerical data. The authors draw on many years of experience with practical and research programs and describe many statistical methods, not readily available elsewhere. A first chapter on Fisherian methods, together with a strong overall emphasis on likelihood, makes the text suitable for mainstream statistics courses whose instructors wish to follow mixed or comparative philosophies. The other chapters contain important sections relating to many areas of statistics such as the linear model, categorical data analysis, time series and forecasting, mixture models, survival analysis, Bayesian smoothing, and non-linear random effects models. The text includes a large number of practi

Statistics do not lie, nor is probability paradoxical. You just have to have the right intuition. In this lively look at both subjects, David Williams convinces mathematics students of the intrinsic interest of statistics and probability, and statistics students that the language of mathematics can bring real insight and clarity to their subject. He helps students build the intuition needed, in a presentation enriched with examples drawn from all manner of applications, e.g., genetics, filtering, the Black–Scholes option-pricing formula, quantum probability and computing, and classical and modern statistical models. Statistics chapters present both the Frequentist and Bayesian approaches, emphasising Confidence Intervals rather than Hypothesis Test, and include Gibbs-sampling techniques for the practical implementation of Bayesian methods. A central chapter gives the theory of Linear Regression and ANOVA, and explains how MCMC methods allow greater flexibility in modelling. C or WinBUG

Statistics do not lie, nor is probability paradoxical. You just have to have the right intuition. In this lively look at both subjects, David Williams convinces mathematics students of the intrinsic interest of statistics and probability, and statistics students that the language of mathematics can bring real insight and clarity to their subject. He helps students build the intuition needed, in a presentation enriched with examples drawn from all manner of applications, e.g., genetics, filtering, the Black–Scholes option-pricing formula, quantum probability and computing, and classical and modern statistical models. Statistics chapters present both the Frequentist and Bayesian approaches, emphasising Confidence Intervals rather than Hypothesis Test, and include Gibbs-sampling techniques for the practical implementation of Bayesian methods. A central chapter gives the theory of Linear Regression and ANOVA, and explains how MCMC methods allow greater flexibility in modelling. C or WinBUG

Kot (applied mathematics, U. of Washington) presents an introductory text on the methods of classical and mathematical models and methods in population ecology. Covering density dependence, bifurcatio

This book provides a thorough and self-contained study of interdependence and complexity in settings of functional analysis, harmonic analysis and stochastic analysis. It focuses on 'dimension' as a basic counter of degrees of freedom, leading to precise relations between combinatorial measurements and various indices originating from the classical inequalities of Khintchin, Littlewood and Grothendieck. The basic concepts of fractional Cartesian products and combinatorial dimension are introduced and linked to scales calibrated by harmonic-analytic and stochastic measurements. Topics include the (two-dimensional) Grothendieck inequality and its extensions to higher dimensions, stochastic models of Brownian motion, degrees of randomness and Frechet measures in stochastic analysis. This book is primarily aimed at graduate students specialising in harmonic analysis, functional analysis or probability theory. It contains many exercises and is suitable to be used as a textbook. It is also o

Elements of Mathematical Ecology provides an introduction to classical and modern mathematical models, methods, and issues in population ecology. The first part of the book is devoted to simple, unstructured population models that ignore much of the variability found in natural populations for the sake of tractability. Topics covered include density dependence, bifurcations, demographic stochasticity, time delays, population interactions (predation, competition, and mutualism), and the application of optimal control theory to the management of renewable resources. The second part of this book is devoted to structured population models, covering spatially-structured population models (with a focus on reaction-diffusion models), age-structured models, and two-sex models. Suitable for upper level students and beginning researchers in ecology, mathematical biology and applied mathematics, the volume includes numerous clear line diagrams that clarify the mathematics, relevant problems thou

This general introduction to the ideas and techniques required for the mathematical modelling of diseases begins with an outline of some disease statistics dating from Daniel Bernoulli's 1760 smallpox data. The authors then describe simple deterministic and stochastic models in continuous and discrete time for epidemics taking place in either homogeneous or stratified (non-homogeneous) populations. Several techniques for constructing and analysing models are provided, mostly in the context of viral and bacterial diseases of human populations. These models are contrasted with models for rumours and vector-borne diseases like malaria. Questions of fitting data to models, and their use in understanding methods for controlling the spread of infection, are discussed. Exercises and complementary results at the end of each chapter extend the scope of the text, which will be useful for students taking courses in mathematical biology who have some basic knowledge of probability and statistics.

Eric Ghysels and Denise R. Osborn provide a thorough and timely review of the recent developments in the econometric analysis of seasonal economic time series, summarizing a decade of theoretical advances in the area. The authors discuss the asymptotic distribution theory for linear nonstationary seasonal stochastic processes. They also cover the latest contributions to the theory and practice of seasonal adjustment, together with its implications for estimation and hypothesis testing. Moreover, a comprehensive analysis of periodic models is provided, including stationary and nonstationary cases. The book concludes with a discussion of some nonlinear seasonal and periodic models. The treatment is designed for an audience of researchers and advanced graduate students.

Eric Ghysels and Denise R. Osborn provide a thorough and timely review of the recent developments in the econometric analysis of seasonal economic time series, summarizing a decade of theoretical advances in the area. The authors discuss the asymptotic distribution theory for linear nonstationary seasonal stochastic processes. They also cover the latest contributions to the theory and practice of seasonal adjustment, together with its implications for estimation and hypothesis testing. Moreover, a comprehensive analysis of periodic models is provided, including stationary and nonstationary cases. The book concludes with a discussion of some nonlinear seasonal and periodic models. The treatment is designed for an audience of researchers and advanced graduate students.

Random matrices arise from, and have important applications to, number theory, probability, combinatorics, representation theory, quantum mechanics, solid state physics, quantum field theory, quantum gravity, and many other areas of physics and mathematics. This 2001 volume of surveys and research results, based largely on lectures given at the Spring 1999 MSRI program of the same name, covers broad areas such as topologic and combinatorial aspects of random matrix theory; scaling limits, universalities and phase transitions in matrix models; universalities for random polynomials; and applications to integrable systems. Its stress on the interaction between physics and mathematics will make it a welcome addition to the shelves of graduate students and researchers in both fields, as will its expository emphasis.

A collection of articles written by mathematicians and physicists, designed to describe the state of the art in climate models with stochastic input. Mathematicians will benefit from a survey of simpl

This book, first published in 2001, explores two shifts in the paradigms of governance in Western bureaucracies. They are the widespread use of privatisation, private firms and market methods to run core public services, and the conscious attempt to transform the role of citizenship from ideals of entitlement and security to notions of mutual obligation, selectivity and risk. Considine examines the most important service of the modern welfare state - unemployment assistance - to explain and theorise the nature of these radical changes. He undertakes research in the United Kingdom, the Netherlands, Australia and New Zealand, four countries which have been among the boldest reformers within the OECD, yet each adopting different models. Each case is a break from the standards of responsible democracy and legal-rational bureaucracy, with at least one government opting for a commercial paradigm based on targets and economic incentives and another opting for a model based on network governan

Twenty-one contributions from scholars of education present models of developmental education programs in higher education. The models consist of methods and techniques for implementing developmental

Independent Component Analysis (ICA) has recently become an important tool for modelling and understanding empirical datasets. It is a method of separating out independent sources from linearly mixed data, and belongs to the class of general linear models. ICA provides a better decomposition than other well-known models such as principal component analysis. This self-contained book contains a structured series of edited papers by leading researchers in the field, including an extensive introduction to ICA. The major theoretical bases are reviewed from a modern perspective, current developments are surveyed and many case studies of applications are described in detail. The latter include biomedical examples, signal and image denoising and mobile communications. ICA is discussed in the framework of general linear models, but also in comparison with other paradigms such as neural network and graphical modelling methods. The book is ideal for researchers and graduate students in the field.

Because of their intuitive layout, extensive mathematical capabilities, and convenient graphics, spreadsheets provide an easy, straightforward route to scientific computing. This textbook for undergraduate and entry-level graduate chemistry and chemical engineering students uses Excel, the most powerful available spreadsheet, to explore and solve problems in general and chemical data analysis. This is the only up-to-date text on the use of spreadsheets in chemistry. The book discusses topics including statistics, chemical equilibria, pH calculations, titrations, and instrumental methods such as chromatography, spectrometry, and electroanalysis. It contains many examples of data analysis, and uses spreadsheets for numerical simulations, and testing analytical procedures. It also treats modern data analysis methods such as linear and non-linear least squares in great detail, as well as methods based on Fourier transformation. The book shows how matrix methods can be powerful tools in dat

Because of their intuitive layout, extensive mathematical capabilities, and convenient graphics, spreadsheets provide an easy, straightforward route to scientific computing. This textbook for undergraduate and entry-level graduate chemistry and chemical engineering students uses Excel, the most powerful available spreadsheet, to explore and solve problems in general and chemical data analysis. This is the only up-to-date text on the use of spreadsheets in chemistry. The book discusses topics including statistics, chemical equilibria, pH calculations, titrations, and instrumental methods such as chromatography, spectrometry, and electroanalysis. It contains many examples of data analysis, and uses spreadsheets for numerical simulations, and testing analytical procedures. It also treats modern data analysis methods such as linear and non-linear least squares in great detail, as well as methods based on Fourier transformation. The book shows how matrix methods can be powerful tools in dat

This collection brings together important contributions by leading econometricians on (i) parametric approaches to qualitative and sample selection models, (ii) nonparametric and semi-parametric approaches to qualitative and sample selection models, and (iii) nonlinear estimation of cross-sectional and time series models. The advances achieved here can have important bearing on the choice of methods and analytical techniques in applied research.

Optimal Reliability Design, first published in 2000, provides a detailed introduction to systems reliability and reliability optimization. Techniques for maximizing system reliability are described, focusing on component reliability enhancement and redundancy arrangement. The authors present several case studies and show how optimization techniques are applied in practice. They also pay particular attention to finding methods that give the optimal trade-off between reliability and cost. The book begins with a review of key background material, and a discussion of a range of optimization models. The authors go on to cover optimization tools, such as heuristics, discrete optimization, nonlinear programming, mixed integer programming, optimal arrangement, and metaheuristic algorithms. They also describe the computational implementation of these tools. Many numerical examples are included, and the book contains over 180 homework exercises. It is suitable as a textbook for graduate-level co

New statistical methods and future directions of research in time series A Course in Time Series Analysis demonstrates how to build time series models for univariate and multivariate time series data.

This textbook introduces students progressively to various aspects of qualitative models and assumes a knowledge of basic principles of statistics and econometrics. Inferring qualitative characteristics of data on socioeconomic class, education, employment status, and the like - given their discrete nature - requires an entirely different set of tools from those applied to purely quantitative data. Written in accessible language and offering cogent examples, students are given valuable means to gauge real-world economic phenomena. After the introduction, early chapters present models with endogenous qualitative variables, examining dichotomous models, model specification, estimation methods, descriptive usage, and qualitative panel data. Professor Gourieroux also looks at Tobit models, in which the exogenous variable is sometimes qualitative and sometimes quantitative, and changing-regime models, in which the dependent variable is qualitative but expressed in quantitative terms. The fi

This textbook introduces students progressively to various aspects of qualitative models and assumes a knowledge of basic principles of statistics and econometrics. Inferring qualitative characteristics of data on socioeconomic class, education, employment status, and the like - given their discrete nature - requires an entirely different set of tools from those applied to purely quantitative data. Written in accessible language and offering cogent examples, students are given valuable means to gauge real-world economic phenomena. After the introduction, early chapters present models with endogenous qualitative variables, examining dichotomous models, model specification, estimation methods, descriptive usage, and qualitative panel data. Professor Gourieroux also looks at Tobit models, in which the exogenous variable is sometimes qualitative and sometimes quantitative, and changing-regime models, in which the dependent variable is qualitative but expressed in quantitative terms. The fi

This book demonstrates that the state-contingent approach provides the best way to think about all problems in the economics of uncertainty, including problems of consumer choice, the theory of the firm, and principal agent relationships. The authors demonstrate that dual methods apply under uncertainty and that the dual representations can be developed for stochastic technologies. Moreover, proper exploitation of the properties of alternative primal and dual representations of preferences allows analysts to generalize and extend the results of the existing literature on preferences under uncertainty, thus making expected-utility theory largely superfluous for many decisions. These insights open the way for developments in the basic theory of production under uncertainty, the theory of hedging behavior, the analysis of agency problems and the theory of production insurance.

Modern policy problems require analysts to capture the interactions between policy and the complexities of economic and social life, as well as between policies of different types. Increasingly, microsimulation is employed to analyse these problems. This book brings together examples of microsimulation modelling that are at the frontiers of developments in the field, either because they extend the range of techniques available to modellers, or because they demonstrate new applications for established methods. It represents the state of the art with chapters on the use of microsimulation for comparative policy research and for challenging conventional assumptions, combining microsimulation with other types of economic models and the much-neglected subjects of model alignment and validation. Data and case studies are taken from regions including Asia-Pacific, Europe and North America.

This book demonstrates that the state-contingent approach provides the best way to think about all problems in the economics of uncertainty, including problems of consumer choice, the theory of the firm, and principal agent relationships. The authors demonstrate that dual methods apply under uncertainty and that the dual representations can be developed for stochastic technologies. Moreover, proper exploitation of the properties of alternative primal and dual representations of preferences allows analysts to generalize and extend the results of the existing literature on preferences under uncertainty, thus making expected-utility theory largely superfluous for many decisions. These insights open the way for developments in the basic theory of production under uncertainty, the theory of hedging behavior, the analysis of agency problems and the theory of production insurance.

This book covers the experimental and theoretical understanding of surface and thin film processes. It presents a unique description of surface processes in adsorption and crystal growth, including bonding in metals and semiconductors. Emphasis is placed on the strong link between science and technology in the description of, and research for, new devices based on thin film and surface science. Practical experimental design, sample preparation and analytical techniques are covered, including detailed discussions of Auger electron spectroscopy and microscopy. Thermodynamic and kinetic models of structure are emphasised throughout. The book provides extensive leads into practical and research literature, as well as resources on the World Wide Web (see http://venables.asu.edu/book). Each chapter contains problems which aim to develop awareness of the subject and the methods used. Aimed as a graduate textbook, this book will also be useful as a sourcebook for graduate students, researchers

This book, first published in 2000, addresses problems in financial mathematics of pricing and hedging derivative securities in an environment of uncertain and changing market volatility. These problems are important to investors from large trading institutions to pension funds. It presents mathematical and statistical tools that exploit the bursty nature of market volatility. The mathematics is introduced through examples and illustrated with simulations and the modeling approach that is described is validated and tested on market data. The material is suitable for a one semester course for graduate students who have had exposure to methods of stochastic modeling and arbitrage pricing theory in finance. It is easily accessible to derivatives practitioners in the financial engineering industry.

Computer simulations provide a powerful tool for understanding ecological and evolutionary systems. Simulating Ecological and Evolutionary Systems in C models a diverse range of biological processes and systems, including competition, foraging, predation, mating systems, and life-history optimization, by simulating large collections of interacting individuals. Using the widely available computer programming language C, the book starts with elementary programs modeling stochastic birth-death processes, slowly increasing programming complexity as the chapters progress. All the important features of C are covered, including arrays, files, pointers, and structures, within biologically motivated simulations. Although computer simulations of extremely complicated biological processes are released from rigid mathematical constraints, each of the simulations is also placed in the context of a mathematical formulation examined either analytically or numerically. Procedures covered include testi

This textbook provides a clear and concise introduction to computer architecture and implementation. Two important themes are interwoven throughout the book. The first is an overview of the major concepts and design philosophies of computer architecture and organization. The second is the early introduction and use of analytic modeling of computer performance. The author begins by describing the classic von Neumann architecture, and then presents in detail a number of performance models and evaluation techniques. He goes on to cover user instruction set design, including RISC architecture. A unique feature of the book is its memory-centric approach - memory systems are discussed before processor implementations. The author also deals with pipelined processors, input/output techniques, queuing modes, and extended instruction set architectures. Each topic is illustrated with reference to actual IBM and Intel architectures. The book contains many worked examples and over 130 homework exer

This collection of articles by well-known experts was originally published in 2000 and is intended for researchers in computer science, practitioners of formal methods, and computer programmers working in safety-critical applications or in the technology of component-based systems. The work brings together several elements of this area that were fast becoming the focus of much research and practice in computing. The introduction by Clemens Szyperski gives a snapshot of research in the field. About half the articles deal with theoretical frameworks, models, and systems of notation; the rest of the book concentrates on case studies by researchers who have built prototype systems and present findings on architectures verification. The emphasis is on advances in the technological infrastructure of component-based systems; how to design and specify reusable components; and how to reason about, verify, and validate systems from components. Thus the book shows how theory might move into pract

This book presents the concepts, methods and applications of kinetic theory to rarefied gas dynamics. After introducing the basic tools, problems in plane geometry are treated using approximation techniques (perturbation and numerical methods). These same techniques are later used to deal with two- and three-dimensional problems. The models include not only monatomic but also polyatomic gases, mixtures, chemical reactions. A special chapter is devoted to evaporation and condensation phenomena. Each section is accompanied by problems which are mainly intended to demonstrate the use of the material in the text and to outline additional subjects, results and equations. This will help ensure that the book can be used for a range of graduate courses in aerospace engineering or applied mathematics.

This book presents the concepts, methods and applications of kinetic theory to rarefied gas dynamics. After introducing the basic tools, problems in plane geometry are treated using approximation techniques (perturbation and numerical methods). These same techniques are later used to deal with two- and three-dimensional problems. The models include not only monatomic but also polyatomic gases, mixtures, chemical reactions. A special chapter is devoted to evaporation and condensation phenomena. Each section is accompanied by problems which are mainly intended to demonstrate the use of the material in the text and to outline additional subjects, results and equations. This will help ensure that the book can be used for a range of graduate courses in aerospace engineering or applied mathematics.

Electronic Concepts provides a detailed introduction to modern microelectronics. Equal emphasis is placed on analog and digital circuits, and the applications of particular devices and circuits are described within the context of actual electronic systems. The author begins with an overview of several important electronic systems, discussing in detail the types of signals that circuits are used to process. In the following chapters, he deals with individual devices. For each device he presents a brief physical description and demonstrates the use of different models in describing the device's behaviour in a particular circuit application. SPICE computer simulations are used throughout the text to supplement analytic descriptions. The book contains over 500 circuit diagrams and figures, over 400 homework problems, and over 100 simulation and design exercises. It includes many worked examples and is an ideal textbook for introductory courses in electronics. Laboratory experiments are ava

Partial differential equations provide mathematical models of many important problems in the physical sciences and engineering. This book, first published in 2000, treats one class of such equations, concentrating on methods involving the use of surface potentials. It provided the first detailed exposition of the mathematical theory of boundary integral equations of the first kind on non-smooth domains. Included are chapters on three specific examples: the Laplace equation, the Helmholtz equation and the equations of linear elasticity. The book is designed to provide an ideal preparation for studying the modern research literature on boundary element methods.

Originally published in 2000, this is the second volume of a comprehensive two-volume treatment of quadratic optimal control theory for partial differential equations over a finite or infinite time horizon, and related differential (integral) and algebraic Riccati equations. Both continuous theory and numerical approximation theory are included. The authors use an abstract space, operator theoretic approach, which is based on semigroups methods, and which unifies across a few basic classes of evolution. The various abstract frameworks are motivated by, and ultimately directed to, partial differential equations with boundary/point control. Volume 2 is focused on the optimal control problem over a finite time interval for hyperbolic dynamical systems. A few abstract models are considered, each motivated by a particular canonical hyperbolic dynamics. It presents numerous fascinating results. These volumes will appeal to graduate students and researchers in pure and applied mathematics and

Partial differential equations provide mathematical models of many important problems in the physical sciences and engineering. This book, first published in 2000, treats one class of such equations, concentrating on methods involving the use of surface potentials. It provided the first detailed exposition of the mathematical theory of boundary integral equations of the first kind on non-smooth domains. Included are chapters on three specific examples: the Laplace equation, the Helmholtz equation and the equations of linear elasticity. The book is designed to provide an ideal preparation for studying the modern research literature on boundary element methods.