Matrix-analytic Methods in Stochastic Models

"In this unique book, management science lifts its view to take in the broader horizons of strategy. the result is a frame work for strategy development, and a range of methods and models to make it o

"In this unique book, management science lifts its view to take in the broader horizons of strategy. the result is a frame work for strategy development, and a range of methods and models to make it o

The small sample properties of estimators and tests are frequently too complex to be useful or are unknown. Much econometric theory is therefore developed for very large or asymptotic samples where it is assumed that the behaviour of estimators and tests will adequately represent their properties in small samples. Refined asymptotic methods adopt an intermediate position by providing improved approximations to small sample behaviour using asymptotic expansions. Dedicated to the memory of Michael Magdalinos, whose work is a major contribution to this area, this book contains chapters directly concerned with refined asymptotic methods. In addition, there are chapters focusing on new asymptotic results; the exploration through simulation of the small sample behaviour of estimators and tests in panel data models; and improvements in methodology. With contributions from leading econometricians, this collection will be essential reading for researchers and graduate students concerned with th

The world's marine fisheries are in trouble, as a direct result of overfishing and the overcapacity of fishing fleets. Despite intensive management efforts, the problems still persist in many areas, resulting in many fisheries being neither sustainable nor profitable. Using bio-economic models of commercial fisheries, this book demonstrates that new management methods, based on individual or community catch quotas, are required to resolve the overfishing problem. Uncertainty about marine systems may be another factor contributing to overfishing. Methods of decision analysis and Bayesian inference are used to discuss risk management and the precautionary principle, arguing that extensive marine reserves may be the best way to protect fisheries, alongside a controlled catch quota system. This book will be of interest to environmental scientists, economists and fisheries managers, providing novel insights into many well-known but poorly understood aspects of fisheries management.

The world's marine fisheries are in trouble, as a direct result of overfishing and the overcapacity of fishing fleets. Despite intensive management efforts, the problems still persist in many areas, resulting in many fisheries being neither sustainable nor profitable. Using bio-economic models of commercial fisheries, this book demonstrates that new management methods, based on individual or community catch quotas, are required to resolve the overfishing problem. Uncertainty about marine systems may be another factor contributing to overfishing. Methods of decision analysis and Bayesian inference are used to discuss risk management and the precautionary principle, arguing that extensive marine reserves may be the best way to protect fisheries, alongside a controlled catch quota system. This book will be of interest to environmental scientists, economists and fisheries managers, providing novel insights into many well-known but poorly understood aspects of fisheries management.

Increases in computer power and technology have rapidly advanced the applications of numerical modelling in environmental and earth sciences. The progress of numerical modelling in atmospheric, oceanic and geophysical sciences was the topic of an international conference held by the National Autonomous University of Mexico. The review articles and research papers in this volume constitute a wide-ranging account of modelling environmental and earth processes through a variety of numerical simulations. Sections are devoted to such topics as general circulation models and global change, methods of geophysical data assimilation, and mathematical and computational methods with geophysical applications. This book forms an excellent introduction and overview for graduate students as well as a critical update for researchers.

Discusses optimization problems encountered in financial models, describes the relevant theory and efficient solution methods, and shows how to apply them to practical problems in mathematical finance

Where did SARS come from? Have we inherited genes from Neanderthals? How do plants use their internal clock? The genomic revolution in biology enables us to answer such questions. But the revolution would have been impossible without the support of powerful computational and statistical methods that enable us to exploit genomic data. Many universities are introducing courses to train the next generation of bioinformaticians: biologists fluent in mathematics and computer science, and data analysts familiar with biology. This readable and entertaining book, based on successful taught courses, provides a roadmap to navigate entry to this field. It guides the reader through key achievements of bioinformatics, using a hands-on approach. Statistical sequence analysis, sequence alignment, hidden Markov models, gene and motif finding and more, are introduced in a rigorous yet accessible way. A companion website provides the reader with Matlab-related software tools for reproducing the steps de

As the analysis of social networks, or networks of interpersonal and social relationships among social groups, has become an increasingly important method of research in several of the social and behavioural sciences, the gathering of network data has outpaced the development of new methods for its analysis. Addressing the need for analytical tools, Philippa Pattison presents a number of algebraic models for the analysis of network data, explaining in the process the rationale for an algebraic approach. Models are developed for both complete networks, meaning those representing the social ties between all pairs of members in a given group, and local networks, meaning those structured around the social ties of one particular group member. Many applications are presented and the ways that these methods can address a number of important issues confronting network analysis are explained.

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

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

This book studies the development of ideas on freedom, coercion and power in the history of economic thought. It focuses on the exchange of goods and services and on terms of exchange (interest rates, prices and wages) and examines the nature of choice, that is, the state of the will of economic actors making exchange decisions. In a social context, anyone's range of choice is restricted by the choices made by others. The first to raise the question of the will in this economic context were the medieval scholastics, drawing on non-economic analytic models inherited from antiquity and mainly from Aristotle. From these origins, views on economic choice, coercion and power are recorded, as they gradually change over the centuries, until they manifest themselves in more contemporary disputes between different branches of institutional economics.

Suitable for a first year graduate course, this textbook unites the applications of numerical mathematics and scientific computing to the practice of chemical engineering. Written in a pedagogic style, the book describes basic linear and nonlinear algebric systems all the way through to stochastic methods, Bayesian statistics and parameter estimation. These subjects are developed at a level of mathematics suitable for graduate engineering study without the exhaustive level of the theoretical mathematical detail. The implementation of numerical methods in MATLAB is integrated within each chapter and numerous examples in chemical engineering are provided, with a library of corresponding MATLAB programs. This book will provide the graduate student with essential tools required by industry and research alike. Supplementary material includes solutions to homework problems set in the text, MATLAB programs and tutorial, lecture slides, and complicated derivations for the more advanced reader.

This book is about the coordinate-free, or geometric, approach to the theory of linear models; more precisely, Model I ANOVA and linear regression models with non-random predictors in a finite-dimensional setting. This approach is more insightful, more elegant, more direct, and simpler than the more common matrix approach to linear regression, analysis of variance, and analysis of covariance models in statistics. The book discusses the intuition behind and optimal properties of various methods of estimating and testing hypotheses about unknown parameters in the models. Topics covered range from linear algebra, such as inner product spaces, orthogonal projections, book orthogonal spaces, Tjur experimental designs, basic distribution theory, the geometric version of the Gauss-Markov theorem, optimal and non-optimal properties of Gauss-Markov, Bayes, and shrinkage estimators under assumption of normality, the optimal properties of F-test, and the analysis of covariance and missing observa

There is a certain body of knowledge and methods that finds application in most branches of fluid mechanics. This book aims to supply a proper theoretical understanding that will permit sensible simplifications to be made in the formulation of problems, and enable the reader to develop analytical models of practical significance. Such analyses can be used to guide more detailed experimental and numerical investigations. As in most technical subjects, such understanding is acquired by detailed study of highly simplified 'model problems'. The first part (Chapters 1-4) is concerned entirely with the incompressible flow of a homogeneous fluid. It was written for the Boston University introductory graduate level course 'Advanced Fluid Mechanics'. The remaining Chapters 5 and 6 deal with dispersive waves and acoustics, and are unashamedly inspired by James Lighthill's masterpiece, Waves in Fluids.

A natural sequel to the author's previous book Combinatorial Matrix Theory written with H. J. Ryser, this is the first book devoted exclusively to existence questions, constructive algorithms, enumeration questions, and other properties concerning classes of matrices of combinatorial significance. Several classes of matrices are thoroughly developed including the classes of matrices of 0's and 1's with a specified number of 1's in each row and column (equivalently, bipartite graphs with a specified degree sequence), symmetric matrices in such classes (equivalently, graphs with a specified degree sequence), tournament matrices with a specified number of 1's in each row (equivalently, tournaments with a specified score sequence), nonnegative matrices with specified row and column sums, and doubly stochastic matrices. Most of this material is presented for the first time in book format and the chapter on doubly stochastic matrices provides the most complete development of the topic to dat

This book presents a full spectrum of views on current approaches to modeling cell mechanics. The authors come from the biophysics, bioengineering and physical chemistry communities and each joins the discussion with a unique perspective on biological systems. Consequently, the approaches range from finite element methods commonly used in continuum mechanics to models of the cytoskeleton as a cross-linked polymer network to models of glassy materials and gels. Studies reflect both the static, instantaneous nature of the structure, as well as its dynamic nature due to polymerization and the full array of biological processes. While it is unlikely that a single unifying approach will evolve from this diversity, it is the hope that a better appreciation of the various perspectives will lead to a highly coordinated approach to exploring the essential problems and better discussions among investigators with differing views.

Macroeconomics is evolving in an almost dialectic fashion. The latest evolution is the development of a new synthesis that combines insights of new classical, new Keynesian and real business cycle traditions into a dynamic, stochastic general equilibrium (DSGE) model that serves as a foundation for thinking about macro policy. That new synthesis has opened up the door to a new antithesis, which is being driven by advances in computing power and analytic techniques. This new synthesis is coalescing around developments in complexity theory, automated general to specific econometric modeling, agent-based models, and non-linear and statistical dynamical models. This book thus provides the reader with an introduction to what might be called a Post Walrasian research program that is developing as the antithesis of the Walrasian DSGE synthesis.

Macroeconomics is evolving in an almost dialectic fashion. The latest evolution is the development of a new synthesis that combines insights of new classical, new Keynesian and real business cycle traditions into a dynamic, stochastic general equilibrium (DSGE) model that serves as a foundation for thinking about macro policy. That new synthesis has opened up the door to a new antithesis, which is being driven by advances in computing power and analytic techniques. This new synthesis is coalescing around developments in complexity theory, automated general to specific econometric modeling, agent-based models, and non-linear and statistical dynamical models. This book thus provides the reader with an introduction to what might be called a Post Walrasian research program that is developing as the antithesis of the Walrasian DSGE synthesis.

Geographical Information Systems has moved from the domain of the computer specialist into the wider archaeological community, providing it with an exciting new research method. This clearly written but rigorous book provides a comprehensive guide to that use. Topics covered include: the theoretical context and the basics of GIS; data acquisition including database design; interpolation of elevation models; exploratory data analysis including spatial queries; statistical spatial analysis; map algebra; spatial operations including the calculation of slope and aspect, filtering and erosion modeling; methods for analysing regions; visibility analysis; network analysis including hydrological modeling; the production of high quality output for paper and electronic publication; and the use and production of metadata. Offering an extensive range of archaeological examples, it is an invaluable source of practical information for all archaeologists, whether engaged in cultural resource manageme

This 2006 book presents a systematic introduction to the theory of parametric stability of structures under both deterministic and stochastic loadings. A comprehensive range of theories are presented and various application problems are formulated and solved, often using more than one approach. Investigation of an elastic system's dynamic stability frequently leads to the study of dynamic behaviour of the solutions of parametrically excited systems. Parametric instability or resonance is more dangerous than ordinary resonance as it is characterised by exponential growth of the response amplitudes even in the presence of damping. The emphasis in this book is on the applications and various analytical and numerical methods for solving engineering problems. The materials presented are as self-contained as possible, with all of the important steps of analysis provided in order to make the book suitable as a graduate-level textbook and especially for self-study.

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/

The traditional demographic regime of ancient Greece and Rome is almost entirely unknown; but our best chance for understanding its characteristics is provided by the three hundred census returns that survive on papyri from Roman Egypt. These returns, which date from the first three centuries AD, list the members of ordinary households living in the Nile valley: not only family members, but lodgers and slaves. The Demography of Roman Egypt has a complete and accurate catalogue of all demographically relevant information contained in the returns. On the basis of this catalogue, the authors use modern demographic methods and models to reconstruct the patterns of mortality, marriage, fertility and migration that are likely to have prevailed in Roman Egypt. They recreate a more or less typical Mediterranean population as it survived and prospered nearly two millennia ago.

Perturbation series expansion methods are sophisticated numerical tools used to provide quantitative calculations in many areas of theoretical physics. This book gives a comprehensive guide to the use of series expansion methods for investigating phase transitions and critical phenomena, and lattice models of quantum magnetism, strongly correlated electron systems and elementary particles. Early chapters cover the classical treatment of critical phenomena through high-temperature expansions, and introduce graph theoretical and combinatorial algorithms. The book then discusses high-order linked-cluster perturbation expansions for quantum lattice models, finite temperature expansions, and lattice gauge models. Also included are numerous detailed examples and case studies, and an accompanying resources website, www.cambridge.org/9780521842426, contains programs for implementing these powerful numerical techniques. A valuable resource for graduate students and postdoctoral researchers work

Theory of Preliminary Test and Stein-Type Estimation with Applications provides a com-prehensive account of the theory and methods of estimation in a variety of standard models used in applied statist

This 2006 book introduces and develops the basic actuarial models and underlying pricing of life-contingent pension annuities and life insurance from a unique financial perspective. The ideas and techniques are then applied to the real-world problem of generating sustainable retirement income towards the end of the human life-cycle. The role of lifetime income, longevity insurance, and systematic withdrawal plans are investigated in a parsimonious framework. The underlying technology and terminology of the book are based on continuous-time financial economics by merging analytic laws of mortality with the dynamics of equity markets and interest rates. Nonetheless, the book requires a minimal background in mathematics and emphasizes applications and examples more than proofs and theorems. It can serve as an ideal textbook for an applied course on wealth management and retirement planning in addition to being a reference for quantitatively-inclined financial planners.

How do three celestial bodies move under their mutual gravitational attraction? This problem has been studied by Isaac Newton and leading mathematicians over the last two centuries. Poincaré's conclusion, that the problem represents an example of chaos in nature, opens the new possibility of using a statistical approach. For the first time this book presents these methods in a systematic way, surveying statistical as well as more traditional methods. The book begins by providing an introduction to celestial mechanics, including Lagrangian and Hamiltonian methods, and both the two and restricted three body problems. It then surveys statistical and perturbation methods for the solution of the general three body problem, providing solutions based on combining orbit calculations with semi-analytic methods for the first time. This book should be essential reading for students in this rapidly expanding field and is suitable for students of celestial mechanics at advanced undergraduate and gr

Suitable for advanced undergraduates and graduate students, this text presents selected aspects of matrix theory that are most useful in developing computational methods for solving linear equations a

The theme of the book is the distribution and abundance of organisms in space and time. The core of the book lies in how local births and deaths are tied to emigration and immigration processes, and how environmental variability at different scales affects population dynamics with stochastic processes and spatial structure and shows how elementary analytical tools can be used to understand population fluctuations, synchrony, processes underlying range distributions and community structure and species coexistence. The book also shows how spatial population dynamics models can be used to understand life history evolution and aspects of evolutionary game theory. Although primarily based on analytical and numerical analyses of spatial population processes, data from several study systems are also dealt with.

Thoroughly revised for its second edition, this advanced textbook provides an introduction to the basic methods of computational physics, and an overview of progress in several areas of scientific computing by relying on free software available from CERN. The book begins by dealing with basic computational tools and routines, covering approximating functions, differential equations, spectral analysis, and matrix operations. Important concepts are illustrated by relevant examples at each stage. The author also discusses more advanced topics, such as molecular dynamics, modeling continuous systems, Monte Carlo methods, genetic algorithm and programming, and numerical renormalization. It includes many more exercises. This can be used as a textbook for either undergraduate or first-year graduate courses on computational physics or scientific computation. It will also be a useful reference for anyone involved in computational research.

The theme of the book is the distribution and abundance of organisms in space and time. The core of the book lies in how local births and deaths are tied to emigration and immigration processes, and how environmental variability at different scales affects population dynamics with stochastic processes and spatial structure and shows how elementary analytical tools can be used to understand population fluctuations, synchrony, processes underlying range distributions and community structure and species coexistence. The book also shows how spatial population dynamics models can be used to understand life history evolution and aspects of evolutionary game theory. Although primarily based on analytical and numerical analyses of spatial population processes, data from several study systems are also dealt with.

This is a book on stochastic dynamic macroeconomics from a Keynesian perspective. It shows that including Keynesian features in intertemporal models considerably contributes to resolve major puzzles

The authoritative reference on NEURON, the simulation environment for modeling biological neurons and neural networks that enjoys wide use in the experimental and computational neuroscience communities. This book shows how to use NEURON to construct and apply empirically based models. Written primarily for neuroscience investigators, teachers, and students, it assumes no previous knowledge of computer programming or numerical methods. Readers with a background in the physical sciences or mathematics, who have some knowledge about brain cells and circuits and are interested in computational modeling, will also find it helpful. The NEURON Book covers material that ranges from the inner workings of this program, to practical considerations involved in specifying the anatomical and biophysical properties that are to be represented in models. It uses a problem-solving approach, with many working examples that readers can try for themselves.

Correlation is a robust and general technique for pattern recognition and is used in many applications, such as automatic target recognition, biometric recognition and optical character recognition. The design, analysis and use of correlation pattern recognition algorithms requires background information, including linear systems theory, random variables and processes, matrix/vector methods, detection and estimation theory, digital signal processing and optical processing. This book provides a needed review of this diverse background material and develops the signal processing theory, the pattern recognition metrics, and the practical application know-how from basic premises. It shows both digital and optical implementations. It also contains technology presented by the team that developed it and includes case studies of significant interest, such as face and fingerprint recognition. Suitable for graduate students taking courses in pattern recognition theory, whilst reaching technical

Occupancy Estimation and Modeling is the first book to examine the latest methods in analyzing presence/absence data surveys. Using four classes of models (single-species, single-season; single-speci

This book describes the most reliable methods available for evaluating the transport properties, such as viscosity, thermal conductivity and diffusion, of pure gases and fluid mixtures. Particular emphasis is placed on recent theoretical advances in our understanding of fluid transport properties in all the different regions of temperature and pressure. In addition to the important theoretical tools, the different methods of data representation are also covered, followed by a section which demonstrates the application of selected models in a range of circumstances. Case studies of transport property analysis for real fluids are then given, and the book concludes with a discussion of various international data banks and prediction packages. Advanced students of kinetic theory, as well as engineers and scientists involved with the design of process equipment or the interpretation of measurements of fluid transport properties, will find this book indispensable.

This volume collects seven of Marc Nerlove's previously published, classic essays on panel data econometrics written over the past thirty-five years, together with a cogent essay on the history of the subject, which began with George Biddell Airey's monograph published in 1861. Since Professor Nerlove's 1966 Econometrica paper with Pietro Balestra, panel data and methods of econometric analysis appropriate to such data have become increasingly important in the discipline. The principal factors in the research environment affecting the future course of panel data econometrics are the phenomenal growth in the computational power available to the individual researcher at his or her desktop and the ready availability of data sets, both large and small, via the Internet. The best way to formulate statistical models for inference is motivated and shaped by substantive problems and understanding of the processes generating the data at hand to resolve them. The essays illustrate both the role

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

This 2002 book introduces the quantum theory of gauge fields. Emphasis is placed on four non-perturbative methods: path integrals, lattice gauge theories, the 1/N expansion, and reduced matrix models, all of which have important contemporary applications. Written as a textbook, it assumes a knowledge of quantum mechanics and elements of perturbation theory, while many relevant concepts are pedagogically introduced at a basic level in the first half of the book. The second half comprehensively covers large-N Yang-Mills theory. The book uses an approach to gauge theories based on path-dependent phase factors known as the Wilson loops, and contains problems with detailed solutions to aid understanding. Suitable for advanced graduate courses in quantum field theory, the book will also be of interest to researchers in high energy theory and condensed matter physics as a survey of recent developments in gauge theory.

The place of money capital in the theory of the firm has remained a relatively neglected question in traditions of economic analysis. In this highly integrative work, issues in production, pricing, capital investment and financial theory are brought to new levels of interdependence. Developing a three-part argument, Money Capital in the Theory of the Firm deals successively with the theoretical issues and analytic motivation, the neoclassical tradition and postclassical perspectives. In doing so, it presents a self-contained foundation in the basic structures of microeconomic analysis relating to optimize decision making in the firm and in the accounting concepts and statistical apparatus of probability theory relevant to the neoclassical aspects of the argument. Additionally, the book provides the essential mathematical development of such advanced topics as utility functions defined over stochastic arguments, the equilibrium theory of financial asset prices and yields, the cost of mo