Matrix-analytic Methods in Stochastic Models

This text presents the classical theory of conics in a modern form. It includes many novel results that are not easily accessible elsewhere. The approach combines synthetic and analytic methods to der

Featuring detailed explanations of the major algorithms used in quantum Monte Carlo simulations, this is the first textbook of its kind to provide a pedagogical overview of the field and its applications. The book provides a comprehensive introduction to the Monte Carlo method, its use, and its foundations, and examines algorithms for the simulation of quantum many-body lattice problems at finite and zero temperature. These algorithms include continuous-time loop and cluster algorithms for quantum spins, determinant methods for simulating fermions, power methods for computing ground and excited states, and the variational Monte Carlo method. Also discussed are continuous-time algorithms for quantum impurity models and their use within dynamical mean-field theory, along with algorithms for analytically continuing imaginary-time quantum Monte Carlo data. The parallelization of Monte Carlo simulations is also addressed. This is an essential resource for graduate students, teachers, and re

English historical linguistics is a subfield of linguistics which has developed theories and methods for exploring the history of the English language. This Handbook provides an account of state-of-the-art research on this history. It offers an in-depth survey of materials, methods, and language-theoretical models used to study the long diachrony of English. The frameworks covered include corpus linguistics, historical sociolinguistics, historical pragmatics and manuscript studies, among others. The chapters, by leading experts, examine the interplay of language theory and empirical data throughout, critically assessing the work in the field. Of particular importance are the diverse data sources which have become increasingly available in electronic form, allowing the discipline to develop in new directions. The Handbook offers access to the rich and many-faceted spectrum of work in English historical linguistics, past and present, and will be useful for researchers and students intere

This wide-ranging comparative account of the legal regimes for controlling administrative power in England, the USA and Australia argues that differences and similarities between control regimes may be partly explained by the constitutional structures of the systems of government in which they are embedded. It applies social-scientific and historical methods to the comparative study of law and legal systems in a novel and innovative way, and combines accounts of long-term and large-scale patterns of power distribution with detailed analysis of features of administrative law and the administrative justice systems of three jurisdictions. It also proposes a new method of analysing systems of government based on two different models of the distribution of public power (diffusion and concentration), a model which proves more illuminating than traditional separation-of-powers analysis.

An Introduction to Applied Cognitive Psychology offers an accessible review of recent research in the application of cognitive methods, theories, and models. Using real-world scenarios and engaging ev

An Introduction to Applied Cognitive Psychology offers an accessible review of recent research in the application of cognitive methods, theories, and models. Using real-world scenarios and engaging ev

This book discusses the development of useful models and their applications in soil and water engineering. It covers various modeling methods, including groundwater recharge estimation, rainfall-runof

Optimization is used to determine the most appropriate value of variables under given conditions. The primary focus of using optimisation techniques is to measure the maximum or minimum value of a function depending on the circumstances. This book discusses problem formulation and problem solving with the help of algorithms such as secant method, quasi-Newton method, linear programming and dynamic programming. It also explains important chemical processes such as fluid flow systems, heat exchangers, chemical reactors and distillation systems using solved examples. The book begins by explaining the fundamental concepts followed by an elucidation of various modern techniques including trust-region methods, Levenberg–Marquardt algorithms, stochastic optimization, simulated annealing and statistical optimization. It studies the multi-objective optimization technique and its applications in chemical engineering and also discusses the theory and applications of various optimization software

This monograph presents an application of concepts and methods from algebraic topology to models ofconcurrent processes in computer science and their analysis.Taking well-known discrete models for con

This book retraces the history of macroeconomics from Keynes's General Theory to the present. Central to it is the contrast between a Keynesian era and a Lucasian - or dynamic stochastic general equilibrium (DSGE) - era, each ruled by distinct methodological standards. In the Keynesian era, the book studies the following theories: Keynesian macroeconomics, monetarism, disequilibrium macroeconomics (Patinkin, Leijongufvud and Clower), non-Walrasian equilibrium models, and first-generation new Keynesian models. Three stages are identified in the DSGE era: new classical macroeconomics (Lucas), RBC modelling, and second-generation new Keynesian modeling. The book also examines a few selected works aimed at presenting alternatives to Lucasian macroeconomics. While not eschewing analytical content, Michel De Vroey focuses on substantive assessments, and the models studied are presented in a pedagogical and vivid yet critical way.

Multi-scale systems, involving complex interacting processes that occur over a range of temporal and spatial scales, are present in a broad range of disciplines. Several methodologies exist to retrieve this multi-scale information from a given time series; however, each method has its own limitations. This book presents the mathematical theory behind the stochastic analysis of scaling time series, including a general historical introduction to the problem of intermittency in turbulence, as well as how to implement this analysis for a range of different applications. Covering a variety of statistical methods, such as Fourier analysis and wavelet transforms, it provides readers with a thorough understanding of the techniques and when to apply them. New techniques to analyse stochastic processes, including empirical mode decomposition, are also explored. Case studies, in turbulence and ocean sciences, are used to demonstrate how these statistical methods can be applied in practice, for st

In this book, author Lorenzo Bergomipresents readers with an examination of the methods used to employ stochastic volatility to address a variety of issues that come from the modeling of derivatives.

This book presents high-quality original contributions on new software engineering models, approaches, methods, and tools and their evaluation in the context of defence and security applications. In a

Internationally recognised researchers look at developing trends in combinatorics with applications in the study of words and in symbolic dynamics. They explain the important concepts, providing a clear exposition of some recent results, and emphasise the emerging connections between these different fields. Topics include combinatorics on words, pattern avoidance, graph theory, tilings and theory of computation, multidimensional subshifts, discrete dynamical systems, ergodic theory, numeration systems, dynamical arithmetics, automata theory and synchronised words, analytic combinatorics, continued fractions and probabilistic models. Each topic is presented in a way that links it to the main themes, but then they are also extended to repetitions in words, similarity relations, cellular automata, friezes and Dynkin diagrams. The book will appeal to graduate students, research mathematicians and computer scientists working in combinatorics, theory of computation, number theory, symbolic d

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

Designing algorithms to recommend items such as news articles and movies to users is a challenging task in numerous web applications. The crux of the problem is to rank items based on users' responses to different items to optimize for multiple objectives. Major technical challenges are high dimensional prediction with sparse data and constructing high dimensional sequential designs to collect data for user modeling and system design. This comprehensive treatment of the statistical issues that arise in recommender systems includes detailed, in-depth discussions of current state-of-the-art methods such as adaptive sequential designs (multi-armed bandit methods), bilinear random-effects models (matrix factorization) and scalable model fitting using modern computing paradigms like MapReduce. The authors draw upon their vast experience working with such large-scale systems at Yahoo! and LinkedIn, and bridge the gap between theory and practice by illustrating complex concepts with examples

The advent of supercomputers has brought computational fluid dynamics (CFD) to the forefront as a tool to analyze increasingly complex simulation scenarios in many fields. Computational aerodynamics problems are also increasingly moving towards being coupled, multi-physics and multi-scale with complex, moving geometries. The latter presents severe geometry handling and meshing challenges. Simulations also frequently use formal design optimization processes. This book explains the evolution of CFD and provides a comprehensive overview of the plethora of tools and methods available for solving complex scenarios while exploring the future directions and possible outcomes. Using numerous examples, illustrations and computational methods the author discusses turbulence modeling, pre and post processing, coupled solutions, the importance of design optimization, multiphysics problems, reduced order models, and large scale computations and the future of CFD. Advanced Computational Fluid and Ae

Mark H.A. Davis introduced the Piecewise-Deterministic Markov Process (PDMP) class of stochastic hybrid models in an article in 1984. Today it is used to model a variety of complex systems in the fiel

Perfect simulation methods, also known as perfect sampling methods, are algorithms that draw random variates from complex physical and statistical models. These methods are used in MCMC simulation to

Recent developments in information processing systems have driven the advancement of computational methods in the engineering realm. New models and simulations enable better solutions for problem-solv

This book deals with fractals in understanding problems encountered in earth science, and their solutions. It starts with an analysis of two classes of methods (homogeneous fractals random models, and

This book is concerned with digital image processing techniques that use partial differential equations (PDEs) for the task of image 'inpainting', an artistic term for virtual image restoration or interpolation, whereby missing or occluded parts in images are completed based on information provided by intact parts. Computer graphic designers, artists and photographers have long used manual inpainting to restore damaged paintings or manipulate photographs. Today, mathematicians apply powerful methods based on PDEs to automate this task. This book introduces the mathematical concept of PDEs for virtual image restoration. It gives the full picture, from the first modelling steps originating in Gestalt theory and arts restoration to the analysis of resulting PDE models, numerical realisation and real-world application. This broad approach also gives insight into functional analysis, variational calculus, optimisation and numerical analysis and will appeal to researchers and graduate studen

This ambitious book looks 'behind the model' to reveal how economists use formal models to generate insights into the economy. Drawing on recent work in the philosophy of science and economic methodology, the book presents a novel framework for understanding the logic of economic modeling. It also reveals the ways in which economic models can mislead rather than illuminate. Importantly, the book goes beyond purely negative critique, proposing a concrete program of methodological reform to better equip economists to detect potential mismatches between their models and the targets of their inquiry. Ranging across economics, philosophy, and social science methods, and drawing on a variety of examples, including the recent financial crisis, Behind the Model will be of interest to anyone who has wondered how economics works - and why it sometimes fails so spectacularly.

This ambitious book looks 'behind the model' to reveal how economists use formal models to generate insights into the economy. Drawing on recent work in the philosophy of science and economic methodology, the book presents a novel framework for understanding the logic of economic modeling. It also reveals the ways in which economic models can mislead rather than illuminate. Importantly, the book goes beyond purely negative critique, proposing a concrete program of methodological reform to better equip economists to detect potential mismatches between their models and the targets of their inquiry. Ranging across economics, philosophy, and social science methods, and drawing on a variety of examples, including the recent financial crisis, Behind the Model will be of interest to anyone who has wondered how economics works - and why it sometimes fails so spectacularly.

This volume presents contributions on handling data in which the postulate of independence in the data matrix is violated. When this postulate is violated and when the methods assuming independence ar

In the development of statistics, models for the analysis of longitudinal data took a particularly important place, especially in biostatistics. This book describes methods available for applied stati

The widespread use of mouse models in developmental, behavioural and genetic studies has sparked wider interest in rodent biology as a whole. This book brings together the latest research on rodents to better understand the evolution of both living and extinct members of this fascinating group. Topics analysed include the role of molecular techniques in the determination of robust phylogenetic frameworks; how geometric morphometric methods help quantify and analyse variation in shape; and the role of developmental biology in elucidating the origins of skeletal elements and the teeth. The editors unite these disciplines to present the current state of knowledge in rodent biology, whilst setting the landscape for future research. This book highlights interdisciplinary links across palaeontology, developmental biology, functional morphology, phylogenetics and biomechanics, making it a valuable resource for evolutionary biologists in all fields.

Data Analysis in the Cloud introduces and discusses models, methods, techniques, and systems to analyze the large number of digital data sources available on the Internet using the computing and stor

An Introduction to Stochastic Orders discusses this powerful tool that can be used in comparing probabilistic models in different areas such as reliability, survival analysis, risks, finance, and econ

In this contribution, several probabilistic tools to study population dynamics are developed. The focus is on scaling limits of qualitatively different stochastic individual based models and the long

This fully updated Sixth Edition of Religion in Sociological Perspective introduces students to the basic theories and methods in the field, and shows them how to apply these analytic tools to new gro

With this comprehensive guide you will learn how to apply Bayesian machine learning techniques systematically to solve various problems in speech and language processing. A range of statistical models is detailed, from hidden Markov models to Gaussian mixture models, n-gram models and latent topic models, along with applications including automatic speech recognition, speaker verification, and information retrieval. Approximate Bayesian inferences based on MAP, Evidence, Asymptotic, VB, and MCMC approximations are provided as well as full derivations of calculations, useful notations, formulas, and rules. The authors address the difficulties of straightforward applications and provide detailed examples and case studies to demonstrate how you can successfully use practical Bayesian inference methods to improve the performance of information systems. This is an invaluable resource for students, researchers, and industry practitioners working in machine learning, signal processing, and sp

This book reports on the latest findings in the study of Stochastic Neural Networks (SNN). The book collects the novel model of the disturbance driven by Levy process, the research method of M-matrix

The second edition of this popular book brings students fully up to date with the latest methods and techniques in choice analysis. Comprehensive yet accessible, it offers a unique introduction to anyone interested in understanding how to model and forecast the range of choices made by individuals and groups. In addition to a complete rewrite of several chapters, new topics covered include ordered choice, scaled MNL, generalized mixed logit, latent class models, group decision making, heuristics and attribute processing strategies, expected utility theory, and prospect theoretic applications. Many additional case studies are used to illustrate the applications of choice analysis with extensive command syntax provided for all Nlogit applications and datasets available online. With its unique blend of theory, estimation, and application, this book has broad appeal to all those interested in choice modeling methods and will be a valuable resource for students as well as researchers, profe

Mathematical models and methods are required for diverse studies in Geosciences and simultaneously, new problems are posing new needs where Mathematics is needed. At the initiative of American and Can

Stochastic Analysis for Gaussian Random Processes and Fields: With Applications presents Hilbert space methods to study deep analytic properties connecting probabilistic notions. In particular, it stu

Summarising the striking advances of the last two decades, this reliable introduction to modern astronomical polarimetry provides a comprehensive review of state-of-the-art techniques, models and research methods. Focusing on optical and near-infrared wavelengths, each detailed, up-to-date chapter addresses a different facet of recent innovations, including new instrumentation, techniques and theories; new methods based on laboratory studies, enabling the modelling of polarimetric characteristics for a wide variety of astronomical objects; emerging fields of polarimetric exploration, including proto-planetary and debris discs, icy satellites, transneptunian objects, exoplanets, and the search for extraterrestrial life; and unique results produced by space telescopes, and polarimeters aboard exploratory spacecraft. With contributions from an international team of accomplished researchers, this is an ideal resource for astronomers and researchers working in astrophysics, earth sciences,

What are the models used in phylogenetic analysis and what exactly is involved in Bayesian evolutionary analysis using Markov chain Monte Carlo (MCMC) methods? How can you choose and apply these models, which parameterisations and priors make sense, and how can you diagnose Bayesian MCMC when things go wrong? These are just a few of the questions answered in this comprehensive overview of Bayesian approaches to phylogenetics. This practical guide: • Addresses the theoretical aspects of the field • Advises on how to prepare and perform phylogenetic analysis • Helps with interpreting analyses and visualisation of phylogenies • Describes the software architecture • Helps developing BEAST 2.2 extensions to allow these models to be extended further. With an accompanying website providing example files and tutorials (http://beast2.org/), this one-stop reference to applying the latest phylogenetic models in BEAST 2 will provide essential guidance for all users – from those using phylogeneti

This book reviews nonparametric Bayesian methods and models that have proven useful in the context of data analysis. Rather than providing an encyclopedic review of probability models, the book’s stru

The aim of the conference is to present and discuss new methods, issues and challenges encountered in all parts of the complex process of gradual development and application of digital surface models.