Matrix-analytic Methods in Stochastic Models

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.

This book covers the latest results in the field of risk analysis. Presented topics include probabilistic models in cancer research, models and methods in longevity, epidemiology of cancer risk, engin

Determination of Metals in Natural Waters, Sediments and Soils provides analytic labs with a comprehensive overview of the various methods available for analysis of metals and serves as a manual to de

This volume in the Mastering Mathematical Finance series strikes just the right balance between mathematical rigour and practical application. Existing books on the challenging subject of stochastic interest rate models are often too advanced for Master's students or fail to include practical examples. Stochastic Interest Rates covers practical topics such as calibration, numerical implementation and model limitations in detail. The authors provide numerous exercises and carefully chosen examples to help students acquire the necessary skills to deal with interest rate modelling in a real-world setting. In addition, the book's webpage at www.cambridge.org/9781107002579 provides solutions to all of the exercises as well as the computer code (and associated spreadsheets) for all numerical work, which allows students to verify the results.

Based on a starter course for beginning graduate students, Core Statistics provides concise coverage of the fundamentals of inference for parametric statistical models, including both theory and practical numerical computation. The book considers both frequentist maximum likelihood and Bayesian stochastic simulation while focusing on general methods applicable to a wide range of models and emphasizing the common questions addressed by the two approaches. This compact package serves as a lively introduction to the theory and tools that a beginning graduate student needs in order to make the transition to serious statistical analysis: inference; modeling; computation, including some numerics; and the R language. Aimed also at any quantitative scientist who uses statistical methods, this book will deepen readers' understanding of why and when methods work and explain how to develop suitable methods for non-standard situations, such as in ecology, big data and genomics.

Based on a starter course for beginning graduate students, Core Statistics provides concise coverage of the fundamentals of inference for parametric statistical models, including both theory and practical numerical computation. The book considers both frequentist maximum likelihood and Bayesian stochastic simulation while focusing on general methods applicable to a wide range of models and emphasizing the common questions addressed by the two approaches. This compact package serves as a lively introduction to the theory and tools that a beginning graduate student needs in order to make the transition to serious statistical analysis: inference; modeling; computation, including some numerics; and the R language. Aimed also at any quantitative scientist who uses statistical methods, this book will deepen readers' understanding of why and when methods work and explain how to develop suitable methods for non-standard situations, such as in ecology, big data and genomics.

Surveying the last sixty years of research, this book describes the physical properties of DNA in the context of its biological functioning. It is designed to enable both students and researchers of molecular biology, biochemistry and physics to better understand the biophysics of DNA, addressing key questions and facilitating further research. The chapters integrate theoretical and experimental approaches, emphasising throughout the importance of a quantitative knowledge of physical properties in building and analysing models of DNA functioning. For example, the book shows how the relationship between DNA mechanical properties and the sequence specificity of DNA-protein binding can be analyzed quantitatively by using our current knowledge of the physical and structural properties of DNA. Theoretical models and experimental methods in the field are critically considered to enable the reader to engage effectively with the current scientific literature on the physical properties of DNA.

Praise for the First Edition"…[t]he book is great for readers who need to apply the methods and models presented but have little background in mathematics and statistics." -MAA Revie

Provides solutions for two- and three-dimensional linear models of controlled-release systemsReal-world applications are taken from used to help illustrate the methods in Cartesian, cylindrical and sp

Bayesian Data Analysis in Ecology Using Linear Models with R, BUGS, and STANintroduces the Bayesian and frequentist methods of conducting data analyses. The book provides the theoretical background in

Focusing on deterministic models in discrete time, this concise yet rigorous textbook provides a clear and systematic introduction to the theory and application of dynamic economic models. It guides students through the most popular model structures and solution concepts, from the simplest dynamic economic models through to complex problems of optimal policy design in dynamic general equilibrium frameworks. Chapters feature theorems and practical hints, and seventy-five worked examples highlight the various methods and results that can be applied in dynamic economic models. Notation and formulation is uniform throughout, so students can easily discern the similarities and differences between various model classes. Chapters include more than sixty exercises for students to self-test their analytical skills, and password-protected solutions are available for instructors on the companion website. Assuming no prior knowledge of dynamic economic analysis or dynamic optimization, this textbo

This volume presents the latest advances and trends in stochastic models and related statistical procedures. Selected peer-reviewed contributions focus on statistical inference, quality control, chang

This book provides an introduction into data mining methods and models, including association rules, clustering, neural networks, logistic regression, and multivariate analysis. In addition, this revi

Dark energy, the mysterious cause of the accelerating expansion of the universe, is one of the most important fields of research in astrophysics and cosmology today. Introducing the theoretical ideas, observational methods and results, this textbook is ideally suited to graduate courses on dark energy, and will also supplement advanced cosmology courses. Providing a thorough introduction to this exciting field, the textbook covers the cosmological constant, quintessence, k-essence, perfect fluid models, extra-dimensional models, and modified gravity. Observational research is reviewed, from the cosmic microwave background to baryon acoustic oscillations, weak lensing and cluster abundances. Every chapter ends with problems, with full solutions provided, and any calculations are worked through step-by-step.

A Practitioner's Guide to Stochastic Frontier Analysis Using Stata provides practitioners in academia and industry with a step-by-step guide on how to conduct efficiency analysis using the stochastic frontier approach. The authors explain in detail how to estimate production, cost, and profit efficiency and introduce the basic theory of each model in an accessible way, using empirical examples that demonstrate the interpretation and application of models. This book also provides computer code, allowing users to apply the models in their own work, and incorporates the most recent stochastic frontier models developed in academic literature. Such recent developments include models of heteroscedasticity and exogenous determinants of inefficiency, scaling models, panel models with time-varying inefficiency, growth models, and panel models that separate firm effects and persistent and transient inefficiency. Immensely helpful to applied researchers, this book bridges the chasm between theory

"This unique monograph, a classic in its field, provides an account of the development of models and methods for the problem of estimating equilibrium traffic flows in urban areas. The text further de

A Practitioner's Guide to Stochastic Frontier Analysis Using Stata provides practitioners in academia and industry with a step-by-step guide on how to conduct efficiency analysis using the stochastic frontier approach. The authors explain in detail how to estimate production, cost, and profit efficiency and introduce the basic theory of each model in an accessible way, using empirical examples that demonstrate the interpretation and application of models. This book also provides computer code, allowing users to apply the models in their own work, and incorporates the most recent stochastic frontier models developed in academic literature. Such recent developments include models of heteroscedasticity and exogenous determinants of inefficiency, scaling models, panel models with time-varying inefficiency, growth models, and panel models that separate firm effects and persistent and transient inefficiency. Immensely helpful to applied researchers, this book bridges the chasm between theory

The Analytic Hierarchy Process (AHP) has been one of the foremost mathematical methods for decision making with multiple criteria and has been widely studied in the operations research literature as w

This book introduces algebraic, combinatorial, and geometric methods for hidden tree models. It presents a focused introduction to some concepts in algebraic statistics and shows how the methods can b

This book opens new avenues in understanding mathematical models within the context of a transition economy. The exposition lays out the methods for combining different mathematical structures and too