Matrix-analytic Methods in Stochastic Models

Most textbooks on regression focus on theory and the simplest of examples. Real statistical problems, however, are complex and subtle. This is not a book about the theory of regression. It is about using regression to solve real problems of comparison, estimation, prediction, and causal inference. Unlike other books, it focuses on practical issues such as sample size and missing data and a wide range of goals and techniques. It jumps right in to methods and computer code you can use immediately. Real examples, real stories from the authors' experience demonstrate what regression can do and its limitations, with practical advice for understanding assumptions and implementing methods for experiments and observational studies. They make a smooth transition to logistic regression and GLM. The emphasis is on computation in R and Stan rather than derivations, with code available online. Graphics and presentation aid understanding of the models and model fitting.

Most textbooks on regression focus on theory and the simplest of examples. Real statistical problems, however, are complex and subtle. This is not a book about the theory of regression. It is about using regression to solve real problems of comparison, estimation, prediction, and causal inference. Unlike other books, it focuses on practical issues such as sample size and missing data and a wide range of goals and techniques. It jumps right in to methods and computer code you can use immediately. Real examples, real stories from the authors' experience demonstrate what regression can do and its limitations, with practical advice for understanding assumptions and implementing methods for experiments and observational studies. They make a smooth transition to logistic regression and GLM. The emphasis is on computation in R and Stan rather than derivations, with code available online. Graphics and presentation aid understanding of the models and model fitting.

Biostatistics with R provides a straightforward introduction on how to analyse data from the wide field of biological research, including nature protection and global change monitoring. The book is centred around traditional statistical approaches, focusing on those prevailing in research publications. The authors cover t-tests, ANOVA and regression models, but also the advanced methods of generalised linear models and classification and regression trees. Chapters usually start with several useful case examples, describing the structure of typical datasets and proposing research-related questions. All chapters are supplemented by example datasets, step-by-step R code demonstrating analytical procedures and interpretation of results. The authors also provide examples of how to appropriately describe statistical procedures and results of analyses in research papers. This accessible textbook will serve a broad audience, from students, researchers or professionals looking to improve their

Biostatistics with R provides a straightforward introduction on how to analyse data from the wide field of biological research, including nature protection and global change monitoring. The book is centred around traditional statistical approaches, focusing on those prevailing in research publications. The authors cover t-tests, ANOVA and regression models, but also the advanced methods of generalised linear models and classification and regression trees. Chapters usually start with several useful case examples, describing the structure of typical datasets and proposing research-related questions. All chapters are supplemented by example datasets, step-by-step R code demonstrating analytical procedures and interpretation of results. The authors also provide examples of how to appropriately describe statistical procedures and results of analyses in research papers. This accessible textbook will serve a broad audience, from students, researchers or professionals looking to improve their

Decision-making in the face of uncertainty is a significant challenge in machine learning, and the multi-armed bandit model is a commonly used framework to address it. This comprehensive and rigorous introduction to the multi-armed bandit problem examines all the major settings, including stochastic, adversarial, and Bayesian frameworks. A focus on both mathematical intuition and carefully worked proofs makes this an excellent reference for established researchers and a helpful resource for graduate students in computer science, engineering, statistics, applied mathematics and economics. Linear bandits receive special attention as one of the most useful models in applications, while other chapters are dedicated to combinatorial bandits, ranking, non-stationary problems, Thompson sampling and pure exploration. The book ends with a peek into the world beyond bandits with an introduction to partial monitoring and learning in Markov decision processes.

Mathematical models of bond markets are of interest to researchers working in applied mathematics, especially in mathematical finance. This book concerns bond market models in which random elements are represented by Lévy processes. These are more flexible than classical models and are well suited to describing prices quoted in a discontinuous fashion. The book's key aims are to characterize bond markets that are free of arbitrage and to analyze their completeness. Nonlinear stochastic partial differential equations (SPDEs) are an important tool in the analysis. The authors begin with a relatively elementary analysis in discrete time, suitable for readers who are not familiar with finance or continuous time stochastic analysis. The book should be of interest to mathematicians, in particular to probabilists, who wish to learn the theory of the bond market and to be exposed to attractive open mathematical problems.

A new and important contribution to the re-emergent field of comparative anthropology, this book argues that comparative ethnographic methods are essential for more contextually sophisticated accounts of a number of pressing human concerns today. The book includes expert accounts from an international team of scholars, showing how these methods can be used to illuminate important theoretical and practical projects. Illustrated with examples of successful inter-disciplinary projects, it highlights the challenges, benefits, and innovative strategies involved in working collaboratively across disciplines. Through its focus on practical methodological and logistical accounts, it will be of value to both seasoned researchers who seek practical models for conducting their own cutting-edge comparative research, and to teachers and students who are looking for first-person accounts of comparative ethnographic research.

A new and important contribution to the re-emergent field of comparative anthropology, this book argues that comparative ethnographic methods are essential for more contextually sophisticated accounts of a number of pressing human concerns today. The book includes expert accounts from an international team of scholars, showing how these methods can be used to illuminate important theoretical and practical projects. Illustrated with examples of successful inter-disciplinary projects, it highlights the challenges, benefits, and innovative strategies involved in working collaboratively across disciplines. Through its focus on practical methodological and logistical accounts, it will be of value to both seasoned researchers who seek practical models for conducting their own cutting-edge comparative research, and to teachers and students who are looking for first-person accounts of comparative ethnographic research.

This must-have manual provides detailed solutions to all of the 300 exercises in Dickson, Hardy and Waters' Actuarial Mathematics for Life Contingent Risks, 3 edition. This groundbreaking text on the modern mathematics of life insurance is required reading for the Society of Actuaries' (SOA) LTAM Exam. The new edition treats a wide range of newer insurance contracts such as critical illness and long-term care insurance; pension valuation material has been expanded; and two new chapters have been added on developing models from mortality data and on changing mortality. Beyond professional examinations, the textbook and solutions manual offer readers the opportunity to develop insight and understanding through guided hands-on work, and also offer practical advice for solving problems using straightforward, intuitive numerical methods. Companion Excel spreadsheets illustrating these techniques are available for free download.

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

Mathematical analysis is key to the modeling and management of natural resources. By presenting required mathematical methods, classic dynamic models for non-renewable and renewable resources, and by exploring several contemporary problems, this text provides a foundation for advanced research. Topics include seminal models in fishery, forestry and non-renewable resource management, as well as an extensive collection of contemporary applications that include the optimal transition from fossil fuels to clean energy, the optimal timing of interventions to save endangered species, pest control and the optimal management of antibiotic resistance. Deterministic and stochastic models in both discrete and continuous time are covered. The book encourages students to pursue a deeper understanding of the analytics of resource problems and to deploy numerical methods when analytical results prove intractable. The combination of analysis, theory and applications will launch the next generation of

Mathematical analysis is key to the modeling and management of natural resources. By presenting required mathematical methods, classic dynamic models for non-renewable and renewable resources, and by exploring several contemporary problems, this text provides a foundation for advanced research. Topics include seminal models in fishery, forestry and non-renewable resource management, as well as an extensive collection of contemporary applications that include the optimal transition from fossil fuels to clean energy, the optimal timing of interventions to save endangered species, pest control and the optimal management of antibiotic resistance. Deterministic and stochastic models in both discrete and continuous time are covered. The book encourages students to pursue a deeper understanding of the analytics of resource problems and to deploy numerical methods when analytical results prove intractable. The combination of analysis, theory and applications will launch the next generation of

Our world is becoming more urban. More than fifty percent of the global population now lives in cities, which poses new challenges for sustainable development. This book integrates theory and methods of sustainability assessment with concepts from systems science to provide guidelines for assessing the sustainability of urban systems. It discusses different aspects of urban sustainability, from energy and housing, to mobility and health, covering social, economic and environmental factors, as well as the various stakeholders and actors involved. The book argues for the need to find models and solutions in order to design sustainable cities of the future in light of the complexity of urban social life. Including diverse case studies from the developed and developing world, this book provides a useful reference for researchers and students from a broad range of disciplines working in the field of sustainability, as well as for environmental consultants and policy makers.

Bringing together contributions on a diverse range of topics, this text explores the relationship between discrete and continuum mechanics as a tool to model new and complex metamaterials. Providing a comprehensive bibliography and historical review of the field, it covers mechanical, acoustic and pantographic metamaterials, discusses Naive Model Theory and Lagrangian discrete models, and their applications, and presents methods for pantographic structures and variational methods for multidisciplinary modeling and computation. The relationship between discrete and continuous models is discussed from both mathematical and engineering viewpoints, making the text ideal for those interested in the foundation of mechanics and computational applications, and innovative viewpoints on the use of discrete systems to model metamaterials are presented for those who want to go deeper into the field. An ideal text for graduate students and researchers interested in continuum approaches to the study

The fundamental algorithms in data mining and machine learning form the basis of data science, utilizing automated methods to analyze patterns and models for all kinds of data in applications ranging from scientific discovery to business analytics. This textbook for senior undergraduate and graduate courses provides a comprehensive, in-depth overview of data mining, machine learning and statistics, offering solid guidance for students, researchers, and practitioners. The book lays the foundations of data analysis, pattern mining, clustering, classification and regression, with a focus on the algorithms and the underlying algebraic, geometric, and probabilistic concepts. New to this second edition is an entire part devoted to regression methods, including neural networks and deep learning.

Building on the Cambridge Element Agent Based Models of Social Life: Fundamentals (Cambridge, 2020), we move on to the next level. We do this by building agent based models of polarization and ethnocentrism. In the process, we develop: stochastic models, which add a crucial element of uncertainty to human interaction; models of human interactions structured by social networks; and 'evolutionary' models in which agents using more effective decision rules are more likely to survive and prosper than others. The aim is to leave readers with an effective toolkit for building, running and analyzing agent based modes of social interaction.

This book provides an introduction to the mathematical and algorithmic foundations of data science, including machine learning, high-dimensional geometry, and analysis of large networks. Topics include the counterintuitive nature of data in high dimensions, important linear algebraic techniques such as singular value decomposition, the theory of random walks and Markov chains, the fundamentals of and important algorithms for machine learning, algorithms and analysis for clustering, probabilistic models for large networks, representation learning including topic modelling and non-negative matrix factorization, wavelets and compressed sensing. Important probabilistic techniques are developed including the law of large numbers, tail inequalities, analysis of random projections, generalization guarantees in machine learning, and moment methods for analysis of phase transitions in large random graphs. Additionally, important structural and complexity measures are discussed such as matrix no

The fundamental mathematical tools needed to understand machine learning include linear algebra, analytic geometry, matrix decompositions, vector calculus, optimization, probability and statistics. These topics are traditionally taught in disparate courses, making it hard for data science or computer science students, or professionals, to efficiently learn the mathematics. This self-contained textbook bridges the gap between mathematical and machine learning texts, introducing the mathematical concepts with a minimum of prerequisites. It uses these concepts to derive four central machine learning methods: linear regression, principal component analysis, Gaussian mixture models and support vector machines. For students and others with a mathematical background, these derivations provide a starting point to machine learning texts. For those learning the mathematics for the first time, the methods help build intuition and practical experience with applying mathematical concepts. Every cha

This book focuses on modeling the anomalous diffusion phenomena, being ubiquitous in the natural world. Both the microscopic models (stochastic processes) and macroscopic models (partial differential

This book provides a complete and reasonably self-contained account of a new classification of connected Lie groups into two classes. The first part describes the use of tools from potential theory to establish the classification and to show that the analytic and algebraic approaches to the classification are equivalent. Part II covers geometric theory of the same classification and a proof that it is equivalent to the algebraic approach. Part III is a new approach to the geometric classification that requires more advanced geometric technology, namely homotopy, homology and the theory of currents. Using these methods, a more direct, but also more sophisticated, approach to the equivalence of the geometric and algebraic classification is made. Background material is introduced gradually to familiarise readers with ideas from areas such as Lie groups, differential topology and probability, in particular, random walks on groups. Numerous open problems inspire students to explore further.

The fundamental mathematical tools needed to understand machine learning include linear algebra, analytic geometry, matrix decompositions, vector calculus, optimization, probability and statistics. These topics are traditionally taught in disparate courses, making it hard for data science or computer science students, or professionals, to efficiently learn the mathematics. This self-contained textbook bridges the gap between mathematical and machine learning texts, introducing the mathematical concepts with a minimum of prerequisites. It uses these concepts to derive four central machine learning methods: linear regression, principal component analysis, Gaussian mixture models and support vector machines. For students and others with a mathematical background, these derivations provide a starting point to machine learning texts. For those learning the mathematics for the first time, the methods help build intuition and practical experience with applying mathematical concepts. Every cha

A comprehensive introduction to both urban and geographical economics: the two dominant approaches used to explain the distribution of economic activity across space. This fully revised and up-to-date third edition gives a full account of the ever-expanding body of knowledge and insights on urban and geographical economics, with an increased emphasis on analytical concepts and empirical methods, reflecting developments in the literature since the last edition. The authors provide both state-of-the-art theories and empirics, introducing new data, methods and models for this edition, including a whole chapter dedicated to measurement issues and empirical methods. Written in a style that is accessible to students who are new to the field, this textbook also includes more advanced concepts that will interest experienced researchers. Unrivalled in its scope and depth, this title is perfect for readers seeking to understand the uneven spatial distribution of economic activity between and wit

A comprehensive introduction to both urban and geographical economics: the two dominant approaches used to explain the distribution of economic activity across space. This fully revised and up-to-date third edition gives a full account of the ever-expanding body of knowledge and insights on urban and geographical economics, with an increased emphasis on analytical concepts and empirical methods, reflecting developments in the literature since the last edition. The authors provide both state-of-the-art theories and empirics, introducing new data, methods and models for this edition, including a whole chapter dedicated to measurement issues and empirical methods. Written in a style that is accessible to students who are new to the field, this textbook also includes more advanced concepts that will interest experienced researchers. Unrivalled in its scope and depth, this title is perfect for readers seeking to understand the uneven spatial distribution of economic activity between and wit

This practical introduction to stochastic reaction-diffusion modelling is based on courses taught at the University of Oxford. The authors discuss the essence of mathematical methods which appear (under different names) in a number of interdisciplinary scientific fields bridging mathematics and computations with biology and chemistry. The book can be used both for self-study and as a supporting text for advanced undergraduate or beginning graduate-level courses in applied mathematics. New mathematical approaches are explained using simple examples of biological models, which range in size from simulations of small biomolecules to groups of animals. The book starts with stochastic modelling of chemical reactions, introducing stochastic simulation algorithms and mathematical methods for analysis of stochastic models. Different stochastic spatio-temporal models are then studied, including models of diffusion and stochastic reaction-diffusion modelling. The methods covered include molecula

This practical introduction to stochastic reaction-diffusion modelling is based on courses taught at the University of Oxford. The authors discuss the essence of mathematical methods which appear (under different names) in a number of interdisciplinary scientific fields bridging mathematics and computations with biology and chemistry. The book can be used both for self-study and as a supporting text for advanced undergraduate or beginning graduate-level courses in applied mathematics. New mathematical approaches are explained using simple examples of biological models, which range in size from simulations of small biomolecules to groups of animals. The book starts with stochastic modelling of chemical reactions, introducing stochastic simulation algorithms and mathematical methods for analysis of stochastic models. Different stochastic spatio-temporal models are then studied, including models of diffusion and stochastic reaction-diffusion modelling. The methods covered include molecula

Doubt over the trustworthiness of published empirical results is not unwarranted and is often a result of statistical mis-specification: invalid probabilistic assumptions imposed on data. Now in its second edition, this bestselling textbook offers a comprehensive course in empirical research methods, teaching the probabilistic and statistical foundations that enable the specification and validation of statistical models, providing the basis for an informed implementation of statistical procedure to secure the trustworthiness of evidence. Each chapter has been thoroughly updated, accounting for developments in the field and the author's own research. The comprehensive scope of the textbook has been expanded by the addition of a new chapter on the Linear Regression and related statistical models. This new edition is now more accessible to students of disciplines beyond economics and includes more pedagogical features, with an increased number of examples as well as review questions and e

This friendly guide is the companion you need to convert pure mathematics into understanding and facility with a host of probabilistic tools. The book provides a high-level view of probability and its most powerful applications. It begins with the basic rules of probability and quickly progresses to some of the most sophisticated modern techniques in use, including Kalman filters, Monte Carlo techniques, machine learning methods, Bayesian inference and stochastic processes. It draws on thirty years of experience in applying probabilistic methods to problems in computational science and engineering, and numerous practical examples illustrate where these techniques are used in the real world. Topics of discussion range from carbon dating to Wasserstein GANs, one of the most recent developments in Deep Learning. The underlying mathematics is presented in full, but clarity takes priority over complete rigour, making this text a starting reference source for researchers and a readable overv

In Strategic Decisions, Planellas and Muni provide an invaluable tool for anyone facing the challenge of taking strategic decisions. Using their 'circle of strategic decisions' framework, they guide readers smoothly through the decision-making process. Following this, they present thirty of the most widely used strategic models, including Porter's Five Forces, Ansoff's Matrix, Blue Ocean Strategy, Open Innovation, and the 8-Step Change Model. For each model, they demonstrate the content, context, and application, using clear and eye-catching graphics. This is a must-have book for all M.B.A. students and business managers.

Written for anyone interested in coastal geomorphology, this is the complete guide to the processes at work on our coastlines and the resulting features seen in coastal systems across the world. Accessible to students from a range of disciplines, the quantitative approach of this book helps to build a solid understanding of wave and current processes that shape coastlines. From sandy beaches to coral reefs, the major coastal features are related to contemporary processes and to sea-level changes over the past 25,000 years. Key equations describing these processes and standard methods and instrumentation used to collect measurements are all presented in this wide-ranging overview. Designed to support a one- or two-semester course and grounded in current research, this second edition has been substantially updated and rewritten - featuring cutting-edge new topics, insights from new models and technologies, additional global examples and an enhanced package of online teaching materials.

In Strategic Decisions, Planellas and Muni provide an invaluable tool for anyone facing the challenge of taking strategic decisions. Using their 'circle of strategic decisions' framework, they guide readers smoothly through the decision-making process. Following this, they present thirty of the most widely used strategic models, including Porter's Five Forces, Ansoff's Matrix, Blue Ocean Strategy, Open Innovation, and the 8-Step Change Model. For each model, they demonstrate the content, context, and application, using clear and eye-catching graphics. This is a must-have book for all M.B.A. students and business managers.

Written for anyone interested in coastal geomorphology, this is the complete guide to the processes at work on our coastlines and the resulting features seen in coastal systems across the world. Accessible to students from a range of disciplines, the quantitative approach of this book helps to build a solid understanding of wave and current processes that shape coastlines. From sandy beaches to coral reefs, the major coastal features are related to contemporary processes and to sea-level changes over the past 25,000 years. Key equations describing these processes and standard methods and instrumentation used to collect measurements are all presented in this wide-ranging overview. Designed to support a one- or two-semester course and grounded in current research, this second edition has been substantially updated and rewritten - featuring cutting-edge new topics, insights from new models and technologies, additional global examples and an enhanced package of online teaching materials.

This friendly guide is the companion you need to convert pure mathematics into understanding and facility with a host of probabilistic tools. The book provides a high-level view of probability and its most powerful applications. It begins with the basic rules of probability and quickly progresses to some of the most sophisticated modern techniques in use, including Kalman filters, Monte Carlo techniques, machine learning methods, Bayesian inference and stochastic processes. It draws on thirty years of experience in applying probabilistic methods to problems in computational science and engineering, and numerous practical examples illustrate where these techniques are used in the real world. Topics of discussion range from carbon dating to Wasserstein GANs, one of the most recent developments in Deep Learning. The underlying mathematics is presented in full, but clarity takes priority over complete rigour, making this text a starting reference source for researchers and a readable overv

This book, geared toward academic researchers and graduate students, brings together research on all facets of how time and causality relate across the sciences. Time is fundamental to how we perceive and reason about causes. It lets us immediately rule out the sound of a car crash as its cause. That a cause happens before its effect has been a core, and often unquestioned, part of how we describe causality. Research across disciplines shows that the relationship is much more complex than that. This book explores what that means for both the metaphysics and epistemology of causes - what they are and how we can find them. Across psychology, biology, and the social sciences, common themes emerge, suggesting that time plays a critical role in our understanding. The increasing availability of large time series datasets allows us to ask new questions about causality, necessitating new methods for modeling dynamic systems and incorporating mechanistic information into causal models.

Bayesian Econometric Methods examines principles of Bayesian inference by posing a series of theoretical and applied questions and providing detailed solutions to those questions. This second edition adds extensive coverage of models popular in finance and macroeconomics, including state space and unobserved components models, stochastic volatility models, ARCH, GARCH, and vector autoregressive models. The authors have also added many new exercises related to Gibbs sampling and Markov Chain Monte Carlo (MCMC) methods. The text includes regression-based and hierarchical specifications, models based upon latent variable representations, and mixture and time series specifications. MCMC methods are discussed and illustrated in detail - from introductory applications to those at the current research frontier - and MATLAB® computer programs are provided on the website accompanying the text. Suitable for graduate study in economics, the text should also be of interest to students studying sta

Bayesian Econometric Methods examines principles of Bayesian inference by posing a series of theoretical and applied questions and providing detailed solutions to those questions. This second edition adds extensive coverage of models popular in finance and macroeconomics, including state space and unobserved components models, stochastic volatility models, ARCH, GARCH, and vector autoregressive models. The authors have also added many new exercises related to Gibbs sampling and Markov Chain Monte Carlo (MCMC) methods. The text includes regression-based and hierarchical specifications, models based upon latent variable representations, and mixture and time series specifications. MCMC methods are discussed and illustrated in detail - from introductory applications to those at the current research frontier - and MATLAB® computer programs are provided on the website accompanying the text. Suitable for graduate study in economics, the text should also be of interest to students studying sta

Cluster analysis finds groups in data automatically. Most methods have been heuristic and leave open such central questions as: how many clusters are there? Which method should I use? How should I handle outliers? Classification assigns new observations to groups given previously classified observations, and also has open questions about parameter tuning, robustness and uncertainty assessment. This book frames cluster analysis and classification in terms of statistical models, thus yielding principled estimation, testing and prediction methods, and sound answers to the central questions. It builds the basic ideas in an accessible but rigorous way, with extensive data examples and R code; describes modern approaches to high-dimensional data and networks; and explains such recent advances as Bayesian regularization, non-Gaussian model-based clustering, cluster merging, variable selection, semi-supervised and robust classification, clustering of functional data, text and images, and co-cl

Doubt over the trustworthiness of published empirical results is not unwarranted and is often a result of statistical mis-specification: invalid probabilistic assumptions imposed on data. Now in its second edition, this bestselling textbook offers a comprehensive course in empirical research methods, teaching the probabilistic and statistical foundations that enable the specification and validation of statistical models, providing the basis for an informed implementation of statistical procedure to secure the trustworthiness of evidence. Each chapter has been thoroughly updated, accounting for developments in the field and the author's own research. The comprehensive scope of the textbook has been expanded by the addition of a new chapter on the Linear Regression and related statistical models. This new edition is now more accessible to students of disciplines beyond economics and includes more pedagogical features, with an increased number of examples as well as review questions and e

This book provides a self-contained introduction to the simulation of flow and transport in porous media, written by a developer of numerical methods. The reader will learn how to implement reservoir simulation models and computational algorithms in a robust and efficient manner. The book contains a large number of numerical examples, all fully equipped with online code and data, allowing the reader to reproduce results, and use them as a starting point for their own work. All of the examples in the book are based on the MATLAB Reservoir Simulation Toolbox (MRST), an open-source toolbox popular popularity in both academic institutions and the petroleum industry. The book can also be seen as a user guide to the MRST software. It will prove invaluable for researchers, professionals and advanced students using reservoir simulation methods. This title is also available as Open Access on Cambridge Core.