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Model and Mathematics: From the 19th to the 21st Century (Trends in the History of Science)
by Michael Friedman Karin KrauthausenThis open access book collects the historical and medial perspectives of a systematic and epistemological analysis of the complicated, multifaceted relationship between model and mathematics, ranging from, for example, the physical mathematical models of the 19th century to the simulation and digital modelling of the 21st century. The aim of this anthology is to showcase the status of the mathematical model between abstraction and realization, presentation and representation, what is modeled and what models.This book is open access under a CC BY 4.0 license.
Model-Assisted Bayesian Designs for Dose Finding and Optimization: Methods and Applications (Chapman & Hall/CRC Biostatistics Series)
by Ying Yuan Ruitao Lin J. Jack LeeBayesian adaptive designs provide a critical approach to improve the efficiency and success of drug development that has been embraced by the US Food and Drug Administration (FDA). This is particularly important for early phase trials as they form the basis for the development and success of subsequent phase II and III trials. The objective of this book is to describe the state-of-the-art model-assisted designs to facilitate and accelerate the use of novel adaptive designs for early phase clinical trials. Model-assisted designs possess avant-garde features where superiority meets simplicity. Model-assisted designs enjoy exceptional performance comparable to more complicated model-based adaptive designs, yet their decision rules often can be pre-tabulated and included in the protocol—making implementation as simple as conventional algorithm-based designs. An example is the Bayesian optimal interval (BOIN) design, the first dose-finding design to receive the fit-for-purpose designation from the FDA. This designation underscores the regulatory agency's support of the use of the novel adaptive design to improve drug development. Features Represents the first book to provide comprehensive coverage of model-assisted designs for various types of dose-finding and optimization clinical trials Describes the up-to-date theory and practice for model-assisted designs Presents many practical challenges, issues, and solutions arising from early-phase clinical trials Illustrates with many real trial applications Offers numerous tips and guidance on designing dose finding and optimization trials Provides step-by-step illustrations of using software to design trials Develops a companion website (www.trialdesign.org) to provide freely available, easy-to-use software to assist learning and implementing model-assisted designs Written by internationally recognized research leaders who pioneered model-assisted designs from the University of Texas MD Anderson Cancer Center, this book shows how model-assisted designs can greatly improve the efficiency and simplify the design, conduct, and optimization of early-phase dose-finding trials. It should therefore be a very useful practical reference for biostatisticians, clinicians working in clinical trials, and drug regulatory professionals, as well as graduate students of biostatistics. Novel model-assisted designs showcase the new KISS principle: Keep it simple and smart!
Model Averaging (SpringerBriefs in Statistics)
by David FletcherThis book provides a concise and accessible overview of model averaging, with a focus on applications. Model averaging is a common means of allowing for model uncertainty when analysing data, and has been used in a wide range of application areas, such as ecology, econometrics, meteorology and pharmacology. The book presents an overview of the methods developed in this area, illustrating many of them with examples from the life sciences involving real-world data. It also includes an extensive list of references and suggestions for further research. Further, it clearly demonstrates the links between the methods developed in statistics, econometrics and machine learning, as well as the connection between the Bayesian and frequentist approaches to model averaging. The book appeals to statisticians and scientists interested in what methods are available, how they differ and what is known about their properties. It is assumed that readers are familiar with the basic concepts of statistical theory and modelling, including probability, likelihood and generalized linear models.
Model-Based Clustering, Classification, and Density Estimation Using mclust in R (Chapman & Hall/CRC The R Series)
by Luca Scrucca Chris Fraley T. Brendan Murphy Raftery Adrian E.Model-Based Clustering, Classification, and Denisty Estimation Using mclust in R Model-based clustering and classification methods provide a systematic statistical approach to clustering, classification, and density estimation via mixture modeling. The model-based framework allows the problems of choosing or developing an appropriate clustering or classification method to be understood within the context of statistical modeling. The mclust package for the statistical environment R is a widely adopted platform implementing these model-based strategies. The package includes both summary and visual functionality, complementing procedures for estimating and choosing models. Key features of the book: An introduction to the model-based approach and the mclust R package A detailed description of mclust and the underlying modeling strategies An extensive set of examples, color plots, and figures along with the R code for reproducing them Supported by a companion website, including the R code to reproduce the examples and figures presented in the book, errata, and other supplementary material Model-Based Clustering, Classification, and Density Estimation Using mclust in R is accessible to quantitatively trained students and researchers with a basic understanding of statistical methods, including inference and computing. In addition to serving as a reference manual for mclust, the book will be particularly useful to those wishing to employ these model-based techniques in research or applications in statistics, data science, clinical research, social science, and many other disciplines.
Model-based Geostatistics for Global Public Health: Methods and Applications (Chapman & Hall/CRC Interdisciplinary Statistics)
by Peter J. Diggle Emanuele GiorgiModel-based Geostatistics for Global Public Health: Methods and Applications provides an introductory account of model-based geostatistics, its implementation in open-source software and its application in public health research. In the public health problems that are the focus of this book, the authors describe and explain the pattern of spatial variation in a health outcome or exposure measurement of interest. Model-based geostatistics uses explicit probability models and established principles of statistical inference to address questions of this kind. <P><P>Features: <li>Presents state-of-the-art methods in model-based geostatistics. <li>Discusses the application these methods some of the most challenging global public health problems including disease mapping, exposure mapping and environmental epidemiology. <li>Describes exploratory methods for analysing geostatistical data, including: diagnostic checking of residuals standard linear and generalized linear models; variogram analysis; Gaussian process models and geostatistical design issues. <li>Includes a range of more complex geostatistical problems where research is ongoing. <li>All of the results in the book are reproducible using publicly available R code and data-sets, as well as a dedicated R package. <li>This book has been written to be accessible not only to statisticians but also to students and researchers in the public health sciences. <P><P>The Authors <P><P>Peter Diggle is Distinguished University Professor of Statistics in the Faculty of Health and Medicine, Lancaster University. He also holds honorary positions at the Johns Hopkins University School of Public Health, Columbia University International Research Institute for Climate and Society, and Yale University School of Public Health. His research involves the development of statistical methods for analyzing spatial and longitudinal data and their applications in the biomedical and health sciences. <P><P>Dr Emanuele Giorgi is a Lecturer in Biostatistics and member of the CHICAS research group at Lancaster University, where he formerly obtained a PhD in Statistics and Epidemiology in 2015. His research interests involve the development of novel geostatistical methods for disease mapping, with a special focus on malaria and other tropical diseases. In 2018, Dr Giorgi was awarded the Royal Statistical Society Research Prize "for outstanding published contribution at the interface of statistics and epidemiology." He is also the lead developer of PrevMap, an R package where all the methodology found in this book has been implemented.
Model Based Parameter Estimation: Theory and Applications
by Johannes P. Schlöder Rolf Rannacher Stefan Körkel Thomas Carraro Willi Jäger Hans Georg BockThis judicious selection of articles combines mathematical and numerical methods to apply parameter estimation and optimum experimental design in a range of contexts. These include fields as diverse as biology, medicine, chemistry, environmental physics, image processing and computer vision. The material chosen was presented at a multidisciplinary workshop on parameter estimation held in 2009 in Heidelberg. The contributions show how indispensable efficient methods of applied mathematics and computer-based modeling can be to enhancing the quality of interdisciplinary research. The use of scientific computing to model, simulate, and optimize complex processes has become a standard methodology in many scientific fields, as well as in industry. Demonstrating that the use of state-of-the-art optimization techniques in a number of research areas has much potential for improvement, this book provides advanced numerical methods and the very latest results for the applications under consideration.
Model Building in Economics
by Lawrence A. BolandConcern about the role and the limits of modeling has heightened after repeated questions were raised regarding the dependability and suitability of the models that were used in the run-up to the 2008 financial crash. In this book, Lawrence Boland provides an overview of the practices of and the problems faced by model builders to explain the nature of models, the modeling process, and the possibility for and nature of their testing. In a reflective manner, the author raises serious questions about the assumptions and judgments that model builders make in constructing models. In making his case, he examines the traditional microeconomics-macroeconomics separation with regard to how theoretical models are built and used and how they interact, paying particular attention to the use of equilibrium concepts in macroeconomic models and game theory and to the challenges involved in building empirical models, testing models, and using models to test theoretical explanations.
Model Checking Software: 26th International Symposium, SPIN 2019, Beijing, China, July 15–16, 2019, Proceedings (Lecture Notes in Computer Science #11636)
by Fabrizio Biondi Thomas Given-Wilson Axel LegayThis book constitutes the refereed proceedings of the 26th International Symposium on Model Checking Software, SPIN 2019, held in Beijing, China, in July 2019. The 11 full papers presented and 2 demo-tool papers, were carefully reviewed and selected from 29 submissions. Topics covered include formal verification techniques for automated analysis of software; formal analysis for modeling languages, such as UML/state charts; formal specification languages, temporal logic, design-by-contract; model checking, automated theorem proving, including SAT and SMT; verifying compilers; abstraction and symbolic execution techniques; and much more.
Model Checking Software: 25th International Symposium, SPIN 2018, Malaga, Spain, June 20-22, 2018, Proceedings (Lecture Notes in Computer Science #10869)
by María Del Gallardo Pedro MerinoThis book constitutes the refereed proceedings of the 25th International Symposium on Model Checking Software, SPIN 2018, held in Malaga, Spain, in June 2018.The 14 papers presented, 1 short paper, and 1 demo-tool paper, were carefully reviewed and selected from 28 submissions. Topics covered include formal verification techniques for automated analysis of software; formal analysis for modeling languages, such as UML/state charts; formal specification languages, temporal logic, design-by-contract; model checking, automated theorem proving, including SAT and SMT; verifying compilers; abstraction and symbolic execution techniques; and much more.
Model Checking Software: 27th International Symposium, SPIN 2021, Virtual Event, July 12, 2021, Proceedings (Lecture Notes in Computer Science #12864)
by Alfons Laarman Ana SokolovaThis book constitutes the refereed proceedings of the 27th International Symposium on Model Checking Software, SPIN 2021, held virtually in July 2021.The 3 full papers, 4 tool papers, and 1 case study presented together with 2 invited talks were carefully reviewed and selected from 20 submissions. Topics covered include formal verification techniques for automated analysis of software; formal analysis for modeling languages, such as UML/state charts; formal specification languages, temporal logic, design-by-contract; model checking, automated theorem proving, including SAT and SMT; verifying compilers; abstraction and symbolic execution techniques; and much more.
Model Choice in Nonnested Families
by Basilio De Pereira Carlos Alberto PereiraThis book discusses the problem of model choice when the statistical models are separate, also called nonnested. Chapter 1 provides an introduction, motivating examples and a general overview of the problem. Chapter 2 presents the classical or frequentist approach to the problem as well as several alternative procedures and their properties. Chapter 3 explores the Bayesian approach, the limitations of the classical Bayes factors and the proposed alternative Bayes factors to overcome these limitations. It also discusses a significance Bayesian procedure. Lastly, Chapter 4 examines the pure likelihood approach. Various real-data examples and computer simulations are provided throughout the text.
Model Discrimination for Nonlinear Regression Models (Statistics: A Series Of Textbooks And Monographs #101)
by Dale S. BorowiakBorowiak (math, U. of Akron) discusses model discrimination based upon incorrect selection probability, presents diagnostic statistics and formal hypothesis test procedures to assess a model's fit and stability, explains the use of computer computations such as the jackknife and bootstrap, and demon
Model Elements and Network Solutions of Heat, Mass and Momentum Transport Processes (Heat and Mass Transfer)
by George L. DankoThis work provides an enormous contribution to the broad effort of modeling heat, mass and momentum transport in multi-physics problems with the development of new solution approaches. It re-visits the time-honored technique of network application using flow network solutions for all transport process components for a coupled modeling task. The book further provides as formulation of the conservation laws for mass, energy and momentum, specifically for the branches and nodes of transport networks using the combination of the Eulerian and Lagrangean modeling methods. With the extension of Bernoulli’s original concept, a new solution is given for the flow field of viscous and compressible fluids as driven by the balance of mechanical energy, coupled to the thermodynamics of the transport system. Applicable to simple or large-scale tasks, the new model elements and methods are built on first principles. Throughout the work, the book provides original formulations, their mathematical derivations as well as applications in a numerical solution scheme.
Model-free Hedging: A Martingale Optimal Transport Viewpoint (Chapman and Hall/CRC Financial Mathematics Series)
by Pierre Henry-LabordereModel-free Hedging: A Martingale Optimal Transport Viewpoint focuses on the computation of model-independent bounds for exotic options consistent with market prices of liquid instruments such as Vanilla options. The author gives an overview of Martingale Optimal Transport, highlighting the differences between the optimal transport and its martingale counterpart. This topic is then discussed in the context of mathematical finance.
Model-Free Prediction and Regression
by Dimitris N. PolitisThe Model-Free Prediction Principle expounded upon in this monograph is based on the simple notion of transforming a complex dataset to one that is easier to work with, e. g. , i. i. d. or Gaussian. As such, it restores the emphasis on observable quantities, i. e. , current and future data, as opposed to unobservable model parameters and estimates thereof, and yields optimal predictors in diverse settings such as regression and time series. Furthermore, the Model-Free Bootstrap takes us beyond point prediction in order to construct frequentist prediction intervals without resort to unrealistic assumptions such as normality. Prediction has been traditionally approached via a model-based paradigm, i. e. , (a) fit a model to the data at hand, and (b) use the fitted model to extrapolate/predict future data. Due to both mathematical and computational constraints, 20th century statistical practice focused mostly on parametric models. Fortunately, with the advent of widely accessible powerful computing in the late 1970s, computer-intensive methods such as the bootstrap and cross-validation freed practitioners from the limitations of parametric models, and paved the way towards the `big data' era of the 21st century. Nonetheless, there is a further step one may take, i. e. , going beyond even nonparametric models; this is where the Model-Free Prediction Principle is useful. Interestingly, being able to predict a response variable Y associated with a regressor variable X taking on any possible value seems to inadvertently also achieve the main goal of modeling, i. e. , trying to describe how Y depends on X. Hence, as prediction can be treated as a by-product of model-fitting, key estimation problems can be addressed as a by-product of being able to perform prediction. In other words, a practitioner can use Model-Free Prediction ideas in order to additionally obtain point estimates and confidence intervals for relevant parameters leading to an alternative, transformation-based approach to statistical inference.
Model Optimization Methods for Efficient and Edge AI: Federated Learning Architectures, Frameworks and Applications
by Pethuru Raj Chelliah Amir Masoud Rahmani Robert Colby Gayathri Nagasubramanian Sunku RanganathComprehensive overview of the fledgling domain of federated learning (FL), explaining emerging FL methods, architectural approaches, enabling frameworks, and applications Model Optimization Methods for Efficient and Edge AI explores AI model engineering, evaluation, refinement, optimization, and deployment across multiple cloud environments (public, private, edge, and hybrid). It presents key applications of the AI paradigm, including computer vision (CV) and Natural Language Processing (NLP), explaining the nitty-gritty of federated learning (FL) and how the FL method is helping to fulfill AI model optimization needs. The book also describes tools that vendors have created, including FL frameworks and platforms such as PySyft, Tensor Flow Federated (TFF), FATE (Federated AI Technology Enabler), Tensor/IO, and more. The first part of the text covers popular AI and ML methods, platforms, and applications, describing leading AI frameworks and libraries in order to clearly articulate how these tools can help with visualizing and implementing highly flexible AI models quickly. The second part focuses on federated learning, discussing its basic concepts, applications, platforms, and its potential in edge systems (such as IoT). Other topics covered include: Building AI models that are destined to solve several problems, with a focus on widely articulated classification, regression, association, clustering, and other prediction problemsGenerating actionable insights through a variety of AI algorithms, platforms, parallel processing, and other enablersCompressing AI models so that computational, memory, storage, and network requirements can be substantially reducedAddressing crucial issues such as data confidentiality, data access rights, data protection, and access to heterogeneous dataOvercoming cyberattacks on mission-critical software systems by leveraging federated learning Written in an accessible manner and containing a helpful mix of both theoretical concepts and practical applications, Model Optimization Methods for Efficient and Edge AI is an essential reference on the subject for graduate and postgraduate students, researchers, IT professionals, and business leaders.
Model Order Reduction and Applications: Cetraro, Italy 2021 (Lecture Notes in Mathematics #2328)
by Michael Hinze J. Nathan Kutz Olga Mula Karsten UrbanThis book addresses the state of the art of reduced order methods for modelling and computational reduction of complex parametrised systems, governed by ordinary and/or partial differential equations, with a special emphasis on real time computing techniques and applications in various fields.Consisting of four contributions presented at the CIME summer school, the book presents several points of view and techniques to solve demanding problems of increasing complexity. The focus is on theoretical investigation and applicative algorithm development for reduction in the complexity – the dimension, the degrees of freedom, the data – arising in these models.The book is addressed to graduate students, young researchers and people interested in the field. It is a good companion for graduate/doctoral classes.
Model-Oriented Design of Experiments (Lecture Notes in Statistics #209)
by Valerii V. Fedorov Peter HacklThis book presents the basic ideas of statistical methods in the design of optimal experiments. This new edition now includes sections on design techniques based on the elemental Fisher information matrices (as opposed to Pearson information/moment matrices), allowing a seamless extension of the design techniques to inferential problems where the shape of distributions is essential for optimal design construction. Topics include designs for nonlinear models, models with random parameters and models with correlated observations, designs for model discrimination and misspecified (contaminated) models, and designs in functional spaces. The authors avoid technical details, assuming a moderate background in calculus, matrix algebra, and statistics. In many places, however, suggestions are made as to how the ideas presented in this book can be extended and elaborated for use in real scientific research and practical engineering problems.
Model Predictive Control: Engineering Methods for Economists (Dynamic Modeling and Econometrics in Economics and Finance #31)
by Lars Grüne Gernot Tragler Josef Haunschmied Aris DaniilidisThe book explores the field of model predictive control (MPC). It reports on the latest developments in MPC, current applications, and presents various subfields of MPC. The book features topics such as uncertain and stochastic MPC variants, learning and neural network approaches, easy-to-use numerical implementations as well as multi-agent systems and scheduling and coordination tasks. While MPC is rooted in engineering science, this book illustrates the potential of using MPC theory and methods in non-engineering sciences and applications such as economics, finance, and environmental sciences.
Model Predictive Control: Approaches Based On The Extended State Space Model And Extended Non-minimal State Space Model
by Ridong Zhang Anke Xue Furong GaoThis monograph introduces the authors’ work on model predictive control system design using extended state space and extended non-minimal state space approaches. It systematically describes model predictive control design for chemical processes, including the basic control algorithms, the extension to predictive functional control, constrained control, closed-loop system analysis, model predictive control optimization-based PID control, genetic algorithm optimization-based model predictive control, and industrial applications. Providing important insights, useful methods and practical algorithms that can be used in chemical process control and optimization, it offers a valuable resource for researchers, scientists and engineers in the field of process system engineering and control engineering.
Model Predictive Vibration Control
by Boris Rohaľ-Ilkiv Gergely TakácsReal-time model predictive controller (MPC) implementation in active vibration control (AVC) is often rendered difficult by fast sampling speeds and extensive actuator-deformation asymmetry. If the control of lightly damped mechanical structures is assumed, the region of attraction containing the set of allowable initial conditions requires a large prediction horizon, making the already computationally demanding on-line process even more complex. Model Predictive Vibration Control provides insight into the predictive control of lightly damped vibrating structures by exploring computationally efficient algorithms which are capable of low frequency vibration control with guaranteed stability and constraint feasibility. In addition to a theoretical primer on active vibration damping and model predictive control, Model Predictive Vibration Control provides a guide through the necessary steps in understanding the founding ideas of predictive control applied in AVC such as: · the implementation of computationally efficient algorithms · control strategies in simulation and experiment and · typical hardware requirements for piezoceramics actuated smart structures. The use of a simple laboratory model and inclusion of over 170 illustrations provides readers with clear and methodical explanations, making Model Predictive Vibration Control the ideal support material for graduates, researchers and industrial practitioners with an interest in efficient predictive control to be utilized in active vibration attenuation.
Model Reduction for Circuit Simulation
by Peter Benner E. Jan ter Maten Michael HinzeSimulation based on mathematical models plays a major role in computer aided design of integrated circuits (ICs). Decreasing structure sizes, increasing packing densities and driving frequencies require the use of refined mathematical models, and to take into account secondary, parasitic effects. This leads to very high dimensional problems which nowadays require simulation times too large for the short time-to-market demands in industry. Modern Model Order Reduction (MOR) techniques present a way out of this dilemma in providing surrogate models which keep the main characteristics of the device while requiring a significantly lower simulation time than the full model. With Model Reduction for Circuit Simulation we survey the state of the art in the challenging research field of MOR for ICs, and also address its future research directions. Special emphasis is taken on aspects stemming from miniturisations to the nano scale. Contributions cover complexity reduction using e.g., balanced truncation, Krylov-techniques or POD approaches. For semiconductor applications a focus is on generalising current techniques to differential-algebraic equations, on including design parameters, on preserving stability, and on including nonlinearity by means of piecewise linearisations along solution trajectories (TPWL) and interpolation techniques for nonlinear parts. Furthermore the influence of interconnects and power grids on the physical properties of the device is considered, and also top-down system design approaches in which detailed block descriptions are combined with behavioral models. Further topics consider MOR and the combination of approaches from optimisation and statistics, and the inclusion of PDE models with emphasis on MOR for the resulting partial differential algebraic systems. The methods which currently are being developed have also relevance in other application areas such as mechanical multibody systems, and systems arising in chemistry and to biology. The current number of books in the area of MOR for ICs is very limited, so that this volume helps to fill a gap in providing the state of the art material, and to stimulate further research in this area of MOR. Model Reduction for Circuit Simulation also reflects and documents the vivid interaction between three active research projects in this area, namely the EU-Marie Curie Action ToK project O-MOORE-NICE (members in Belgium, The Netherlands and Germany), the EU-Marie Curie Action RTN-project COMSON (members in The Netherlands, Italy, Germany, and Romania), and the German federal project System reduction in nano-electronics (SyreNe).
Model Reduction of Complex Dynamical Systems (International Series of Numerical Mathematics #171)
by Peter Benner Tobias Breiten Heike Faßbender Michael Hinze Tatjana Stykel Ralf ZimmermannThis contributed volume presents some of the latest research related to model order reduction of complex dynamical systems with a focus on time-dependent problems. Chapters are written by leading researchers and users of model order reduction techniques and are based on presentations given at the 2019 edition of the workshop series Model Reduction of Complex Dynamical Systems – MODRED, held at the University of Graz in Austria. The topics considered can be divided into five categories:system-theoretic methods, such as balanced truncation, Hankel norm approximation, and reduced-basis methods; data-driven methods, including Loewner matrix and pencil-based approaches, dynamic mode decomposition, and kernel-based methods;surrogate modeling for design and optimization, with special emphasis on control and data assimilation;model reduction methods in applications, such as control and network systems, computational electromagnetics, structural mechanics, and fluid dynamics; andmodel order reduction software packages and benchmarks.This volume will be an ideal resource for graduate students and researchers in all areas of model reduction, as well as those working in applied mathematics and theoretical informatics.
Model Selection and Error Estimation in a Nutshell (Modeling and Optimization in Science and Technologies #15)
by Luca OnetoHow can we select the best performing data-driven model? How can we rigorously estimate its generalization error? Statistical learning theory answers these questions by deriving non-asymptotic bounds on the generalization error of a model or, in other words, by upper bounding the true error of the learned model based just on quantities computed on the available data. However, for a long time, Statistical learning theory has been considered only an abstract theoretical framework, useful for inspiring new learning approaches, but with limited applicability to practical problems. The purpose of this book is to give an intelligible overview of the problems of model selection and error estimation, by focusing on the ideas behind the different statistical learning theory approaches and simplifying most of the technical aspects with the purpose of making them more accessible and usable in practice. The book starts by presenting the seminal works of the 80’s and includes the most recent results. It discusses open problems and outlines future directions for research.
Model Theoretic Algebra With Particular Emphasis on Fields, Rings, Modules
by Christian.U JensenThis volume highlights the links between model theory and algebra. The work contains a definitive account of algebraically compact modules, a topic of central importance for both module and model theory. Using concrete examples, particular emphasis is given to model theoretic concepts, such as axiomizability. Pure mathematicians, especially algebraists, ring theorists, logicians, model theorists and representation theorists, should find this an absorbing and stimulating book.