Uncertainty Quantification With R
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Uncertainty Quantification With R
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Author : Eduardo Souza de Cursi
language : en
Publisher: Springer Nature
Release Date : 2024-05-06
Uncertainty Quantification With R written by Eduardo Souza de Cursi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-05-06 with Business & Economics categories.
This book is a rigorous but practical presentation of the Bayesian techniques of uncertainty quantification, with applications in R. This volume includes mathematical arguments at the level necessary to make the presentation rigorous and the assumptions clearly established, while maintaining a focus on practical applications of Bayesian uncertainty quantification methods. Practical aspects of applied probability are also discussed, making the content accessible to students. The introduction of R allows the reader to solve more complex problems involving a more significant number of variables. Users will be able to use examples laid out in the text to solve medium-sized problems. The list of topics covered in this volume includes basic Bayesian probabilities, entropy, Bayesian estimation and decision, sequential Bayesian estimation, and numerical methods. Blending theoretical rigor and practical applications, this volume will be of interest to professionals, researchers, graduate and undergraduate students interested in the use of Bayesian uncertainty quantification techniques within the framework of operations research and mathematical programming, for applications in management and planning.
Uncertainty Quantification And Predictive Computational Science
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Author : Ryan G. McClarren
language : en
Publisher: Springer
Release Date : 2018-11-23
Uncertainty Quantification And Predictive Computational Science written by Ryan G. McClarren and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-23 with Science categories.
This textbook teaches the essential background and skills for understanding and quantifying uncertainties in a computational simulation, and for predicting the behavior of a system under those uncertainties. It addresses a critical knowledge gap in the widespread adoption of simulation in high-consequence decision-making throughout the engineering and physical sciences. Constructing sophisticated techniques for prediction from basic building blocks, the book first reviews the fundamentals that underpin later topics of the book including probability, sampling, and Bayesian statistics. Part II focuses on applying Local Sensitivity Analysis to apportion uncertainty in the model outputs to sources of uncertainty in its inputs. Part III demonstrates techniques for quantifying the impact of parametric uncertainties on a problem, specifically how input uncertainties affect outputs. The final section covers techniques for applying uncertainty quantification to make predictions under uncertainty, including treatment of epistemic uncertainties. It presents the theory and practice of predicting the behavior of a system based on the aggregation of data from simulation, theory, and experiment. The text focuses on simulations based on the solution of systems of partial differential equations and includes in-depth coverage of Monte Carlo methods, basic design of computer experiments, as well as regularized statistical techniques. Code references, in python, appear throughout the text and online as executable code, enabling readers to perform the analysis under discussion. Worked examples from realistic, model problems help readers understand the mechanics of applying the methods. Each chapter ends with several assignable problems. Uncertainty Quantification and Predictive Computational Science fills the growing need for a classroom text for senior undergraduate and early-career graduate students in the engineering and physical sciences and supports independent study by researchers and professionals who must include uncertainty quantification and predictive science in the simulations they develop and/or perform.
Princeton Companion To Applied Mathematics
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Author : Nicholas J. Higham
language : en
Publisher: Princeton University Press
Release Date : 2015-09-09
Princeton Companion To Applied Mathematics written by Nicholas J. Higham and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-09 with Mathematics categories.
The must-have compendium on applied mathematics This is the most authoritative and accessible single-volume reference book on applied mathematics. Featuring numerous entries by leading experts and organized thematically, it introduces readers to applied mathematics and its uses; explains key concepts; describes important equations, laws, and functions; looks at exciting areas of research; covers modeling and simulation; explores areas of application; and more. Modeled on the popular Princeton Companion to Mathematics, this volume is an indispensable resource for undergraduate and graduate students, researchers, and practitioners in other disciplines seeking a user-friendly reference book on applied mathematics. Features nearly 200 entries organized thematically and written by an international team of distinguished contributors Presents the major ideas and branches of applied mathematics in a clear and accessible way Explains important mathematical concepts, methods, equations, and applications Introduces the language of applied mathematics and the goals of applied mathematical research Gives a wide range of examples of mathematical modeling Covers continuum mechanics, dynamical systems, numerical analysis, discrete and combinatorial mathematics, mathematical physics, and much more Explores the connections between applied mathematics and other disciplines Includes suggestions for further reading, cross-references, and a comprehensive index
An Introduction To Data Analysis And Uncertainty Quantification For Inverse Problems
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Author : Luis Tenorio
language : en
Publisher: SIAM
Release Date : 2017-07-06
An Introduction To Data Analysis And Uncertainty Quantification For Inverse Problems written by Luis Tenorio and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-06 with Mathematics categories.
Inverse problems are found in many applications, such as medical imaging, engineering, astronomy, and geophysics, among others. To solve an inverse problem is to recover an object from noisy, usually indirect observations. Solutions to inverse problems are subject to many potential sources of error introduced by approximate mathematical models, regularization methods, numerical approximations for efficient computations, noisy data, and limitations in the number of observations; thus it is important to include an assessment of the uncertainties as part of the solution. Such assessment is interdisciplinary by nature, as it requires, in addition to knowledge of the particular application, methods from applied mathematics, probability, and statistics. This book bridges applied mathematics and statistics by providing a basic introduction to probability and statistics for uncertainty quantification in the context of inverse problems, as well as an introduction to statistical regularization of inverse problems. The author covers basic statistical inference, introduces the framework of ill-posed inverse problems, and explains statistical questions that arise in their applications. An Introduction to Data Analysis and Uncertainty Quantification for Inverse Problems?includes many examples that explain techniques which are useful to address general problems arising in uncertainty quantification, Bayesian and non-Bayesian statistical methods and discussions of their complementary roles, and analysis of a real data set to illustrate the methodology covered throughout the book.
Uncertainty Quantification
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Author : Ralph C. Smith
language : en
Publisher: SIAM
Release Date : 2013-12-02
Uncertainty Quantification written by Ralph C. Smith and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-02 with Science categories.
The field of uncertainty quantification is evolving rapidly because of increasing emphasis on models that require quantified uncertainties for large-scale applications, novel algorithm development, and new computational architectures that facilitate implementation of these algorithms. Uncertainty Quantification: Theory, Implementation, and Applications provides readers with the basic concepts, theory, and algorithms necessary to quantify input and response uncertainties for simulation models arising in a broad range of disciplines. The book begins with a detailed discussion of applications where uncertainty quantification is critical for both scientific understanding and policy. It then covers concepts from probability and statistics, parameter selection techniques, frequentist and Bayesian model calibration, propagation of uncertainties, quantification of model discrepancy, surrogate model construction, and local and global sensitivity analysis. The author maintains a complementary web page where readers can find data used in the exercises and other supplementary material.
Uncertainty Quantification Using R
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Author : Eduardo Souza de Cursi
language : en
Publisher: Springer Nature
Release Date : 2023-02-22
Uncertainty Quantification Using R written by Eduardo Souza de Cursi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-22 with Business & Economics categories.
This book is a rigorous but practical presentation of the techniques of uncertainty quantification, with applications in R and Python. This volume includes mathematical arguments at the level necessary to make the presentation rigorous and the assumptions clearly established, while maintaining a focus on practical applications of uncertainty quantification methods. Practical aspects of applied probability are also discussed, making the content accessible to students. The introduction of R and Python allows the reader to solve more complex problems involving a more significant number of variables. Users will be able to use examples laid out in the text to solve medium-sized problems. The list of topics covered in this volume includes linear and nonlinear programming, Lagrange multipliers (for sensitivity), multi-objective optimization, game theory, as well as linear algebraic equations, and probability and statistics. Blending theoretical rigor and practical applications, this volume will be of interest to professionals, researchers, graduate and undergraduate students interested in the use of uncertainty quantification techniques within the framework of operations research and mathematical programming, for applications in management and planning.
Using R For Digital Soil Mapping
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Author : Brendan P. Malone
language : en
Publisher: Springer
Release Date : 2016-11-17
Using R For Digital Soil Mapping written by Brendan P. Malone and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-17 with Nature categories.
This book describes and provides many detailed examples of implementing Digital Soil Mapping (DSM) using R. The work adheres to Digital Soil Mapping theory, and presents a strong focus on how to apply it. DSM exercises are also included and cover procedures for handling and manipulating soil and spatial data in R. The book also introduces the basic concepts and practices for building spatial soil prediction functions, and then ultimately producing digital soil maps.
Predictive Soil Mapping With R
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Author : Tomislav Hengl
language : en
Publisher: Lulu.com
Release Date : 2018-12-20
Predictive Soil Mapping With R written by Tomislav Hengl and has been published by Lulu.com this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-20 with Technology & Engineering categories.
Predictive Soil Mapping (PSM) is based on applying statistical and/or machine learning techniques to fit models for the purpose of producing spatial and/or spatiotemporal predictions of soil variables i.e. maps of soil properties and classes at different resolutions. It is a multidisciplinary field combining statistics, data science, soil science, physical geography, remote sensing, geoinformation science and a number of other sciences. Predictive Soil Mapping with R is about understanding the main concepts behind soil mapping, mastering R packages that can be used to produce high quality soil maps, and about optimizing all processes involved so that also the production costs can be reduced. The online version of the book is available at: https: //envirometrix.github.io/PredictiveSoilMapping/ Pull requests and general comments are welcome. These materials are based on technical tutorials initially developed by the ISRIC's Global Soil Information Facilities (GSIF) development team over the period 2014-2017
Basics And Trends In Sensitivity Analysis Theory And Practice In R
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Author : Sébastien Da Veiga
language : en
Publisher: SIAM
Release Date : 2021-10-14
Basics And Trends In Sensitivity Analysis Theory And Practice In R written by Sébastien Da Veiga and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-14 with Mathematics categories.
This book provides an overview of global sensitivity analysis methods and algorithms, including their theoretical basis and mathematical properties. The authors use a practical point of view and real case studies as well as numerous examples, and applications of the different approaches are illustrated throughout using R code to explain their usage and usefulness in practice. Basics and Trends in Sensitivity Analysis: Theory and Practice in R covers a lot of material, including theoretical aspects of Sobol’ indices as well as sampling-based formulas, spectral methods, and metamodel-based approaches for estimation purposes; screening techniques devoted to identifying influential and noninfluential inputs; variance-based measures when model inputs are statistically dependent (and several other approaches that go beyond variance-based sensitivity measures); and a case study in R related to a COVID-19 epidemic model where the full workflow of sensitivity analysis combining several techniques is presented. This book is intended for engineers, researchers, and undergraduate students who use complex numerical models and have an interest in sensitivity analysis techniques and is appropriate for anyone with a solid mathematical background in basic statistical and probability theories who develops and uses numerical models in all scientific and engineering domains.
Spatio Temporal Statistics With R
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Author : Christopher K. Wikle
language : en
Publisher: CRC Press
Release Date : 2019-02-18
Spatio Temporal Statistics With R written by Christopher K. Wikle and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-18 with Mathematics categories.
The world is becoming increasingly complex, with larger quantities of data available to be analyzed. It so happens that much of these "big data" that are available are spatio-temporal in nature, meaning that they can be indexed by their spatial locations and time stamps. Spatio-Temporal Statistics with R provides an accessible introduction to statistical analysis of spatio-temporal data, with hands-on applications of the statistical methods using R Labs found at the end of each chapter. The book: Gives a step-by-step approach to analyzing spatio-temporal data, starting with visualization, then statistical modelling, with an emphasis on hierarchical statistical models and basis function expansions, and finishing with model evaluation Provides a gradual entry to the methodological aspects of spatio-temporal statistics Provides broad coverage of using R as well as "R Tips" throughout. Features detailed examples and applications in end-of-chapter Labs Features "Technical Notes" throughout to provide additional technical detail where relevant Supplemented by a website featuring the associated R package, data, reviews, errata, a discussion forum, and more The book fills a void in the literature and available software, providing a bridge for students and researchers alike who wish to learn the basics of spatio-temporal statistics. It is written in an informal style and functions as a down-to-earth introduction to the subject. Any reader familiar with calculus-based probability and statistics, and who is comfortable with basic matrix-algebra representations of statistical models, would find this book easy to follow. The goal is to give as many people as possible the tools and confidence to analyze spatio-temporal data.