Uncertainty quantification: theory, implementation, and applications
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Philadelphia
SIAM, Society for Industrial and Applied Mathematics
[2014]
|
| Schriftenreihe: | Computational science and engineering
12 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XVIII, 382 Seiten Illustrationen, Diagramme |
| ISBN: | 9781611973211 |
Internformat
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| 264 | 1 | |a Philadelphia |b SIAM, Society for Industrial and Applied Mathematics |c [2014] | |
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Datensatz im Suchindex
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| adam_text | Contents Preface įx Notation xjji Acronyms andInitialisms xvii 1 2 3 4 Introduction լ 1.1 1.2 4 8 Nature of Uncertainties and Errors............................................ Predictive Estimation.................................................................... Large-ScaleApplications 11 2.1 2.2 2.3 2.4 2.5 H 21 33 36 44 Weather Models............................................................................. Climate Models............................................................................. Subsurface Hydrology and Geology............................................ Nuclear Reactor Design................................................................. Biological Models.......................................................................... Prototypical Models 51 3.1 3.2 3.3 3.4 3.5 51 61 63 65 66 Models............................................................................................ Evolution, Stationary, and Algebraic Models............................. Abstract Modeling Framework..................................................... Notation for Parameters and Inputs............................................ Exercises........................................................................................ Fundamentals of Probability, Random Processes, and Statistics 67 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10 Random Variables, Distributions, and Densities........................ 67 Estimators, Estimates, and Sampling Distributions .................. 79 Ordinary Least Squares and Maximum Likelihood Estimators . 82 Modes of Convergence and
Limit Theorems................................. 85 Random Processes.......................................................................... 87 Markov Chains ............................................................................. 90 Random versus Stochastic Differential Equations........................ 96 Statistical Inference....................................................................... 98 Notes and References....................................................................... 104 Exercises............................................................................................ 105 v
Contents 5 Representation of Random Inputs 5.1 5.2 5.3 5.4 6 Parameter Selection Techniques 6.1 6.2 6.3 6.4 6.5 7 8 9 10 187 Direct Evaluation for Linear Models................................................ 188 Sampling Methods.............................................................................. 191 Perturbation Methods........................................................................ 192 Prediction Intervals........................................................................... 197 Notes and References........................................................................ 203 Exercises.............................................................................................204 Stochastic Spectral Methods 10.1 10.2 10.3 10.4 10.5 10.6 155 Parameter Estimation from a Bayesian Perspective..................... 155 Markov Chain Monte Carlo (MCMC) Techniques........................ 159 Metropolis and Metropolis-Hastings Algorithms........................... 159 Stationary Distribution and Convergence Criteria........................ 168 Parameter Identifiability.................................................................. 171 Delayed Rejection Adaptive Metropolis (DRAM) ........................ 172 DiffeRential Evolution Adaptive Metropolis (DREAM)............... 181 Notes and References........................................................................ 184 Exercises............................................................................................. 184 Uncertainty Propagation in Models 9.1 9.2 9.3 9.4 9.5 9.6 131 Parameter Estimation
from a Frequentist Perspective.................. 133 Linear Regression..............................................................................134 Nonlinear Parameter Estimation Problem....................................... 141 Notes and References........................................................................ 152 Exercises.............................................................................................153 Bayesian Techniques for Parameter Estimation 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9 113 Linearly Parameterized Problems................................................... 115 Nonlinearly Parameterized Problems............................................. 122 Parameter Correlation versus Identifiability.................................... 125 Notes and References........................................................................ 127 Exercises.............................................................................................128 Frequentist Techniques for ParameterEstimation 7.1 7.2 7.3 7.4 7.5 ^7 Mutually Independent Random Parameters.................................... Ю7 Correlated Random Parameters.......................................................Ю8 Finite-Dimensional Representation of Random Coefficients ... 109 Exercises.......................................................................................... 207 Spectral Representation of Random Processes.............................. 207 Galerkin, Collocation, and Discrete Projection Frameworks . . . 214 Stochastic Galerkin
Method—Examples.......................................... 226 Discrete Projection Method—Example.......................................... 234 Stochastic Polynomial Packages...................................................... 235 Exercises.................................................................. 230
Contents vii 11 Sparse Grid Quadrature and InterpolationTechniques 239 11.1 Quadrature Techniques.......................................................................239 11.2 Interpolating Polynomials for Collocation........................................250 11.3 Sparse Grid Software..........................................................................254 11.4 Exercises............................................................................................... 255 12 Prediction in the Presence of ModelDiscrepancy 257 12.1 Effects of Unaccommodated Model Discrepancy........................... 261 12.2 Incorporation of Missing Physical Mechanisms...............................263 12.3 Techniques to Quantify Model Errors..............................................265 12.4 Issues Pertaining to Model Discrepancy Representations .... 267 12.5 Notes and References..........................................................................269 12.6 Exercises............................................................................................... 269 13 Surrogate Models 271 13.1 Regression or Interpolation-Based Models........................................273 13.2 Projection-Based Models................................................................... 280 13.3 Eigenfunction or Modal Expansions.................................................283 13.4 Snapshot-Based Methods including POD........................................284 13.5 High-Dimensional Model Representation (HDMR) Techniques . 289 13.6 Surrogate-Based Bayesian Model
Calibration..................................298 13.7 Notes and References..........................................................................299 13.8 Exercises............................................................................................... 300 14 Local 14.1 14.2 14.3 14.4 15 Global Sensitivity Analysis 321 15.1 Variance-Based Methods................................................................... 323 15.2 Morris Screening...................................................................................331 15.3 Time- or Space-Dependent Responses..............................................337 15.4 Notes and References..........................................................................343 15.5 Exercises............................................................................................... 344 A Concepts from Functional Analysis 345 A.l Exercises................................................................................................ 351 Sensitivity Analysis 303 Motivating Examples—Neutron Diffusion........................................306 Functional Analytic Framework for FSAP and ASAP.................. 312 Notes and References..........................................................................318 Exercises............................................................................................... 319 Bibliography 353 Index 373
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| isbn | 9781611973211 |
| language | English |
| lccn | 013034432 |
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| spelling | Smith, Ralph C. 1960- Verfasser (DE-588)1048465861 aut Uncertainty quantification theory, implementation, and applications Ralph C. Smith Philadelphia SIAM, Society for Industrial and Applied Mathematics [2014] XVIII, 382 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Computational science and engineering 12 Includes bibliographical references and index Measurement uncertainty (Statistics) Estimation theory Unsicheres Schließen (DE-588)4361044-4 gnd rswk-swf Messgenauigkeit (DE-588)4138706-5 gnd rswk-swf Statistische Entscheidungstheorie (DE-588)4077850-2 gnd rswk-swf Schätztheorie (DE-588)4121608-8 gnd rswk-swf Messgenauigkeit (DE-588)4138706-5 s Unsicheres Schließen (DE-588)4361044-4 s DE-604 Schätztheorie (DE-588)4121608-8 s Statistische Entscheidungstheorie (DE-588)4077850-2 s Erscheint auch als Online-Ausgabe 978-1-61197-322-8 Computational science and engineering 12 (DE-604)BV022382702 12 Digitalisierung UB Bamberg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027585917&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Smith, Ralph C. 1960- Uncertainty quantification theory, implementation, and applications Computational science and engineering Measurement uncertainty (Statistics) Estimation theory Unsicheres Schließen (DE-588)4361044-4 gnd Messgenauigkeit (DE-588)4138706-5 gnd Statistische Entscheidungstheorie (DE-588)4077850-2 gnd Schätztheorie (DE-588)4121608-8 gnd |
| subject_GND | (DE-588)4361044-4 (DE-588)4138706-5 (DE-588)4077850-2 (DE-588)4121608-8 |
| title | Uncertainty quantification theory, implementation, and applications |
| title_auth | Uncertainty quantification theory, implementation, and applications |
| title_exact_search | Uncertainty quantification theory, implementation, and applications |
| title_full | Uncertainty quantification theory, implementation, and applications Ralph C. Smith |
| title_fullStr | Uncertainty quantification theory, implementation, and applications Ralph C. Smith |
| title_full_unstemmed | Uncertainty quantification theory, implementation, and applications Ralph C. Smith |
| title_short | Uncertainty quantification |
| title_sort | uncertainty quantification theory implementation and applications |
| title_sub | theory, implementation, and applications |
| topic | Measurement uncertainty (Statistics) Estimation theory Unsicheres Schließen (DE-588)4361044-4 gnd Messgenauigkeit (DE-588)4138706-5 gnd Statistische Entscheidungstheorie (DE-588)4077850-2 gnd Schätztheorie (DE-588)4121608-8 gnd |
| topic_facet | Measurement uncertainty (Statistics) Estimation theory Unsicheres Schließen Messgenauigkeit Statistische Entscheidungstheorie Schätztheorie |
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