Modelling Under Risk and Uncertainty An Introduction to Statistical, Phenomenological and Computational Methods

Note: Supplemental materials are not guaranteed with Rental or Used book purchases.

ISBN: 9780470695142 | 0470695145
Cover: Hardcover
Copyright: 4/30/2012

Rent

(Recommended)

$88.21

Term

Due

Price

Semester

Dec 12

$98.01

Quarter

Sep 3

$93.11

Short Term

Aug 13

$88.21

*This item is part of an exclusive publisher rental program and requires an additional convenience fee. This fee will be reflected in the shopping bag.
Buy New

Currently Available, Usually Ships in 24-48 Hours

$125.48

There is a growing demand from institutional bodies for the justification of industrial methodologies and practices (e.g., safety criteria, environmental protection and control, maintenance, and design optimization). Previous books in this area have either been too theoretical, or too specific in their scope. This book aims to provide a practical reference on uncertainty treatment for all types of industry, enabling the adoption of universal practices. The text is built upon a wide range of examples taken from within relevant industries, including nuclear technology, aeronautics, civil structures, and mechanical engineering.

Preface	p. xv
Acknowledgements	p. xvii
Introduction and reading guide	p. xix
Notation	p. xxxiii
Acronyms and abbreviations	p. xxxvii
Applications and practices of modelling, risk and uncertainty	p. 1
Protection against natural risk	p. 1
The popular 'initiator/frequency approach'	p. 3
Recent developments towards an 'extended frequency approach'	p. 5
Engineering design, safety and structural reliability analysis (SRA)	p. 7
The domain of structural reliability	p. 8
Deterministic safety margins and partial safety factors	p. 9
Probabilistic structural reliability analysis	p. 10
Links and differences with natural risk studies	p. 11
Industrial safety, system reliability and probabilistic risk assessment (PRA)	p. 12
The context of systems analysis	p. 12
Links and differences with structural reliability analysis	p. 14
The case of elaborate PRA (multi-state, dynamic)	p. 16
Integrated probabilistic risk assessment (IPRA)	p. 17
Modelling under uncertainty in metrology, environmental/sanitary assessment and numerical analysis	p. 20
Uncertainty and sensitivity analysis (UASA)	p. 21
Specificities in metrology/industrial quality control	p. 23
Specificities in environmental/health impact assessment	p. 24
Numerical code qualification (NCQ), calibration and data assimilation	p. 25
Forecast and time-based modelling in weather, operations research, economics or finance	p. 27
Conclusion: The scope for generic modelling under risk and uncertainty	p. 28
Similar and dissimilar features in modelling, risk and uncertainty studies	p. 28
Limitations and challenges motivating a unified framework	p. 30
References	p. 31
A generic modelling framework	p. 34
The system under uncertainty	p. 34
Decisional quantities and goals of modelling under risk and uncertainty	p. 37
The key concept of risk measure or quantity of interest	p. 37
Salient goals of risk/uncertainty studies and decision-making	p. 38
Modelling under uncertainty: Building separate system and uncertainty models	p. 41
The need to go beyond direct statistics	p. 41
Basic system models	p. 42
Building a direct uncertainty model on variable inputs	p. 45
Developing the underlying epistemic/aleatory structure	p. 46
Summary	p. 49
Modelling under uncertainty - the general case	p. 50
Phenomenological models under uncertainty and residual model error	p. 50
The model building process	p. 51
Combining system and uncertainty models into an integrated statistical estimation problem	p. 55
The combination of system and uncertainty models: A key information choice	p. 57
The predictive model combining system and uncertainty components	p. 59
Combining probabilistic and deterministic settings	p. 60
Preliminary comments about the interpretations of probabilistic uncertainty models	p. 60
Mixed deterministic-probabilistic contexts	p. 61
Computing an appropriate risk measure or quantity of interest and associated sensitivity indices	p. 64
Standard risk measures or q.i. (single-probabilistic)	p. 65
A fundamental case: The conditional expected utility	p. 67
Relationship between risk measures, uncertainty model and actions	p. 68
Double probabilistic risk measures	p. 69
The delicate issue of propagation/numerical uncertainty'	p. 71
Importance ranking and sensitivity analysis	p. 71
Summary: Main steps of the studies and later issues	p. 73
Exercises	p. 74
References	p. 75
A generic tutorial example: Natural risk in an industrial installation	p. 77
Phenomenology and motivation of the example	p. 77
The hydro component	p. 78
The system's reliability component	p. 80
The economic component	p. 83
Uncertain inputs, data and expertise available	p. 84
A short introduction to gradual illustrative modelling steps	p. 86
Step one: Natural risk standard statistics	p. 87
Step two: Mixing statistics and a QRA model	p. 89
Step three: Uncertainty treatment of a physical/engineering model (SRA)	p. 91
Step four: Mixing SRA and QRA	p. 91
Step five: Level-2 uncertainty study on mixed SRA-QRA model	p. 94
Step six: Calibration of the hydro component and updating of risk measure	p. 96
Step seven: Economic assessment and optimisation under risk and/or uncertainty	p. 97
Summary of the example	p. 99
Exercises	p. 101
References	p. 101
Understanding natures of uncertainty, risk margins and time bases for probabilistic decision-making	p. 102
Natures of uncertainty: Theoretical debates and practical implementation	p. 103
Defining uncertainty - ambiguity about the reference	p. 103
Risk vs. uncertainty - an impractical distinction	p. 104
The aleatory/epistemic distinction and the issue of reducibility	p. 105
Variability or uncertainty - the need for careful system specification	p. 107
Other distinctions	p. 109
Understanding the impact on margins of deterministic vs. probabilistic formulations	p. 110
Understanding probabilistic averaging, dependence issues and deterministic maximisation and in the linear case	p. 110
Understanding safety factors and quantiles in the monotonous case	p. 114
Probability limitations, paradoxes of the maximal entropy principle	p. 117
Deterministic settings and interval computation û uses and limitations	p. 119
Conclusive comments on the use of probabilistic and deterministic risk measures	p. 120
Handling time-cumulated risk measures through frequencies and probabilities	p. 121
The underlying time basis of the state of the system	p. 121
Understanding frequency vs. probability	p. 124
Fundamental risk measures defined over a period of interest	p. 126
Handling a time process and associated simplifications	p. 128
Modelling rare events through extreme value theory	p. 130
Choosing an adequate risk measure - decision-theory aspects	p. 135
The salient goal involved	p. 135
Theoretical debate and interpretations about the risk measure when selecting between risky alternatives (or controlling compliance with a risk target)	p. 136
The choice of financial risk measures	p. 137
The challenges associated with using double-probabilistic or conditional probabilistic risk measures	p. 138
Summary recommendations	p. 140
Exercises	p. 140
References	p. 141
Direct statistical estimation techniques	p. 143
The general issue	p. 143
Introducing estimation techniques on independent samples	p. 147
Estimation basics	p. 147
Goodness-of-fit and model selection techniques	p. 150
A non-parametric method: Kernel modelling	p. 154
Estimating physical variables in the flood example	p. 157
Discrete events and time-based statistical models (frequencies, reliability models, time series)	p. 159
Encoding phenomenological knowledge and physical constraints inside the choice of input distributions	p. 163
Modelling dependence	p. 165
Linear correlations	p. 165
Rank correlations	p. 168
Copula model	p. 172
Multi-dimensional non-parametric modelling	p. 173
Physical dependence modelling and concluding comments	p. 174
Controlling epistemic uncertainty through classical or Bayesian estimators	p. 175
Epistemic uncertainty in the classical approach	p. 175
Classical approach for Gaussian uncertainty models (small samples)	p. 177
Asymptotic covariance for large samples	p. 179
Bootstrap and resampling techniques	p. 185
Bayesian-physical settings (small samples with expert judgement)	p. 186
Understanding rare probabilities and extreme value statistical modelling	p. 194
The issue of extrapolating beyond data û advantages and limitations of the extreme value theory	p. 194
The significance of extremely low probabilities	p. 201
Exercises	p. 203
References	p. 204
Combined model estimation through inverse techniques	p. 206
Introducing inverse techniques	p. 206
Handling calibration data	p. 206
Motivations for inverse modelling and associated literature	p. 208
Key distinctions between the algorithms: The representation of time and uncertainty	p. 210
One-dimensional introduction of the gradual inverse algorithms	p. 216
Direct least square calibration with two alternative interpretations	p. 216
Bayesian updating, identification and calibration	p. 223
An alternative identification model with intrinsic uncertainty	p. 225
Comparison of the algorithms	p. 227
Illustrations in the flood example	p. 229
The general structure of inverse algorithms: Residuals, identifiability, estimators, sensitivity and epistemic uncertainty	p. 233
The general estimation problem	p. 233
Relationship between observational data and predictive outputs for decision-making	p. 233
Common features to the distributions and estimation problems associated to the general structure	p. 236
Handling residuals and the issue of model uncertainty	p. 238
Additional comments on the model-building process	p. 242
Identifiability	p. 243
Importance factors and estimation accuracy	p. 249
Specificities for parameter identification, calibration or data assimilation algorithms	p. 251
The BLUE algorithm for linear Gaussian parameter identification	p. 251
An extension with unknown variance: Multidimensional model calibration	p. 254
Generalisations to non-linear calibration	p. 255
Bayesian multidimensional model updating	p. 256
Dynamic data assimilation	p. 257
Intrinsic variability identification	p. 260
A general formulation	p. 260
Linearised Gaussian case	p. 261
Non-linear Gaussian extensions	p. 263
Moment methods	p. 264
Recent algorithms and research fields	p. 264
Conclusion: The modelling process and open statistical and computing challenges	p. 267
Exercises	p. 267
References	p. 268
Computational methods for risk and uncertainty propagation	p. 271
Classifying the risk measure computational issues	p. 272
Risk measures in relation to conditional and combined uncertainty distributions	p. 273
Expectation-based single probabilistic risk measures	p. 275
Simplified integration of sub-parts with discrete inputs	p. 277
Non-expectation based single probabilistic risk measures	p. 280
Other risk measures (double probabilistic, mixed deterministic-probabilistic)	p. 281
The generic Monte-Carlo simulation method and associated error control	p. 283
Undertaking Monte-Carlo simulation on a computer	p. 283
Dual interpretation and probabilistic properties of Monte-Carlo simulation	p. 285
Control of propagation uncertainty: Asymptotic results	p. 290
Control of propagation uncertainty: Robust results for quantiles (Wilks formula)	p. 292
Sampling double-probabilistic risk measures	p. 298
Sampling mixed deterministic-probabilistic measures	p. 299
Classical alternatives to direct Monte-Carlo sampling	p. 299
Overview of the computation alternatives to MCS	p. 299
Taylor approximation (linear or polynomial system models)	p. 300
Numerical integration	p. 305
Accelerated sampling (or variance reduction)	p. 306
Reliability methods (FORM-SORM and derived methods)	p. 312
Polynomial chaos and stochastic developments	p. 316
Response surface or meta-models	p. 316
Monotony, regularity and robust risk measure computation	p. 317
Simple examples of monotonous behaviours	p. 317
Direct consequences of monotony for computing the risk measure	p. 319
Robust computation of exceedance probability in the monotonous case	p. 322
Use of other forms of system model regularity	p. 329
Sensitivity analysis and importance ranking	p. 330
Elementary indices and importance measures and then-equivalence in linear system models	p. 330
Sobol sensitivity indices	p. 336
Specificities of Boolean input/output events û importance measures in risk assessment	p. 339
Concluding remarks and further research	p. 341
Numerical challenges, distributed computing and use of direct or adjoint differentiation of codes	p. 342
Exercises	p. 342
References	p. 343
Optimising under uncertainty: Economics and computational challenges	p. 347
Getting the costs inside risk modelling - from engineering economics to financial modelling	p. 347
Moving to costs as output variables of interest û elementary engineering economics	p. 347
Costs of uncertainty and the value of information	p. 351
The expected utility approach for risk aversion	p. 353
Non-linear transformations	p. 355
Robust design and alternatives mixing cost expectation and variance inside the optimisation procedure	p. 356
The role of time - cash flows and associated risk measures	p. 358
Costs over a time period - the cash flow model	p. 358
The issue of discounting	p. 361
Valuing time flexibility of decision-making and stochastic optimisation	p. 362
Computational challenges associated to optimisation	p. 366
Static optimisation (utility-based)	p. 367
Stochastic dynamic programming	p. 368
Computation and robustness challenges	p. 368
The promise of high performance computing	p. 369
The computational load of risk and uncertainty modelling	p. 369
The potential of high-performance computing	p. 371
Exercises	p. 372
References	p. 372
Conclusion: Perspectives of modelling in the context of risk and uncertainty and further research	p. 374
Open scientific challenges	p. 374
Challenges involved by the dissemination of advanced modelling in the context of risk and uncertainty	p. 377
References	p. 377
Annexes	p. 378
Annex 1 - refresher on probabilities and statistical modelling of uncertainty	p. 378
Modelling through a random variable	p. 378
The impact of data and the estimation uncertainty	p. 380
Continuous probabilistic distributions	p. 382
Dependence and stationarity	p. 382
Non-statistical approach of probabilistic modelling	p. 384
Annex 2 - comments about the probabilistic foundations of the uncertainty models	p. 386
The overall space of system states and the output space	p. 386
Correspondence to the Kaplan/Garrick risk analysis triplets	p. 389
The model and model input space	p. 389
Estimating the uncertainty model through direct data	p. 391
Model calibration and estimation through indirect data and inversion techniques	p. 393
Annex 3 - introductory reflections on the sources of macroscopic uncertainty	p. 394
Annex 4 - details about the pedagogical example	p. 397
Data samples	p. 397
Reference probabilistic model for the hydro component	p. 399
Systems reliability component - expert information on elementary failure probabilities	p. 399
Economic component - cost functions and probabilistic model	p. 403
Detailed results on various steps	p. 404
Annex 5 - detailed mathematical demonstrations	p. 414
Basic results about vector random variables and matrices	p. 414
Differentiation results and solutions of quadratic likelihood maximisation	p. 415
Proof of the Wilks formula	p. 419
Complements on the definition and chaining of monotony	p. 420
Proofs on level-2 quantiles of monotonous system models	p. 422
Proofs on the estimator of adaptive Monte-Carlo under monotony (section 7.4.3)	p. 423
References	p. 426
Epilogue	p. 427
Index	p. 429
Table of Contents provided by Ingram. All Rights Reserved.

Please wait while the item is added to your bag...

FREE SHIPPING

Rent More, Save More! Use code: BBRENTAL

5% off 1 book, 7% off 2 books, 10% off 3+ books

Modelling Under Risk and Uncertainty An Introduction to Statistical, Phenomenological and Computational Methods

Summary

Author Biography

Table of Contents

Supplemental Materials

FREE SHIPPING

Rent More, Save More! Use code: BBRENTAL

5% off 1 book, 7% off 2 books, 10% off 3+ books

Modelling Under Risk and Uncertainty An Introduction to Statistical, Phenomenological and Computational Methods

Summary

Author Biography

Table of Contents

Supplemental Materials

Digital License