Modelling under risk and uncertainty: an introduction to statistical, phenomenological and computational methods
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| Format: | Buch |
| Sprache: | English |
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Chichester
Wiley
2012
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| Schriftenreihe: | Wiley series in probability and statistics
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| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXXV, 434 S. graph. Darst. |
| ISBN: | 9780470695142 |
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Datensatz im Suchindex
| _version_ | 1804149256199602176 |
|---|---|
| adam_text | Titel: Modelling under risk and uncertainty
Autor: Rocquigny, Etienne de
Jahr: 2012
Contents
Preface xv
Acknowledgements xvii
Introduction and reading guide xix
Notation xxxiii
Acronyms and abbreviations xxxvii
1 Applications and practices of modelling, risk and uncertainty 1
1.1 Protection against natural risk 1
1.1.1 The popular initiator/frequency approach 3
1.1.2 Recent developments towards an extended frequency approach 5
1.2 Engineering design, safety and structural reliability analysis (SRA) 7
1.2.1 The domain of structural reliability 8
1.2.2 Deterministic safety margins and partial safety factors 9
1.2.3 Probabilistic structural reliability analysis 10
1.2.4 Links and differences with natural risk studies 11
1.3 Industrial safety, system reliability and probabilistic risk
assessment (PRA) 12
1.3.1 The context of systems analysis 12
1.3.2 Links and differences with structural reliability analysis 14
1.3.3 The case of elaborate PRA (multi-state, dynamic) 16
1.3.4 Integrated probabilistic risk assessment (IPRA) 17
1.4 Modelling under uncertainty in metrology, environmental/sanitary
assessment and numerical analysis 20
1.4.1 Uncertainty and sensitivity analysis (UASA) 21
1.4.2 Specificities in metrology/industrial quality control 23
1.4.3 Specificities in environmental/health impact assessment 24
1.4.4 Numerical code qualification (NCQ), calibration and data
assimilation 25
1.5 Forecast and time-based modelling in weather, operations research,
economics or finance 27
1.6 Conclusion: The scope for generic modelling under risk and uncertainty 28
1.6.1 Similar and dissimilar features in modelling, risk and
uncertainty studies 28
1.6.2 Limitations and challenges motivating a unified framework 30
References 31
viii CONTENTS
2 A generic modelling framework 34
2.1 The system under uncertainty 34
2.2 Decisional quantities and goals of modelling under risk and uncertainty 37
2.2.1 The key concept of risk measure or quantity of interest 37
2.2.2 Salient goals of risk/uncertainty studies and decision-making 38
2.3 Modelling under uncertainty: Building separate system
and uncertainty models 41
2.3.1 The need to go beyond direct statistics 41
2.3.2 Basic system models 42
2.3.3 Building a direct uncertainty model on variable inputs 45
2.3.4 Developing the underlying epistemic/aleatory structure 46
2.3.5 Summary 49
2.4 Modelling under uncertainty - the general case 50
2.4.1 Phenomenological models under uncertainty and residual
model error 50
2.4.2 The model building process 51
2.4.3 Combining system and uncertainty models into an integrated
statistical estimation problem 55
2.4.4 The combination of system and uncertainty models:
A key information choice 57
2.4.5 The predictive model combining system and uncertainty
components 59
2.5 Combining probabilistic and deterministic settings 60
2.5.1 Preliminary comments about the interpretations of probabilistic
uncertainty models 60
2.5.2 Mixed deterministic-probabilistic contexts 61
2.6 Computing an appropriate risk measure or quantity of interest and
associated sensitivity indices 64
2.6.1 Standard risk measures or q.i. (single-probabilistic) 65
2.6.2 A fundamental case: The conditional expected utility 67
2.6.3 Relationship between risk measures, uncertainty model and actions 68
2.6.4 Double probabilistic risk measures 69
2.6.5 The delicate issue of propagation/numerical uncertainty 71
2.6.6 Importance ranking and sensitivity analysis 71
2.7 Summary: Main steps of the studies and later issues 73
Exercises 74
References 75
3 A generic tutorial example: Natural risk in an industrial installation 77
3.1 Phenomenology and motivation of the example 77
3.1.1 The hydro component 78
3.1.2 The system s reliability component 80
3.1.3 The economic component 83
3.1.4 Uncertain inputs, data and expertise available 84
3.2 A short introduction to gradual illustrative modelling steps 86
3.2.1 Step one: Natural risk standard statistics 87
3.2.2 Step two: Mixing statistics and a QRA model 89
CONTENTS ix
3.2.3 Step three: Uncertainty treatment of a physical/engineering
model (SRA) 91
3.2.4 Step four: Mixing SRA and QRA 91
3.2.5 Step five: Level-2 uncertainty study on mixed SRA-QRA model 94
3.2.6 Step six: Calibration of the hydro component and updating
of risk measure 96
3.2.7 Step seven: Economic assessment and optimisation under risk
and/or uncertainty 97
3.3 Summary of the example 99
Exercises 101
References 101
Understanding natures of uncertainty, risk margins and time bases
for probabilistic decision-making 102
4.1 Natures of uncertainty: Theoretical debates and practical implementation 103
4.1.1 Defining uncertainty - ambiguity about the reference 103
4.1.2 Risk vs. uncertainty - an impractical distinction 104
4.1.3 The aleatory/epistemic distinction and the issue
of reducibility 105
4.1.4 Variability or uncertainty - the need for careful system
specification 107
4.1.5 Other distinctions 109
4.2 Understanding the impact on margins of deterministic vs. probabilistic
formulations 110
4.2.1 Understanding probabilistic averaging, dependence issues
and deterministic maximisation and in the linear case 110
4.2.2 Understanding safety factors and quantiles in the
monotonous case 114
4.2.3 Probability limitations, paradoxes of the maximal
entropy principle 117
4.2.4 Deterministic settings and interval computation - uses
and limitations 119
4.2.5 Conclusive comments on the use of probabilistic and
deterministic risk measures 120
4.3 Handling time-cumulated risk measures through frequencies
and probabilities 121
4.3.1 The underlying time basis of the state of the system 121
4.3.2 Understanding frequency vs. probability 124
4.3.3 Fundamental risk measures defined over a period of interest 126
4.3.4 Handling a time process and associated simplifications 128
4.3.5 Modelling rare events through extreme value theory 130
4.4 Choosing an adequate risk measure - decision-theory aspects 135
4.4.1 The salient goal involved 135
4.4.2 Theoretical debate and interpretations about the risk measure
when selecting between risky alternatives (or controlling
compliance with a risk target) 136
4.4.3 The choice of financial risk measures 137
x CONTENTS
4.4.4 The challenges associated with using double-probabilistic
or conditional probabilistic risk measures 138
4.4.5 Summary recommendations 140
Exercises 140
References 141
5 Direct statistical estimation techniques 143
5.1 The general issue 143
5.2 Introducing estimation techniques on independent samples 147
5.2.1 Estimation basics 147
5.2.2 Goodness-of-fit and model selection techniques 150
5.2.3 A non-parametric method: Kernel modelling 154
5.2.4 Estimating physical variables in the flood example 157
5.2.5 Discrete events and time-based statistical models
(frequencies, reliability models, time series) 159
5.2.6 Encoding phenomenological knowledge and physical
constraints inside the choice of input distributions 163
5.3 Modelling dependence 165
5.3.1 Linear correlations 165
5.3.2 Rank correlations 168
5.3.3 Copula model 172
5.3.4 Multi-dimensional non-parametric modelling 173
5.3.5 Physical dependence modelling and concluding comments 174
5.4 Controlling epistemic uncertainty through classical or Bayesian estimators 175
5.4.1 Epistemic uncertainty in the classical approach 175
5.4.2 Classical approach for Gaussian uncertainty models (small samples) 177
5.4.3 Asymptotic covariance for large samples 179
5.4.4 Bootstrap and resampling techniques 185
5.4.5 Bayesian-physical settings (small samples with expert judgement) 186
5.5 Understanding rare probabilities and extreme value statistical modelling 194
5.5.1 The issue of extrapolating beyond data - advantages
and limitations of the extreme value theory 194
5.5.2 The significance of extremely low probabilities 201
Exercises 203
References 204
6 Combined model estimation through inverse techniques 206
6.1 Introducing inverse techniques 206
6.1.1 Handling calibration data 206
6.1.2 Motivations for inverse modelling and associated literature 208
6.1.3 Key distinctions between the algorithms: The representation
of time and uncertainty 210
6.2 One-dimensional introduction of the gradual inverse algorithms 216
6.2.1 Direct least square calibration with two alternative interpretations 216
6.2.2 Bayesian updating, identification and calibration 223
6.2.3 An alternative identification model with intrinsic uncertainty 225
6.2.4 Comparison of the algorithms 227
6.2.5 Illustrations in the flood example 229
CONTENTS xi
6.3 The general structure of inverse algorithms: Residuals, identifiability,
estimators, sensitivity and epistemic uncertainty 233
6.3.1 The general estimation problem 233
6.3.2 Relationship between observational data and predictive outputs
for decision-making 233
6.3.3 Common features to the distributions and estimation problems
associated to the general structure 236
6.3.4 Handling residuals and the issue of model uncertainty 238
6.3.5 Additional comments on the model-building process 242
6.3.6 Identifiability 243
6.3.7 Importance factors and estimation accuracy 249
6.4 Specificities for parameter identification, calibration or data
assimilation algorithms 251
6.4.1 The BLUE algorithm for linear Gaussian parameter identification 251
6.4.2 An extension with unknown variance: Multidimensional
model calibration 254
6.4.3 Generalisations to non-linear calibration 255
6.4.4 Bayesian multidimensional model updating 256
6.4.5 Dynamic data assimilation 257
6.5 Intrinsic variability identification 260
6.5.1 A general formulation 260
6.5.2 Linearised Gaussian case 261
6.5.3 Non-linear Gaussian extensions 263
6.5.4 Moment methods 264
6.5.5 Recent algorithms and research fields 264
6.6 Conclusion: The modelling process and open statistical and
computing challenges 267
Exercises 267
References 268
Computational methods for risk and uncertainty propagation 271
7.1 Classifying the risk measure computational issues 272
7.1.1 Risk measures in relation to conditional and combined uncertainty
distributions 273
7.1.2 Expectation-based single probabilistic risk measures 275
7.1.3 Simplified integration of sub-parts with discrete inputs 277
7.1.4 Non-expectation based single probabilistic risk measures 280
7.1.5 Other risk measures (double probabilistic, mixed
deterministic-probabilistic) 281
7.2 The generic Monte-Carlo simulation method and associated error control 283
7.2.1 Undertaking Monte-Carlo simulation on a computer 283
7.2.2 Dual interpretation and probabilistic properties of Monte-Carlo
simulation 285
7.2.3 Control of propagation uncertainty: Asymptotic results 290
7.2.4 Control of propagation uncertainty: Robust results for quantiles
(Wilks formula) 292
7.2.5 Sampling double-probabilistic risk measures 298
7.2.6 Sampling mixed deterministic-probabilistic measures 299
xii CONTENTS
7.3 Classical alternatives to direct Monte-Carlo sampling 299
7.3.1 Overview of the computation alternatives to MCS 299
7.3.2 Taylor approximation (linear or polynomial system models) 300
7.3.3 Numerical integration 305
7.3.4 Accelerated sampling (or variance reduction) 306
7.3.5 Reliability methods (FORM-SORM and derived methods) 312
7.3.6 Polynomial chaos and stochastic developments 316
7.3.7 Response surface or meta-models 316
7.4 Monotony, regularity and robust risk measure computation 317
7.4.1 Simple examples of monotonous behaviours 317
7.4.2 Direct consequences of monotony for computing the
risk measure 319
7.4.3 Robust computation of exceedance probability in the
monotonous case 322
7.4.4 Use of other forms of system model regularity 329
7.5 Sensitivity analysis and importance ranking 330
7.5.1 Elementary indices and importance measures and their
equivalence in linear system models 330
7.5.2 Sobol sensitivity indices 336
7.5.3 Specificities of Boolean input/output events - importance
measures in risk assessment 339
7.5.4 Concluding remarks and further research 341
7.6 Numerical challenges, distributed computing and use of direct or
adjoint differentiation of codes 342
Exercises 342
References 343
8 Optimising under uncertainty: Economics and computational challenges 347
8.1 Getting the costs inside risk modelling - from engineering economics
to financial modelling 347
8.1.1 Moving to costs as output variables of interest - elementary
engineering economics 347
8.1.2 Costs of uncertainty and the value of information 351
8.1.3 The expected utility approach for risk aversion 353
8.1.4 Non-linear transformations 355
8.1.5 Robust design and alternatives mixing cost expectation
and variance inside the optimisation procedure 356
8.2 The role of time - cash flows and associated risk measures 358
8.2.1 Costs over a time period - the cash flow model 358
8.2.2 The issue of discounting 361
8.2.3 Valuing time flexibility of decision-making and
stochastic optimisation 362
8.3 Computational challenges associated to optimisation 366
8.3.1 Static optimisation (utility-based) 367
8.3.2 Stochastic dynamic programming 368
8.3.3 Computation and robustness challenges 368
8.4 The promise of high performance computing 369
8.4.1 The computational load of risk and uncertainty modelling 369
CONTENTS xiii
8.4.2 The potential of high-performance computing 371
Exercises 372
References 372
9 Conclusion: Perspectives of modelling in the context of risk and uncertainty
and further research 374
9.1 Open scientific challenges 374
9.2 Challenges involved by the dissemination of advanced modelling
in the context of risk and uncertainty 377
References 377
10 Annexes 378
10.1 Annex 1 - refresher on probabilities and statistical modelling
of uncertainty 378
10.1.1 Modelling through a random variable 378
10.1.2 The impact of data and the estimation uncertainty 380
10.1.3 Continuous probabilistic distributions 382
10.1.4 Dependence and stationarity 382
10.1.5 Non-statistical approach of probabilistic modelling 384
10.2 Annex 2 - comments about the probabilistic foundations
of the uncertainty models 386
10.2.1 The overall space of system states and the output space 386
10.2.2 Correspondence to the Kaplan/Garrick risk analysis triplets 389
10.2.3 The model and model input space 389
10.2.4 Estimating the uncertainty model through direct data 391
10.2.5 Model calibration and estimation through indirect data
and inversion techniques 393
10.3 Annex 3 - introductory reflections on the sources of macroscopic
uncertainty 394
10.4 Annex 4 - details about the pedagogical example 397
10.4.1 Data samples 397
10.4.2 Reference probabilistic model for the hydro component 399
10.4.3 Systems reliability component - expert information on
elementary failure probabilities 399
10.4.4 Economic component - cost functions and probabilistic model 403
10.4.5 Detailed results on various steps 404
10.5 Annex 5 - detailed mathematical demonstrations 414
10.5.1 Basic results about vector random variables and matrices 414
10.5.2 Differentiation results and solutions of quadratic likelihood maximisation 415
10.5.3 Proof of the Wilks formula 419
10.5.4 Complements on the definition and chaining of monotony 420
10.5.5 Proofs on level-2 quantiles of monotonous system models 422
10.5.6 Proofs on the estimator of adaptive Monte-Carlo under
monotony (section 7.4.3) 423
References 426
Epilogue 427
Index 429
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| spelling | Rocquigny, Etienne de Verfasser aut Modelling under risk and uncertainty an introduction to statistical, phenomenological and computational methods Etienne de Rocquigny Chichester Wiley 2012 XXXV, 434 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley series in probability and statistics HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025112664&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rocquigny, Etienne de Modelling under risk and uncertainty an introduction to statistical, phenomenological and computational methods |
| title | Modelling under risk and uncertainty an introduction to statistical, phenomenological and computational methods |
| title_auth | Modelling under risk and uncertainty an introduction to statistical, phenomenological and computational methods |
| title_exact_search | Modelling under risk and uncertainty an introduction to statistical, phenomenological and computational methods |
| title_full | Modelling under risk and uncertainty an introduction to statistical, phenomenological and computational methods Etienne de Rocquigny |
| title_fullStr | Modelling under risk and uncertainty an introduction to statistical, phenomenological and computational methods Etienne de Rocquigny |
| title_full_unstemmed | Modelling under risk and uncertainty an introduction to statistical, phenomenological and computational methods Etienne de Rocquigny |
| title_short | Modelling under risk and uncertainty |
| title_sort | modelling under risk and uncertainty an introduction to statistical phenomenological and computational methods |
| title_sub | an introduction to statistical, phenomenological and computational methods |
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