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Several points of disagreement exist between different modelling traditions as to whether complex models are always better than simpler models, as to how to combine results from different models and how to propagate model uncertainty into forecasts. This book represents the result of collaboration between scientists from many disciplines to show how these conflicts can be resolved.
Key Features:
This book provides a much-needed reference guide to approaching statistical modelling. Scientists involved with modelling complex systems in areas such as climate change, flood prediction and prevention, financial market modelling and systems engineering will benefit from this book. It will also be a useful source of modelling case histories.
“In short, this book offers plenty. While reading it cannot entirely replace first-hand experience of actually working with statistical modelling, I think it can be highly useful, either for a course on Ph.D. level, or for a statistician setting out on her own to improve her competence in applying statistical techniques and modelling in non-trivial situations.
(International Statistical Review, 1 December 2012)
Acknowledgements xi
Contributing authors xiii
1 Introduction 1
Mike Christie, Andrew Cliffe, Philip Dawid and Stephen Senn
1.1 The origins of the SCAM project 1
1.2 The scope of modelling in the modern world 2
1.3 The different professions and traditions engaged in modelling 3
1.4 Different types of models 3
1.5 Different purposes for modelling 5
1.6 The purpose of the book 6
1.7 Overview of the chapters 6
References 8
2 Statistical model selection 11
Philip Dawid and Stephen Senn
2.1 Introduction 11
2.2 Explanation or prediction? 12
2.3 Levels of uncertainty 12
2.4 Bias–variance trade-off 13
2.5 Statistical models 15
2.5.1 Within-model inference 16
2.6 Model comparison 18
2.7 Bayesian model comparison 18
2.7.1 Model uncertainty 19
2.7.2 Laplace approximation 20
2.8 Penalized likelihood 20
2.8.1 Bayesian information criterion 21
2.9 The Akaike information criterion 21
2.9.1 Inconsistency of AIC 23
2.10 Significance testing 23
2.11 Many variables 27
2.12 Data-driven approaches 28
2.12.1 Cross-validation 29
2.12.2 Prequential analysis 29
2.13 Model selection or model averaging? 30
References 31
3 Modelling in drug development 35
Stephen Senn
3.1 Introduction 35
3.2 The nature of drug development and scope for statistical modelling 36
3.3 Simplicity versus complexity in phase III trials 36
3.3.1 The nature of phase III trials 36
3.3.2 The case for simplicity in analysing phase III trials 37
3.3.3 The case for complexity in modelling clinical trials 38
3.4 Some technical issues 39
3.4.1 The effect of covariate adjustment in linear models 40
3.4.2 The effect of covariate adjustment in non-linear models 42
3.4.3 Random effects in multi-centre trials 44
3.4.4 Subgroups and interactions 45
3.4.5 Bayesian approaches 46
3.5 Conclusion 46
3.6 Appendix: The effect of covariate adjustment on the variance multiplier in least squares 47
References 48
4 Modelling with deterministic computer models 51
Jeremy E. Oakley
4.1 Introduction 51
4.2 Metamodels and emulators for computationally expensive simulators 52
4.2.1 Gaussian processes emulators 53
4.2.2 Multivariate outputs 56
4.3 Uncertainty analysis 57
4.4 Sensitivity analysis 58
4.4.1 Variance-based sensitivity analysis 58
4.4.2 Value of information 61
4.5 Calibration and discrepancy 63
4.6 Discussion 64
References 65
5 Modelling future climates 69
Peter Challenor and Robin Tokmakian
5.1 Introduction 69
5.2 What is the risk from climate change? 70
5.3 Climate models 70
5.4 An anatomy of uncertainty 72
5.4.1 Aleatoric uncertainty 72
5.4.2 Epistemic uncertainty 73
5.5 Simplicity and complexity 75
5.6 An example: The collapse of the thermohaline circulation 77
5.7 Conclusions 79
References 79
6 Modelling climate change impacts for adaptation assessments 83
Suraje Dessai and Jeroen van der Sluijs
6.1 Introduction 83
6.1.1 Climate impact assessment 84
6.2 Modelling climate change impacts: From world development paths to localized impacts 87
6.2.1 Greenhouse gas emissions 87
6.2.2 Climate models 90
6.2.3 Downscaling 93
6.2.4 Regional/local climate change impacts 94
6.3 Discussion 95
6.3.1 Multiple routes of uncertainty assessment 96
6.3.2 What is the appropriate balance between simplicity and complexity? 96
References 98
7 Modelling in water distribution systems 103
Zoran Kapelan
7.1 Introduction 103
7.2 Water distribution system models 104
7.2.1 Water distribution systems 104
7.2.2 WDS hydraulic models 104
7.2.3 Uncertainty in WDS hydraulic modelling 107
7.3 Calibration of WDS hydraulic models 108
7.3.1 Calibration problem 108
7.3.2 Existing approaches 109
7.3.3 Case study 113
7.4 Sampling design for calibration 116
7.4.1 Sampling design problem 116
7.4.2 Existing approaches 116
7.4.3 Case study 120
7.5 Summary and conclusions 120
References 122
8 Modelling for flood risk management 125
Jim Hall
8.1 Introduction 125
8.2 Flood risk management 126
8.2.1 Long-term change 130
8.2.2 Uncertainty 131
8.3 Multi-purpose management 131
8.4 Modelling for flood risk management 132
8.4.1 Source 132
8.4.2 Pathway 132
8.4.3 Receptors 135
8.4.4 An example of a system model: Towyn 135
8.5 Model choice 137
8.6 Conclusions 143
References 144
9 Uncertainty quantification and oil reservoir modelling 147
Mike Christie
9.1 Introduction 147
9.2 Bayesian framework 148
9.2.1 Solution errors 149
9.3 Quantifying uncertainty in prediction of oil recovery 150
9.3.1 Stochastic sampling algorithms 151
9.3.2 Computing uncertainties from multiple history matched models 153
9.4 Inverse problems and reservoir model history matching 155
9.4.1 Synthetic problems 155
9.4.2 Imperial college fault model 157
9.4.3 Comparison of algorithms on a real field example 158
9.5 Selecting appropriate detail in models 162
9.5.1 Adaptive multiscale estimation 162
9.5.2 Bayes factors 165
9.5.3 Application of solution error modelling 167
9.6 Summary 170
References 171
10 Modelling in radioactive waste disposal 173
Andrew Cliffe
10.1 Introduction 173
10.2 The radioactive waste problem 174
10.2.1 What is radioactive waste? 174
10.2.2 How much radioactive waste is there? 175
10.2.3 What are the options for long-term management of radioactive waste? 175
10.3 The treatment of uncertainty in radioactive waste disposal 177
10.3.1 Deep geological disposal 177
10.3.2 Repository performance assessment 177
10.3.3 Modelling 179
10.3.4 Model verification and validation 180
10.3.5 Strategies for dealing with uncertainty 182
10.4 Summary and conclusions 184
References 184
11 Issues for modellers 187
Mike Christie, Andrew Cliffe, Philip Dawid and Stephen Senn
11.1 What are models and what are they useful for? 187
11.2 Appropriate levels of complexity 189
11.3 Uncertainty 190
11.3.1 Model inputs and parameter uncertainty 190
11.3.2 Model uncertainty 191
References 192
Glossary 193
Index 201
Overview
Several points of disagreement exist between different modelling traditions as to whether complex models are always better than simpler models, as to how to combine results from different models and how to propagate model uncertainty into forecasts. This book represents the result of collaboration between scientists from many disciplines to show how these conflicts can be resolved.
Key Features: