Simplicity, Complexity and Modelling

This book is based upon an EPSRC funded project aimed at sharing understanding of modelling complex phenomena. The aim of the book is to ease communication between modellers in different disciplines. The book is useful to physicists wishing to find out about statistical approaches to modelling and to statisticians wishing to learn about modelling in the physical sciences. It is also a useful source of modelling case histories. The book provides a much-needed reference guide for approaching statistical modeling and a useful source for modeling case histories.The book consists of four sections An introductory section covering important concepts in modeling and outlining different traditions as regards the relative utility of simple and complex modeling in statistics. Subject specific chapters illustrating modeling approaches in various disciplines A summary chapter explaining what issues have been resolved and which remain unresolved A glossary giving terms commonly used in different modeling traditions.This book covers a number of case studies of complex modeling, including climate change, flood risk, deterministic computer modeling and how well the model can predict reality, water distribution systems and looks at how this has evolved, new drug development models and its usage and the petroleum industry and uncertainty of accurate forecasts.General lessons for modelers are presented and the book is supported by downloadable datasets via website link.

Stephen Senn Professor of Statistics, Department of Statistics, University of Glasgow. Senior Professor and Editor of the Wiley Statistics in Practice Series. His research concerns statistics applied to drug development, a subject he has written many papers on.

Philip Dawid is a Professor in Statistics at Cambridge University. Researching fundamentally into the logical foundation of probability and statistics in terms of forecasting. He is currently an Editor of the journal Bayesian Analysis.

Mike Christie is Professor of Reservoir Engineering at Heriot-Way University. His research interests lie in accurate numerical modeling of fluid flow, in porous media primarily.

Andrew Cliffe Professor of Computational Applied Mathematics at the University of Nottingham. His research interests include fluid dynamics and nuclear waste disposal.

Preface	p. ix
Acknowledgements	p. xi
Contributing authors	p. xiii
Introduction	p. 1
The origins of the SCAM project	p. 1
The scope of modelling in the modern world	p. 2
The different professions and traditions engaged in modelling	p. 3
Different types of models	p. 3
Different purposes for modelling	p. 5
The purpose of the book	p. 6
Overview of the chapters	p. 6
References	p. 8
Statistical model selection	p. 11
Introduction	p. 11
Explanation or prediction?	p. 12
Levels of uncertainty	p. 12
Bias-variance trade-off	p. 13
Statistical models	p. 15
Within-model inference	p. 16
Model comparison	p. 18
Bayesian model comparison	p. 18
Model uncertainty	p. 19
Laplace approximation	p. 20
Penalized likelihood	p. 20
Bayesian information criterion	p. 21
The Akaike information criterion	p. 21
Inconsistency of AIC	p. 23
Significance testing	p. 23
Many variables	p. 27
Data-driven approaches	p. 28
Cross-validation	p. 29
Prequential analysis	p. 29
Model selection or model averaging?	p. 30
References	p. 31
Modelling in drug development	p. 35
Introduction	p. 35
The nature of drug development and scope for statistical modelling	p. 36
Simplicity versus complexity in phase III trials	p. 36
The nature of phase III trials	p. 36
The case for simplicity in analysing phase III trials	p. 37
The case for complexity in modelling clinical trials	p. 38
Some technical issues	p. 39
The effect of covariate adjustment in linear models	p. 40
The effect of covariate adjustment in non-linear models	p. 42
Random effects in multi-centre trials	p. 44
Subgroups and interactions	p. 45
Bayesian approaches	p. 46
Conclusion	p. 46
Appendix: The effect of covariate adjustment on the variance multiplier in least squares	p. 47
References	p. 48
Modelling with deterministic computer models	p. 51
Introduction	p. 51
Metamodels and emulators for computationally expensive simulators	p. 52
Gaussian processes emulators	p. 53
Multivariate outputs	p. 56
Uncertainty analysis	p. 57
Sensitivity analysis	p. 58
Variance-based sensitivity analysis	p. 58
Value of information	p. 61
Calibration and discrepancy	p. 63
Discussion	p. 64
References	p. 65
Modelling future climates	p. 69
Introduction	p. 69
What is the risk from climate change?	p. 70
Climate models	p. 70
An anatomy of uncertainty	p. 72
Aleatoric uncertainty	p. 72
Epistemic uncertainty	p. 73
Simplicity and complexity	p. 75
An example: The collapse of the thermohaline circulation	p. 77
Conclusions	p. 79
References	p. 79
Modelling climate change impacts for adaptation assessments	p. 83
Introduction	p. 83
Climate impact assessment	p. 84
Modelling climate change impacts: From world development paths to localized impacts	p. 87
Greenhouse gas emissions	p. 87
Climate models	p. 90
Downscaling	p. 93
Regional/local climate change impacts	p. 94
Discussion	p. 95
Multiple routes of uncertainty assessment	p. 96
What is the appropriate balance between simplicity and complexity?	p. 96
References	p. 98
Modelling in water distribution systems	p. 103
Introduction	p. 103
Water distribution system models	p. 104
Water distribution systems	p. 104
WDS hydraulic models	p. 104
Uncertainty in WDS hydraulic modelling	p. 107
Calibration of WDS hydraulic models	p. 108
Calibration problem	p. 108
Existing approaches	p. 109
Case study	p. 113
Sampling design for calibration	p. 116
Sampling design problem	p. 116
Existing approaches	p. 116
Case study	p. 120
Summary and conclusions	p. 120
References	p. 122
Modelling for flood risk management	p. 125
Introduction	p. 125
Flood risk management	p. 126
Long-term change	p. 130
Uncertainty	p. 131
Multi-purpose management	p. 131
Modelling for flood risk management	p. 132
Source	p. 132
Pathway	p. 132
Receptors	p. 135
An example of a system model: Towyn	p. 135
Model choice	p. 137
Conclusions	p. 143
References	p. 144
Uncertainty quantification and oil reservoir modelling	p. 147
Introduction	p. 147
Bayesian framework	p. 148
Solution errors	p. 149
Quantifying uncertainty in prediction of oil recovery	p. 150
Stochastic sampling algorithms	p. 151
Computing uncertainties from multiple history matched models	p. 153
Inverse problems and reservoir model history matching	p. 155
Synthetic problems	p. 155
Imperial college fault model	p. 157
Comparison of algorithms on a real field example	p. 158
Selecting appropriate detail in models	p. 162
Adaptive multiscale estimation	p. 162
Bayes factors	p. 165
Application of solution error modelling	p. 167
Summary	p. 170
References	p. 171
Modelling in radioactive waste disposal	p. 173
Introduction	p. 173
The radioactive waste problem	p. 174
What is radioactive waste?	p. 174
How much radioactive waste is there?	p. 175
What are the options for long-term management of radioactive waste?	p. 175
The treatment of uncertainty in radioactive waste disposal	p. 177
Deep geological disposal	p. 177
Repository performance assessment	p. 177
Modelling	p. 179
Model verification and validation	p. 180
Strategies for dealing with uncertainty	p. 182
Summary and conclusions	p. 184
References	p. 184
Issues for modellers	p. 187
What are models and what are they useful for?	p. 187
Appropriate levels of complexity	p. 189
Uncertainty	p. 190
Model inputs and parameter uncertainty	p. 190
Model uncertainty	p. 191
References	p. 192
Glossary	p. 193
Index	p. 201
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Simplicity, Complexity and Modelling

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