Jonathan Rougier

Bayesian Forecasting for Complex Systems Using Computer Simulators

Although computer models are often used for forecasting future outcomes of complex systems, the uncertainties in such forecasts are not usually treated formally. We describe a general Bayesian approach for using a computer model or simulator of a complex system to forecast system outcomes. The approach is based on constructing beliefs derived from a combination of expert judgments and experiments on the computer model. These beliefs, which are systematically updated as we make runs of the computer model, are used for either Bayesian or Bayes linear forecasting for the system. Issues of design and diagnostics are described in the context of forecasting. The methodology is applied to forecasting for an active hydrocarbon reservoir.

Sensitivity analysis of environmental models

Sensitivity Analysis (SA) investigates how the variation in the output of a numerical model can be attributed to variations of its input factors. SA is increasingly being used in environmental modelling for a variety of purposes, including uncertainty assessment, model calibration and diagnostic evaluation, dominant control analysis and robust decision-making. In this paper we review the SA literature with the goal of providing: (i) a comprehensive view of SA approaches also in relation to other methodologies for model identification and application; (ii) a systematic classification of the most commonly used SA methods; (iii) practical guidelines for the application of SA. The paper aims at delivering an introduction to SA for non-specialist readers, as well as practical advice with best practice examples from the literature; and at stimulating the discussion within the community of SA developers and users regarding the setting of good practices and on defining priorities for future research. We present an overview of SA and its link to uncertainty analysis, model calibration and evaluation, robust decision-making.We provide a systematic review of existing approaches, which can support users in the choice of an SA method.We provide practical guidelines by developing a workflow for the application of SA and discuss critical choices.We give best practice examples from the literature and highlight trends and gaps for future research.

Analyzing the climate sensitivity of the HadSM3 climate model using ensembles from different but related experiments

Global climate models (GCMs) contain imprecisely defined parameters that account, approximately, for subgrid-scale physical processes. The response of a GCM to perturbations in its parameters, which is crucial for quantifying uncertainties in simulations of climate change, can—in principle—be assessed by simulating the GCM many times. In practice, however, such “perturbed physics” ensembles are small because GCMs are so expensive to simulate. Statistical tools can help in two ways. First, they can be used to combine ensembles from different but related experiments, increasing the effective number of simulations. Second, they can be used to describe the GCM’s response in ways that cannot be extracted directly from the ensemble(s). The authors combine two experiments to learn about the response of the Hadley Centre Slab Climate Model version 3 (HadSM3) climate sensitivity to 31 model parameters. A Bayesian statistical framework is used in which expert judgments are required to quantify the relationship between the two experiments; these judgments are validated by detailed diagnostics. The authors identify the entrainment rate coefficient of the convection scheme as the most important single parameter and find that this interacts strongly with three of the large-scale-cloud parameters.

Efficient Emulators for Multivariate Deterministic Functions

One of the challenges with emulating the response of a multivariate function to its inputs is the quantity of data that must be assimilated, which is the product of the number of model evaluations and the number of outputs. This article shows how even large calculations can be made tractable. It is already appreciated that gains can be made when the emulator residual covariance function is treated as separable in the model-inputs and model-outputs. Here, an additional simplification on the structure of the regressors in the emulator mean function allows very substantial further gains. The result is that it is now possible to emulate rapidly—on a desktop computer—models with hundreds of evaluations and hundreds of outputs. This is demonstrated through calculating costs in floating-point operations, and in an illustration. Even larger sets of outputs are possible if they have additional structure, for example, spatial-temporal.

Probabilistic Formulations for Transferring Inferences from Mathematical Models to Physical Systems

We outline a probabilistic framework for linking mathematical models to the physical systems that they represent, taking account of all sources of uncertainty including model and simulator imperfections. This framework is a necessary precondition for making probabilistic statements about the system on the basis of evaluations of computer simulators. We distinguish simulators according to their quality and the nature of their inputs. Where necessary, we introduce further hypothetical simulators as modelling constructs to account for imperfections in the available simulators and to unify the available simulators with the underlying system.

Bayes Linear Calibrated Prediction for Complex Systems

A calibration-based approach is developed for predicting the behavior of a physical system that is modeled by a computer simulator. The approach is based on Bayes linear adjustment using both system observations and evaluations of the simulator at parameterizations that appear to give good matches to those observations. This approach can be applied to complex high-dimensional systems with expensive simulators, where a fully Bayesian approach would be impractical. It is illustrated with an example concerning the collapse of the thermohaline circulation (THC) in the Atlantic Ocean.

The retirement behaviour of the self-employed in Britain

We analyze the retirement behaviour of older self-employed workers, using a life cycle framework and a multinomial logit model of dynamic employment and retirement choices. Using data from the two-wave Retirement Survey, we find that greater actual or potential earnings decrease the probability of retirement among the self-employed. In contrast to employees, none of gender, health or family circumstances appear to affect self-employed retirement decisions. The dynamic analysis reveals that relatively few employees and virtually no retirees switch into self-employment in later life. The switches that do occur are motivated less by attempts to use self-employment as a bridge job or ‘stepping stone’ to full retirement, than by self-employment being a last resort for less affluent workers with job histories of weak attachment to the labour market. We compare self-employed and employee retirement behaviour and discuss the policy implications of our results.

Inference in ensemble experiments

We consider inference based on ensembles of climate model evaluations, and contrast the Monte Carlo approach, in which the evaluations are selected at random from the model-input space, with a more overtly statistical approach using emulators and experimental design.

Risk and Uncertainty Assessment for Natural Hazards

List of contributors Preface 1. Risk and uncertainty assessment in natural hazards L. J. Hill, R. S. J. Sparks and J. C. Rougier 2. Quantifying natural hazard risk J. C. Rougier 3. Model limitations: the sources and implications of epistemic uncertainty J. C. Rougier and K. J. Beven 4. Expert elicitation and judgment W. P. Aspinall and R. M. Cooke 5. Risk and uncertainty in hydrometeorological hazards T. L. Edwards and P. G. Challenor 6. Hydrometeorological hazards under future climate change T. L. Edwards and P. G. Challenor 7. Hydrological flood uncertainty and risk research J. Freer, K. J. Beven, J. Neal, G. Schumann, J. Hall and P. Bates 8. Uncertainties in probabilistic seismic hazard assessment W. P. Aspinall 9. Landslide and avalanche hazards T. K. Hincks, W. P. Aspinall, R. S. J. Sparks, E. A. Holcombe and M. Kern 10. Tsunami hazard and risk T. K. Hincks, R. S. J. Sparks and W. P. Aspinall 11. Risk and uncertainty assessment of volcanic hazards R. S. J. Sparks, W. P. Aspinall, H. S. Crosweller and T. K. Hincks 12. Risk assessment and management of wildfires T. K. Hincks, B. D. Malamud, R. S. J. Sparks, M. J. Wooster and T. J. Lynham 13. Technological facilities, infrastructure and hazardous materials, including some notes on space weather R. S. J. Sparks, W. P. Aspinall, N. A. Chapman, B. E. Hill, D. J. Kerridge, J. Pooley and C. A. Taylor 14. Statistical aspects of risk characterization in ecotoxicology G. L. Hickey and A. Hart 15. Social science perspectives on natural hazards risk and uncertainty S. Cornell and M. Jackson 16. Human responses to natural hazard risk: considerations for improving the effectiveness of risk management systems H. S. Crosweller and J. Wilmshurst Index.

Second-Order Exchangeability Analysis for Multimodel Ensembles

The challenge of understanding complex systems often gives rise to a multiplicity of models. It is natural to consider whether the outputs of these models can be combined to produce a system prediction that is more informative than the output of any one of the models taken in isolation. And, in particular, to consider the relationship between the spread of model outputs and system uncertainty. We describe a statistical framework for such a combination, based on the exchangeability of the models, and their coexchangeability with the system. We demonstrate the simplest implementation of our framework in the context of climate prediction. Throughout we work entirely in means and variances to avoid the necessity of specifying higher-order quantities for which we often lack well-founded judgments.