Peter Challenor (Exeter)

The Statistical Analysis of Complex Numerical Models in the Environmental Sciences

Complex, usually deterministic, numerical models are now widely used in environmental science. Predictions from such models are normally presented without any measure of uncertainty. In this talk I shall show how statistical methods can be used to not only estimate the uncertainty on model predictions but also to carry out sensitivity analysis and to calibrate the models. Our basic tool is the emulator. The emulator is a statistical approximation to the full numerical simulator; we use a Gaussian process. We build the emulator from an initial designed set of model runs. Because it is fast to run and we know its statistical properties, the emulator we can be used for inference, either analytically or using Monte Carlo methods. Drawing on examples in climate and oceanography I will illustrate the construction and use of statistical emulators from the design of experiments to the estimation of extreme values.