Emulation of random output simulators

Computer models, or simulators, are widely used in a range of scientific fields to aid understanding of the processes involved and make predictions. Such simulators are often computationally demanding and are thus not amenable to statistical analysis. Emulators provide a statistical approximation, or surrogate, for the simulators accounting for the additional approximation uncertainty. This thesis develops a novel sequential screening method to reduce the set of simulator variables considered during emulation. This screening method is shown to require fewer simulator evaluations than existing approaches. Utilising the lower dimensional active variable set simplifies subsequent emulation analysis. For random output, or stochastic, simulators the output dispersion, and thus variance, is typically a function of the inputs. This work extends the emulator framework to account for such heteroscedasticity by constructing two new heteroscedastic Gaussian process representations and proposes an experimental design technique to optimally learn the model parameters. The design criterion is an extension of Fisher information to heteroscedastic variance models. Replicated observations are efficiently handled in both the design and model inference stages. Through a series of simulation experiments on both synthetic and real world simulators, the emulators inferred on optimal designs with replicated observations are shown to outperform equivalent models inferred on space-filling replicate-free designs in terms of both model parameter uncertainty and predictive variance.

An efficient screening method for computer experiments

Computer simulators of real-world processes are often computationally expensive and require many inputs. The problem of the computational expense can be handled using emulation technology; however, highly multidimensional input spaces may require more simulator runs to train and validate the emulator. We aim to reduce the dimensionality of the problem by screening the simulators inputs for nonlinear effects on the output rather than distinguishing between negligible and active effects. Our proposed method is built upon the elementary effects (EE) method for screening and uses a threshold value to separate the inputs with linear and nonlinear effects. The technique is simple to implement and acts in a sequential way to keep the number of simulator runs down to a minimum, while identifying the inputs that have nonlinear effects. The algorithm is applied on a set of simulated examples and a rabies disease simulator where we observe run savings ranging between 28% and 63% compared with the batch EE method. Supplementary materials for this article are available online.