Lightweight Emulators for Multivariate Deterministic Functions

An emulator is a statistical model of a deterministic function, to be used where the function itself is too expensive to evaluate within-the-loop of an inferential calculation. Typically, emulators are deployed when dealing with complex functions that have large and heterogeneous input and output spaces: environmental models, for example. In this challenging situation we should be sceptical about our statistical models, no matter how sophisticated, and adopt approaches that prioritise interpretative and diagnostic information, and the flexibility to respond. This paper presents one such approach, candidly rejecting the standard Smooth Gaussian Process approach in favour of a fully-Bayesian treatment of multivariate regression which, by permitting sequential updating, allows for very detailed predictive diagnostics. It is argued directly and by illustration that the incoherence of such a treatment (which does not impose continuity on the model outputs) is more than compensated for by the wealth of available information, and the possibilities for generalisation. Draft copy: not to be circulated or cited without the author’s prior approval. ∗Department of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, U.K.; e-mail [email protected]. 1