TITLE: Emulating Computer Simulators Using Compactly Supported Correlation Functions

SPEAKER: Derek Bingham

ABSTRACT:

Statistical emulators of computer simulators have proven to be useful in a variety of applications. However, a widely adopted model for building these emulators, using a Gaussian process distribution with strictly positive correlation function, can be computationally intractable when the number of evaluated input values is large. We propose a modification of this model that uses a combination of low-order regression terms and compactly supported correlation functions to recreate the desired predictive behavior of the simulator at a fraction of the computational cost. Following the usual approach of taking the correlation to be a product of correlations in each input dimension, we show how to impose restrictions on the range of each correlation, giving sparsity, while also allowing the ranges to trade off against one another in a data-adaptive way, thereby giving good predictive performance when the data are non-isotropic. We illustrate the method using data from a computer simulator of photometric red-shift.