EFFICIENT EMULATORS OF COMPUTER EXPERIMENTS USINGCOMPACTLY SUPPORTED CORRELATION FUNCTIONS, WITHAN APPLICATION TO COSMOLOGY

摘要

Statistical emulators of computer simulators have proven to be useful in a variety of applications. The widely adopted model for emulator build-ing, using a Gaussian process model with strictly positive correlation func-tion, is computationally intractable when the number of simulator evaluations is large. We propose a new model that uses a combination of low-order re-gression terms and compactly supported correlation functions to recreate the desired predictive behavior of the emulator 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 ranges of the correlations, giving sparsity, while also allowing the ranges to trade off against one another, thereby giving good predictive performance. We illustrate the method using data from a computer simulator of photometric redshift with 20,000 simulator evaluations and 80,000 predictions.