EFFICIENT EMULATORS OF COMPUTER EXPERIMENTS USING COMPACTLY SUPPORTED CORRELATION FUNCTIONS, WITH AN APPLICATION TO COSMOLOGY

• 成果类型: Article
• 署名作者: Kaufman, Cari G.; Bingham, Derek; Habib, Salman; Heitmann, Katrin; Frieman, Joshua A.
• 署名单位: University of California System; University of California Berkeley; Simon Fraser University; United States Department of Energy (DOE); Argonne National Laboratory; United States Department of Energy (DOE); Los Alamos National Laboratory; United States Department of Energy (DOE); University of Chicago; Fermi National Accelerator Laboratory
• 刊物名称: ANNALS OF APPLIED STATISTICS
• ISSN/ISSBN: 1932-6157
• DOI: 10.1214/11-AOAS489
• 发表日期: 2011
• 页码: 2470-2492
• 关键词: models

摘要

Statistical emulators of computer simulators have proven to be useful in a variety of applications. The widely adopted model for emulator building, using a Gaussian process model with strictly positive correlation function, is computationally intractable when the number of simulator evaluations is large. We propose a new model that uses a combination of low-order regression 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.