UCSC-SOE-19-11: Specification of Basis Spacing for Process Convolution Gaussian Process Models

Waley W. J. Liang and Herbert K. H. Lee
11/27/2019 10:46 PM
Gaussian process (GP) models have been widely used for statistical modeling of point-referenced data in many scientific applications, including regression, classification, and clustering problems. Standard specification of GP models is computationally inefficient for applications with a large sample size. One solution is to construct the GP by convolving a smoothing kernel with a discretized white noise process, which requires choosing the number of bases. The distance between adjacent bases plays a key role in model accuracy. In this paper, we perform a series of simulations to find a general rule for the basis spacing required for accurate representation of a discrete process convolution GP model. Under certain common conditions, we find that using a basis spacing of one-quarter the practical range of the process works well in practice.