B1990
Title: Quantifying uncertainty for spatial predictions: Fast algorithms for large data sets
Authors: Douglas Nychka - Colorado School of Mines (United States) [presenting]
Abstract: A benefit of a Gaussian process (GP) model for surface fitting is the companion estimates of the functions' uncertainty. The standard method for assessing the uncertainty of a GP estimate is through conditional simulation, a Monte Carlo sampling algorithm of the multivariate Gaussian distribution. Conditional simulation is a powerful tool, for example allowing for Monte Carlo based uncertainty on surface contours (level sets), a difficult and nonlinear inference problem. Thus, it serves as the basic strategy for nearly all applications to spatial and spatial-temporal inference. This algorithm, however, is limited for large data sets. Accurate approximations are proposed that allow for fast computation. The computational efficiency is achieved by relying on the fast Fourier transform for 2D convolution and also sparse matrix multiplication. Under common spatial applications, a speedup by a factor of 10 to 100 or more is obtained and makes it possible to determine the uncertainty of GP estimates on a laptop and often in an interactive session. Besides the practical benefits of this speedup, the two approximations are examples of interesting features of GP analysis. Namely exploiting the screening effect for spatial prediction and the error bounds in interpolation when the GP is related to an element in a reproducing kernel Hilbert space.
