B0209
Title: Fast methods for conditional simulation, the key to spatial inference
Authors: Douglas Nychka - Colorado School of Mines (United States) [presenting]
Abstract: An advantage of a Gaussian process (GP) model for surface fitting is the companion estimates of the functions uncertainty. The standard method for assessing 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. This algorithm, however, has two bottlenecks: generating spatial predictions on large, but regular grids and also simulation of a Gaussian process on both a large regular grid and at irregular locations. Accurate approximations are proposed that allow for for fast computation of both these steps. 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 from 10 to a 100 or more is obtained and makes it possible to determine uncertainty of GP estimates on a laptop and in often an interactive setting. Besides the practical benefits of this speedup their accuracy are examples of the screening effect for spatial prediction and are related to the errors bounds in interpolation when the GP is related to an element in a reproducing kernel Hilbert space.
