STATISTICS COLLOQUIUM
Julio E. Castrillon
Mathematics and Statistics Department
Boston University
Large Scale Kriging: A High Performance Multi-Level Computational Mathematics Approach
Julio E. Castrillon, Marc G. Genton, Rio Yokota
Abstract
Large scale kriging problems usually become numerically expensive and unstable to solve as the number of observations are increased. In this talk we introduce techniques from Computational Applied Mathematics (CAM), Partial Differential Equations (PDEs), and High Performance Computing (HPC) to efficiently estimate the covariance function parameters and compute the best unbiased predictor with high accuracy. Our approach is based on multi-level spaces that have been successful for solving PDEs. The first advantage is that the estimation problem is decoupled and the covariance parameters are efficiently and accurately solved. In addition, the covariance matrix of the multi-level spaces exhibit fast decay and is much better conditioned than the original covariance matrix. Furthermore, we show that the prediction problem can be remapped into a numerically stable form without any loss of accuracy. We demonstrate our approach on test problems of up to 512,000 observations with a Matern covariance function and flexible placements of the observations. Many of these test examples are numerically unstable and hard to solve.
DATE: Wednesday, November 6, 2019
TIME: 4:00 pm
PLACE: Philip E. Austin Bldg., Rm. 344
Coffee will be served at 3:30 pm in the Noether Lounge (AUST 326)
For more information, contact: Tracy Burke at tracy.burke@uconn.edu