Title
Covariance Tapering for Interpolation of Large Spatial Datasets
Speaker
Reinhard Furrer, Geophysical Statistics Project, National Center for Atmospheric Research
Abstract
Interpolation of a spatially correlated random process is used in many areas. The best unbiased linear predictor, often called kriging in geostatistical science, requires the solution of a large linear system based on the covariance matrix of the observations. As a motivating example for climate science, estimating monthly precipitation fields over the US involves more than 5900 station location at its peak network size and must be repeated over the more than 1200 months of the historical record. Each estimated field should be evaluated on a fine grid of resolution of approximately $1000\times1000$. Tapering the correct covariance matrix with an appropriate compactly supported covariance function reduces the computational burden significantly and still has an asymptotic optimal mean squared error. The effect of tapering is to create a sparse approximate linear system that can then be solved using sparse matrix algorithms. In the precipitation dataset one achieves a speedup by more than 500 to solve the linear system. Further, the manageable size of the observed and predicted fields can be far bigger than with classical approaches. The net result is the ability to analyze spatial data sets that are several orders of magnitude larger than past work in a high level interactive environment such as R.
Meet the speaker in Room 212 Cockins Hall at 4:30 p.m. Refreshments will be served.
