Multi-Resolution Kriging for Anisotropic Gaussian Spatial Process

• Activity Number: 687
• Type: Contributed
• Date/Time: Thursday, August 13, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Siddhartha Nandy* and Doug Nychka
• Companies: Michigan State University and National Center for Atmospheric Research
• Keywords: Lattice kriging ; Spatial autoregression ; Anisotropic covariace ; Homogeneity pursuit ; Group LASSO ; Block Coordinate Descent Algorithm

Abstract

We developed a multi-resolution model for kriging on two-dimensional irregularly spaced spatial fields that can account for anisotropy of the spatial process. Our model represents the field as a sum of basis functions multiplied by coefficients. The basis consists of level of multiple levels of radial basis with their centers (nodes ) organized on a regular grid and the kernel being a compacted supported function. The spatial dependence is modeled through dependence among the coefficients of the basis functions. Here the coefficients are assumed to follow a second order spatial autoregressive model and variation in the autoregressive parameters can control elliptical nature and tilt in the direction of an anisotropic covariance matrix. The flexibility over parameter values of neighborhood matrix gives us the freedom of modeling through an anisotropic covariance matrix. One of the most important features of this model is that it can be applied to statistical inference for large spatial datasets because key matrices in the computations are sparse. This computational efficiency is applicable to evaluation of both likelihood, spatial prediction, and spatial inference.