Multi-Resolution Gaussian Process Models: Parameter Choices

• Activity Number: 569
• Type: Invited
• Date/Time: Wednesday, August 7, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Computing
• Author(s): Dorit Hammerling*+ and Douglas Nychka
• Companies: Statistical and Applied Mathematics Sciences Institute and National Center for Atmospheric Research
• Keywords: Spatial statistics ; nonstationarity ; large data

Abstract

The development of multi-resolution Gaussian process models has been driven by increasingly large spatial data sets with nonstationary covariance structures. The model discussed here combines the representation of a field using a multi-resolution basis with statistical models for processes on a lattice. The main principle is to expand the two dimensional spatial field in a sequence of basis functions that are organized on regular grids of increasing resolution. The basis functions are assumed to be fixed; however, the coefficients have a stochastic structure, which is modeled using a Markov random field. This results in a computationally efficient model applicable to very large data sets. Key model parameters include the grid spacing of the basis functions at the highest level, which also defines the spacing at lower levels, and the number of levels. These choices influence the computational properties and the ability to successfully model a given random field. We show results for different parameter settings and present guidelines how to choose the grid spacing and number of levels as a function of the characteristics of the field, such as smoothness and spatial range.