Statistics and Data Science Seminar: Inverses of Matern Covariances on Grids

Abstract: We begin with a review of the spectral approach for studying stationary covariance functions (a.k.a positive definite functions or kernels). We then apply this approach to conduct a theoretical analysis of the aliased spectral densities and inverse operators of Matern covariance functions on regular grids. Our results provide clarity on the properties of a popular approximation arising from a stochastic partial differential equation (SPDE) representation for the Matern; although there is a sense in which it approximates the covariances well, it does not provide increasingly accurate approximations to the inverse operator as the grid spacing goes to zero. These results are supported by numerical calculations and simulations which show that the SPDE approximation over-estimates spatial dependence.

This talk will be over Zoom at the following link: https://wustl.zoom.us/j/91475142799