Department Seminar Series: Joe Guiness, Fast Matrix-Free Methods for Massive Multivariate Spatial Lattice Data
Abstract: The Whittle likelihood is a computationally efficient and matrix-free Gaussian likelihood approximation that has enjoyed great success in fitting parametric models to evenly-spaced time series data. There are multidimensional versions of the Whittle likelihood that can be used to fit stationary Gaussian models to rectangular spatial lattice data, but applied in its most naive form, the Whittle likelihood produces biased parameter estimates when the spatial dimension is greater than one. To alleviate these issues, data tapers can be employed and have been shown to have the ability to produce asymptotically efficient parameter estimates in two and three dimensions. However, for highly correlated data, significant amounts of tapering are usually required, which leads to noticeable losses in efficiency in finite samples, especially in three or more dimensions. We outline a new computationally efficient estimation framework that employs an augmentation of the spatial lattice data and MCMC estimation to overcome the deficiencies in data tapering with the Whittle likelihood. The new framework naturally handles multivariate data and missing observations as well and thus can be applied to lattice data with irregular boundaries. We demonstrate the effectiveness of the new methods in various simulation studies and apply them to multivariate soil composition data.