B0329
Title: Non-separable diffusion-based spatio-temporal Gaussian fields
Authors: Finn Lindgren - University of Edinburgh (United Kingdom) [presenting]
David Bolin - King Abdullah University of Science and Technology (KAUST) (Saudi Arabia)
Elias Krainski - KAUST (Brazil)
Haavard Rue - KAUST (Saudi Arabia)
Haakon Bakka - King Abdullah University of Science and Technology (Saudi Arabia)
Abstract: Gaussian random fields with Matern covariance functions are popular models in spatial statistics and machine learning. The easiest approach to constructing space-time models is by taking the product between a spatial covariance kernel and a temporal covariance kernel. However, these space-time separable models have both theoretical and practical drawbacks. An alternative is to take advantage of temporal extensions of the spatial Whittle-Matern model to define non-separable models as solutions to stochastic partial differential equations. Such models can keep the marginal Matern covariance in space, but besides the parameters of the spatial covariance (variance, smoothness, and practical correlation range), they include parameters controlling the practical correlation range in time, the smoothness in time, and the degree of non-separability of the spatio-temporal covariance. A sparse representation based on a finite element approximation can be constructed in closed form for the Markovian subset of models, which is well suited for statistical inference on flat domains, spheres, as well as other manifolds. This has been implemented in the R-INLA software. The full range of models can be handled either through spectral representations or by using new methods for fractional operators. The flexibility of the model is illustrated in an application to spatio-temporal modelling of global temperature data.
