Non-stationary Gaussian models with physical barriers

The classical tools in spatial statistics are stationary models, like the Matern field. However, in some applications there are boundaries, holes, or physical barriers in the study area, e.g. a coastline, and stationary models will inappropriately smooth over these features, requiring the use of a non-stationary model. We propose a new model, the Barrier model, which is different from the established methods as it is not based on the shortest distance around the physical barrier, nor on boundary conditions. The Barrier model is based on viewing the Matern correlation, not as a correlation function on the shortest distance between two points, but as a collection of paths through a Simultaneous Autoregressive (SAR) model. We then manipulate these local dependencies to cut off paths that are crossing the physical barriers. To make the new SAR well behaved, we formulate it as a stochastic partial differential equation (SPDE) that can be discretised to represent the Gaussian field, with a sparse precision matrix that is automatically positive definite. The main advantage with the Barrier model is that the computational cost is the same as for the stationary model. The model is easy to use, and can deal with both sparse data and very complex barriers, as shown in an application in the Finnish Archipelago Sea. Additionally, the Barrier model is better at reconstructing the modified Horseshoe test function than the standard models used in R-INLA. (C) 2019 Elsevier B.V. All rights reserved.Peer reviewe

...you might like to give a talk about how priors are useful for modelling spatial data but we certainly would not hold you to that

Non UBCUnreviewedAuthor affiliation: King Abdullah University of Science and TechnologyFacult

Gaussian Markov random fields: theory and applications

Gaussian Markov Random Field (GMRF) models are most widely used in spatial statistics - a very active area of research in which few up-to-date reference works are available. This is the first book on the subject that provides a unified framework of GMRFs with particular emphasis on the computational aspects. This book includes extensive case-studies and, online, a c-library for fast and exact simulation. With chapters contributed by leading researchers in the field, this volume is essential reading for statisticians working in spatial theory and its applications, as well as quantitative researchers in a wide range of science fields where spatial data analysis is important