Building practical, computationally efficient, non-stationary spatio-temporal models

The aim of this research project, is to construct good statistical models for spatial and spatio-temporal data. The models shall also be able to represent local variation. The challenge, is to construct these models so that their computational properties make them practical in use. We are making progress on all these topics, but we are not there yet.

The aim of this project is to provide practical, computationally efficient tools for modelling complicated, non-stationary, spatio-temporal phenomena. It is of particular importance that these tools are made available to practitioners?there is little poin t developing statistical methods that cannot be easily used by the wider community. We will develop these tools by merging two main ideas: Idea 1 The representation of Gaussian fields on manifolds as Gaussian Markov random fields, as described in the rec ent ?read paper? by Lindgren et al. (2011). A key feature of this representation is that it is easy to extend to non-stationary spatio-temporal fields, which are difficult to construct using standard methods. Idea 2 The approximate Bayesian inference sch eme called Integrated Nested Laplace Approximation, introduced in the ?read paper? by Rue et al. (2009). This method computes posterior marginals in latent Gaussian models and is usually more accurate and orders of magnitude faster than any Markov chain M onte Carlo alternative. There is a well-used, user-friendly R front-end for this method (www.r-inla.org). The project will investigate the parameterisation of non-stationarity in the models described in idea 1. The methods described in idea 2 will be us ed to examine and fit these new models to real data, in collaboration with Dr Janine B. Illian, Prof. Peter Guttorp and Prof. Otso Ovaskainen.