The aim of this project is to provide solutions for two common
challenges in spatio-temporal applications: making Bayesian
inference in reasonable time, and provide a good approach to modeling
and representing stationary and non-stationary Gau ssian random
fields. This is done by merging and developing two main ideas:
1. The approximate Bayesian inference scheme called Integrated Nested Laplace Approximation. This inference scheme computes posterior marginals in latent Gaussian models, in most cases more
accurate and faster than any Markov chain Monte Carlo alternative.
2. The representation of Gaussian fields on manifolds as Gaussian Markov random fields. The
modelling approach uses stochastic partial differential equations to define Gaussian fields and finite-element methods to construct the explicit Gaussian Markov random field representation.
The project takes advantage of the synergy effects of these two ideas: By using the representation in idea 2 in spatio-temporal modelling w e enable the inference scheme of idea 1. Similarly, idea 1 makes inference for non-stationary fields from idea 2 possible.
The synergy effects will be large for spatio-temporal models.
Our strategy is to work in close co-operation with applied groups to highlight the specific needs. One group is lead by Professor Sylvia Richardson, Imperial College, another lead by Professor Leonhard Held, University of Zurich. Both work on highly relevant spatio-temporal data.