Towards useable models for complex spatial data

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As data gets bigger, models become more complex and the available statistical tools become less and less able to cope. This is particularly true for datasets with a spatial or spatiotemporal component, which are increasingly being collected in fields as diverse as ecology, epidemiology, atmospheric science, fisheries science, and forestry. For these problems, it is not just computational methods that are failing to scale to modern data. Our methods for building spatial models also need to be re-thought in light of both the advantages and challenges of analysing large data sets. ******The proposed programme of research has three main threads. The first is to extend existing methods of modelling large-scale spatial data to account for multiple sources of uncertainty, design issues, and multilevel structure. The second looks at the general problem of specifying and evaluating prior distributions for the class of latent Gaussian models, which includes the spatial models considered in the first thread as a special case. The third thread looks to improve the current state-of-the-art methods for fast Bayesian computing for these types of models. In it we will focus particularly on extensions of the Integrated Nested Laplace Approximation (INLA) for approximate Bayesian inference and the MCMC methods implemented in the Stan probabilistic programming language. These advances will increase the class of spatial and spatiotemporal models that can be routinely fit to large data sets, while implementing the outcomes in a tool that can be used by applied statisticians and scientists. *****