Stochastic adventures in space and time

Abstract: The standard geostatistics toolbox includes methods for modelling spatial dependence between georeferenced observations, as well as methods for modelling the occurrence of random points. The core model building blocks are often some form of Gaussian random fields.

The easiest approach to constructing space-time models is by taking the product between a spatial covariance kernel and a temporal covariance kernel. These are called covariance separable models. An alternative that may better capture the spatio-temporal dynamics is to take inspiration for physics motivated partial differential equations such as the heat equation, which leads to non-separable models. Non-separable models are in general more computationally expensive, but one can sometimes use the model structure to retain a lot of the simplicity of separable models, for example allowing these models to be used as components of larger hierarchical generalised additive models. For point process observations, such as observations of a moving animal, the temporal dynamics poses an additional challenge.

I will discuss some of these aspects, including a basic construction of non-separable space-time models, as well as an application of the INLA/inlabru framework to estimate the parameters of a dynamical animal movement model by rephrasing it as a point process model, with a parametric movement kernel, and a random field as an unknown "resource selection function".

ecologymachine learningprobabilitystatistics theory

Audience: researchers in the discipline

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Gothenburg statistics seminar

Series comments: Gothenburg statistics seminar is open to the interested public, everybody is welcome. It usually takes place in MVL14 (http://maps.chalmers.se/#05137ad7-4d34-45e2-9d14-7f970517e2b60, see specific talk).

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