Gaussian random fields on metric graphs: From stochastic PDEs to statistical inference
Alexandre De Bustamante Simas (KAUST)
Wednesday 28th October 12:00-13:00
Maths 311B
Abstract
Many spatial datasets are naturally observed on networks, such as roads and rivers, where both the geometry and connectivity of the network play an important role in the dependence structure. Standard Euclidean spatial models do not adequately account for this network structure and may therefore be unsuitable for such data. Metric graphs provide a natural mathematical framework for developing statistical models on these domains.
In this talk, I will introduce Gaussian Whittle–Matérn fields on metric graphs, constructed through stochastic partial differential equations involving differential operators on the graph. I will discuss some of their main theoretical properties, with particular emphasis on regularity and Markov properties. I will then present two complementary approaches to computationally efficient statistical inference: exact methods that exploit the Markov structure of the fields, when available, and finite element approximations of the underlying SPDEs. I will explain how both approaches lead to efficient methods for inference and prediction, illustrating the main ideas with examples involving data observed on networks.
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