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Title: Matern fields on graphs and their edges Authors:  Jonas Wallin - Lund University (Sweden) [presenting]
Abstract: The focus is on Gaussian processes defined on edges of a Graph, which for example is relevant when modelling traffic data on road networks. It is difficult to define a proper covariance function on such a topology, and even harder to define a covariance function with Markov properties, which is one of our main goals. We show how one can construct Matern-type processes using precision operators acting on each edge independently. Then through (random) boundary conditions, such as Neumann-Kirchhoff conditions, one can tie the edges together to form a process acting on the entire graph. For models of this type, we demonstrate how to efficiently evaluate log-likelihoods and to perform Kriging prediction.