B0993
Title: Gaussian Whittle Matern fields on metric graphs
Authors: Jonas Wallin - Lund University (Sweden) [presenting]
David Bolin - King Abdullah University of Science and Technology (KAUST) (Saudi Arabia)
Alexandre de Bustamante Simas - King Abdullah University of Science and Technology (Saudi Arabia)
Abstract: A new class of Gaussian processes on compact metric graphs such as street or river networks is defined. The proposed models, the Whittle Matern fields, are defined via a fractional stochastic partial differential equation on the compact metric graph and are a natural extension of Gaussian fields with Matern covariance functions on Euclidean domains to the non-Euclidean metric graph setting. The existence of the processes, as well as their sample path regularity properties, are derived. The processes are stable in the sense that they do not change when vertices are added to existing edges of the graph, or when vertices of degree two are removed. This property is important for applications and is lacking for Gaussian processes based on the graph Laplacian on non-metric graphs. The model class contains, as particular cases, differentiable Gaussian processes. This is the first construction of a valid differentiable Gaussian field on general compact metric graphs.
