Statistical modeling of data on metric graphs

Abstract

There is a growing interest in the statistical modeling of data on compact metric graphs such as street or river networks based on Gaussian random fields.  In this work, we introduce the Whittle-Matérn fields, which is a class of models specified as solutions to a fractional-order stochastic differential equation on the metric graph. Contrary to earlier covariance-based approaches for specifying Gaussian fields on metric graphs, the Whittle-Matérn fields are well-defined for any compact metric graph and can provide Gaussian processes with differentiable sample paths given that the fractional exponent is large enough.

We present some of the main statistical properties of the models, discuss various extensions, and finally illustrate the usage of the models through an application where we use recently introduced MetricGraph R package to perform full Bayesian inference of a traffic data set.