Nonseparable Space-Time Stationary Covariance Functions on Networks cross Time

Abstract

The advent of data science has provided an increasing number of challenges with high data complexity. This paper addresses the challenge of space-time data where the spatial domain is not a planar surface, a sphere, or a linear network, but a generalized network (termed a graph with Euclidean edges). Additionally, data are repeatedly measured over different temporal instants. We provide new classes of nonseparable space-time stationary covariance functions where space can be a generalized network, a Euclidean tree, or a linear network, and where time can be linear or circular (seasonal). Because the construction principles are technical, we focus on illustrations that guide the reader through the construction of statistically interpretable examples. A simulation study demonstrates that we can recover the correct model when compared to misspecified models. In addition, our simulation studies show that we effectively recover simulation parameters. In our data analysis, we consider a traffic accident dataset that shows improved model performance based on covariance specifications and network-based metrics.

The Matérn Model: A Journey through Statistics, Numerical Analysis and Machine Learning

“…Bolin et al [32] adopt a different approach to build random fields with their covariance structure on metric graphs. Space-time version of the Matérn model, for graphs with Euclidean edges, have been considered by Tang and Zimmerman [155] and Porcu et al [127]. These efforts considerably extend the applicability of the Matérn model.…”

“…Recently, [32] adopt a different approach to build random fields with their covariance structure on metric graphs. Space-time version of the Matérn class, for space being a graph with Euclidean edges, have been considered by [155] and by [127]. d) Space-time.…”