Gaussian processes on metric graphs

The aim of this project is to develop spatial and temporal models that incorporate dependence based on the structure of a metric graph, utilizing Gaussian processes as the primary tool.

The derivation processes for general metric graphs are highly innovative, and their development will advance our theoretical understanding of Gaussian processes acting on complex geometries.

Furthermore, this approach will be highly valuable for research areas where dependence structures are better explained by graphs or networks rather than Euclidean distances, such as ecology, traffic research, and criminology, among others.

The objective of this project is to contribute to several statistical research areas, which include:Theoretical problems related to the asymptotic consistency of parameters, with a particular focus on infill asymptotics.Methodological: like defining space-time processes, that incorporate drift and parameters that control it.

Or, explore the application of Gaussian processes on graphs to point process data, such as car accidents.Numerical: how to efficiently making predictions and inferences for Gaussian processes on graphs, especially for large datasets over space and time.Moreover, the project aims to implement the developed methods in open-source software to make them widely accessible to the research community.