Gaussian Random Fields on Metric Graphs
This talk presents a comprehensive mathematical and statistical theory, along with user-friendly software, for modeling data with Gaussian random fields on metric graphs by developing valid covariance functions based on network distance.
Overview
There is a growing interest in modeling data on networks and graphs. In statistics, typical applications are modeling traffic accidents or street crimes on road networks and modeling temperature or pollutants in river networks. In these cases, the statistical model is defined on both the edges and vertices of the graph, where the edges represent the roads or river segments. Importantly, the distance between locations should then be measured on the network, and not by using the Euclidean distance. A graph coupled with a metric like this is referred to as a metric graph. Gaussian random fields are essential for modeling spatially dependent data; however, the study of Gaussian random fields on metric graphs is challenging because it is difficult to construct valid covariance functions that are isotropic in the metric on the graph. In this talk, I will give an overview of our ongoing work on developing a complete mathematical and statistical theory for Gaussian random fields on metric graphs, complemented by an easy-to-use statistical software.
Presenters
Brief Biography
David Bolin is a Professor of Statistics in the CEMSE Division at KAUST, where he leads the Stochastic Processes and Applied Statistics research group. Before joining KAUST, he was an associate professor of Mathematical Statistics at the University of Gothenburg. He received his Ph.D. in mathematical statistics from Lund University in 2012.
Bolin's research focuses on stochastic partial differential equations (SPDEs) and their applications in statistics, with an emphasis on developing practical, computationally efficient tools for modeling non-stationary and non-Gaussian processes. He has made significant contributions to the theory of Gaussian processes, optimal linear prediction, fractional-order SPDEs, and stochastic processes on metric graphs. He has also developed and maintains several widely used software packages for advanced statistical modeling.
Bolin serves as an associate editor for the Scandinavian Journal of Statistics, is an elected member of the International Statistical Institute, and has received multiple honors, including the Section on Statistics and the Environment Early Investigator Award from the American Statistical Association and the Cramér Prize from the Cramér section of the Swedish Statistical Society.
