Seminarium Wydziałowe

Najbliższe spotkanie odbędzie się 29.10.2024 (wtorek) o godz. 11.15 w sali A.4.1 w budynku C-19 Politechniki Wrocławskiej.

Wykład wygłosi:

prof. Jonas Wallin

Lund University

Gaussian Whittle–Matern fields on metric graphs

Random fields are popular models in statistics and machine learning for spatially dependent data on Euclidean domains. However, in many applications, data is observed on non-Euclidean domains such as street networks, or river networks. In this case, it is much more difficult to construct valid random field models. In this talk, we discuss some recent approaches to modeling data in this setting, and in particular define a new class of Gaussian processes on compact metric graphs. The proposed models, the Whittle-Matérn fields, are defined via a stochastic partial differential equation with Kirchhoff boundary on conditions on the compact metric graph and are a natural extension of Gaussian fields with Matérn covariance functions on Euclidean domains to the non-Euclidean metric graph setting. We discuss various properties of the models, and show how to use them for statistical inference. We illustrate the model via an application to traffic data.
Finaly, I will present some more recent work, where we study the process on directional trees..