Stochastic modelling of interacting shapes: from sweat droplets to tree canopies

Research Project, 2026 – 2030

In this project, we will develop mathematical and statistical methodology to provide a toolbox with new models for time-evolving interacting complex shapes, such as sweat droplets or treetops, and methods to fit such models to data. More specifically, our aims are to develop novel spatial and spatio-temporal marked point process models for multiple interacting shapes and simulation-based methods to estimate the model parameters, as well as to apply the new methods to complex datasets and provide software tools to practitioners. In addition to appearance of new shapes and disappearance of existing shapes, we will treat the important challenge of the collision or merging of two shapes. To estimate the parameters of the models and to quantify the associated uncertainties, we will use Bayesian approaches coupled with simulation-based methods.  We will contribute to early diagnosis of neuropathy based on sweat gland activation and improved estimation of the growth of forests.The project will be done in collaboration with Moritz Schauer (co-applicant), with statisticians at Humboldt University in Germany, the Natural Resources Institute Finland, and the University of Rennes in France, as well as with neurologist Adam Loevenbruck at the University of Minnesota. In addition, we will hire a postdoc for two years.