Stein’s method is a probabilistic technique of controlling distances between probability distributions in terms of certain differential operators. Initially used in order to bound the rate of convergence in various distributional limit results, it has recently seen numerous applications to mathematical statistics, such as goodness-of-fit testing and parameter estimation. In this context, the statistical objects based on Stein's method are often of a simple form as the operators are independent of a possibly complicated normalising constant. 

The abundance of topics covered in the literature will be reflected in the presentations of the three proposed speakers, who represent different areas of expertise. All three of them have agreed to participate if the session is approved. They are all of very high calibre and at different career stages – early career researcher (Postdoc), established career researcher (“Akademischer Oberrat” equivalent to Assistant Professor), and a senior researcher (Associate Professor). 
This session would be of interest to the applied probability community, for theoretical statisticians, and also to the machine learning community as it will present open problems as well as new ideas in this quickly developing field.

Wenkai Xu (University of Tuebingen, Chinese) received his PhD from University College London under the supervision of Arthur Gretton. Before starting his current position at the University of Tuebingen, he held a postdoctoral position at the University of Oxford. He works on topics lying at the interface of applied probability, computational statistics and machine learning, with a particular focus on applications. His publications have contributed to the area of nonparametric testing based on kernelised Stein discrepancies.
Wenkai Xu would talk on Stein's method for assessing and generating graphs.

Bruno Ebner (Karlsruhe Institute of Technology, German) is an “Akademischer Oberrat” (equivalent to Assistant Professor) at the Karlsruhe Institute of Technology. He received his PhD from the same university under supervision of Norbert Henze. His areas of expertise include parametric estimation as well as non-parametric methods. His work has contributed significantly to the understanding of the applications of Stein’s method to goodness-of-fit testing.
Bruno Ebner would talk on new goodness-of-fit tests on the hypersphere based on Stein characterizations.

Bojana Milosevic (University of Belgrade, Serbian) received her PhD from the University of Belgrade in 2016. Between 2016 and 2022 she held an Assistant Professorship and is now an Associate Professor at the same university. Since 2022 she is also the Chair of the Department of Probability and Statistics. Her work has contributed to the areas of testing for goodness-of-fit, exponentiality and symmetry among others.
Bojana Milosevic would talk on a novel goodness-of-fit test for the Wishart distribution based on a Stein-type characterisation.
The format of the session will be three talks of 30 min, including questions. In order to increase coherence, the speakers will be encouraged to liaise with each other before the event regarding coverage.