All phenomena in science and society are ruled by randomness, sometimes partially or to a considerable extent. The branches of mathematics that enable us to understand, predict and control such phenomena are Probability Theory, Statistics, Stochastic Operations Research and Financial Mathematics. Collectively they go by the name Stochastics. All aforementioned branches are represented within the stochastics programme at the Korteweg-de Vries Institute. The programme is organised in two groups: Probability Theory and Mathematical Statistics.
Project leader: Prof. Michel Mandjes
Probability Theory studies the behaviour of a stochastic system of which the underlying chance mechanism is known: given this chance mechanism certain system characteristics are analyzed. Probability Theory is rooted in Analysis, more specifically in Measure and Integration Theory, and it nourishes the other branches of Stochastics.
Central research themes in the group Probability Theory are Probability, Stochastic Process Theory, Stochastic Operations Research and Mathematical Finance, all of them viewed from an applied as well as a foundational angle. Specific themes are stochastic integration-based techniques and stochastic-process limits, for instance for systems operating under Markov modulation; queueing theory and its relation to mathematical finance; rare-event analysis and importance sampling; stochastic analysis of road traffic and energy networks. New application areas include the stochastic analysis of road traffic and energy networks.
Project leader: Prof. Joris Mooij
Observing the behaviour of a stochastic system of which the underlying chance mechanism is unknown, one may try to induce which is the true underlying chance mechanism. The mathematics of this problem is called Mathematical Statistics. Our statistics research is motivated by both theoretical issues and by problems raised in application areas.
The research in the group Mathematical Statistics has both fundamental and applied components. Until the beginning of 2020, the fundamental work focused mainly on developing mathematical theory for modern high-dimensional statistical problems. Applied statistical work was carried out in various domains, in collaboration with domain experts. Central themes were nonparametric and semiparametric statistics, nonparametric Bayesian statistics, Forensic Statistics and Statistics for Climate Science. The group went through a major transition due to personnel changes: Dr. Harry van Zanten, who led the group until early 2020, was succeeded by Prof. dr. Joris Mooij. Dr. Bert van Es retired and was succeeded by dr. Tim van Erven (2020). Dr. Bas Kleijn moved from the Mathematical Statistics group to the Analysis programme, which provides a better fit with his current research interests. Through the SBT, a new staff member was hired, dr. Eni Musta (2020). All this has resulted in a shift of research focus towards the applications of statistical methods in AI, Machine Learning and Causal Inference in Data Science. Besides these topics, the group focusses on Forensic Science (prof. dr. Marjan Sjerps) and Medical applications (prof. Mooij, dr. Musta).
The KdVI, and in particular the Stochastics group, plays an important role in the NWO Gravitation programme NETWORKS. It is hosted by University of Amsterdam, Eindhoven University of Technology, Leiden University, and Center for Mathematics and Computer Science, with UvA being coordinator ("penvoerder") and Mandjes the programme leader. NETWORKS covers a broad range of topics dealing with stochastic and algorithmic aspects of networks, with specific attention to their interaction. The programme, which took off in 2014, underwent its midterm evaluation in 2017. The evaluation committee was highly positive about the achievements so far, and advised to continue the programme. For the second part of the funding period (2019-2024), the programme's objectives are (somewhat) adjusted. Apart from the original scope, additional attention will be paid to intensifying the interactions with other disciplines and domains (at the methodological level machine learning and data-science, at the application level e.g. the brain, citizen science projects, applications in biology).
Finally, the Stochastics programme is responsible for the Stochastics track in the Mathematics Master’s and the Master Stochastics and Financial Mathematics (SFM), and contributes significantly to the Forensic Science Master’s.