3.2. Statistics

Description of the programme.

This programme focuses on the practical implementation and theoretical study of techniques for modelling stochastic phenomena, such as arising from the sciences, epidemiological and medical studies, economic processes, and industrial settings. The programme emphasizes the use of infinite-dimensional statistical models. This is motivated in part by the fact that present-day data sets are often large, which allows one to fit more complex models. Moreover, a lack of structure in the data set often necessitates the use of complex models. Data may result from observational rather than from experimentally controlled studies, and are often subject to censoring (missing or partially observed data). These and other situations cannot be reliably modelled by classical, low-dimensional statistical models. Modern computing power and large data sets make the implementation of infinite-dimensional models feasible. This development is recent and much work remains to be done, including a better understanding of existing methods and the development of new algorithms.

Mathematical keywords are: semi- and non-parametric models, likelihood and Bayes methods, inverse problems, model selection and adaptive methods, time series, computer simulation, functional estimation, extreme value theory, efficiency bounds, image analysis, resampling techniques, statistical quality control, experimental design, and empirical processes. There are strong interactions with other projects, in particular probability.

Status of the programme.

The research group has numerous important international contacts and an excellent international reputation. The researchers form a notable group within the large international community of statisticians, which is a mix of mathematicians, applied statisticians and data analysts. At a national level the research group has good connections with the statisticians in the Mathematical Research Institute, for instance within the context of the Vereniging voor Statistiek and through the Aio-network Stochastics, which organizes the national graduate program in stochastics. There are regular workshops, which are organized with the help of the Stieltjes Institute. The European research institute in stochastics "Eurandom" in Eindhoven will be a further meeting point for the statisticians of the Stieltjes Institute, and will also stimulate interaction with other groups in stochastics.