But even our theoretical research is often motived and influenced by physical or biological questions and settings.
One branch of our research in probability theory studies the behavior of physical systems of so many particles or components that only a probabilistic approach is feasible. In percolation theory, we study parametrized infinite networks with special attention to the critical point, that is, the value of the parameter around which qualitative changes in the network occur. Our modern research in this direction uses ideas from complex analysis. We also work in other classical areas of probability theory like random walks, queueing systems, and the Ising model for describing ferro magnetics.
The second, much more applied, branch of our research in probability is forensic probability theory. The evaluation of the evidential value of, say, (partial) DNA matches is not straightforward, with many practical, philosophical, and theoretical questions. We have strong connections with the Netherlands Forensic Institute. We monitor the need for, and carry out the application of probability theory in this rapidly developing domain. Sometimes, this research leads to new probabilistic or statistical concepts which we also study.
Our research in statistics includes high-dimensional inference, nonparametric Bayesian inference, model selection and recovery problems, as well as estimation of convergence rates of parameter estimation. There is special attention for uncertainty quantification, non- and semiparametric inference for complex survival analysis, and resampling techniques for multivariate data and empirical processes. Many of these subjects are motivated by practical questions from science at large.
The applied part of our statistics research focusses on Statistics in Life Sciences Amsterdam and includes development, assessment and application of statistical models and tools for complex data structures such as networks. Important aspects are dependency, heterogeneity, integration of different data types and big data. We consider mathematical models ranging from -- often multivariate -- (non)linear regression, Markov and hidden Markov models to queueing processes, and frequentist as well as Bayesian estimation techniques. We have a special interest in modeling electrophysiological and neuroimaging data, where we focus on inference problems for spatio-temporal dynamics of ongoing cortical activity such as wave propagation. Another line of research is in cellular and genetic networks. By using dedicated multivariate statistical methods for big data, we aim to deduce biological tangible conclusions about genetic networks that are applicable to cancer research. We have strong connections with the VU Medical Centre, our partner in this research direction.