Research interests

Much of my interest in theoretical statistics centers around infinite dimensional statistical models. These are models that use functions rather than finite-dimensional vectors as the unknowns, with the aim of avoiding misspecification. Such models have become standard in for instance epidemiology or econometrics. One may study nonparametric estimation or classification (or "learning"), but also estimation of quantitative functionals, such as relative risks, or regression parameters. For the latter "semiparametric problems" a theory of "information" was developed in the 1980/90s and appropriately defined "maximum likelihood" and "likelihood ratio" procedures were shown to behave as predicted by this theory in the 1990s/2000s.

Empirical process theory is an important tool in these investigations, as it is for many other learning problems.

A more recent interest is in very high-dimensional models, where completely new phenomena occur. Such models are appropriate in epidemiological studies, where one wants (or needs) to control for many "covariate variables", and in many other areas where causal conclusions must be drawn from non-experimental data. Information theory is still relevant, but must be combined with approximation and bias-variance trade-off, even for the estimation of a numerical causal effect.

Since 2000 I also study Bayesian procedures for (mostly) infinite-dimensional models. The Bayesian approach in statistics has gained much popularity in the past fifteen years. While the elegance of the paradigm is undeniable, my interest is in understanding the properties of Bayesian procedures from a frequentist perspective more than in the philosophical issues that have clouded the Bayes-non Bayes debate in the past. Besides general theory on contraction rates and hierarchical models, we studied special classes of priors such as Dirichlet mixtures, Gaussian processes or spike-and-slab priors for high-dimensional sparse models. Most recently we study the validity (or not) of uncertainty quantification through posterior distributions, with a special interest for inverse problems and causal inference.

I have also published on statistical procedures for networks, and other structured models.

Most of my applied work was motivated by collaborations with scientists in other fields, many on the Vrije Universiteit campus. At this university, as everywhere, there is much interest in genetics and life sciences, including the analysis of data from new platforms such as RNA and DNA-arrays, proteomics, SNPs,.., and also more classical "statistical genetics" centering around linkage and association. I was also involved in medical imaging and signal processing (PET and MEG), financial risk management, (historical) population dynamics, and pharmaceutical science. Occasionally I am involved in commercial consultation.

List of publications

Books

This page was last updated in 2021.