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 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.

My most 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.

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.

Most of my applied work is motivated by collaborations with scientists 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. The page Statistics for Life Sciences Amsterdam lists most of our collaborators. We are also involved in medical imaging and signal processing (PET and MEG), financial risk management, and (historical) population dynamics. Occasionally we are involved in commercial consultation.

List of publications

Books

• Statistical Estimation in Large Parameter Spaces
• Weak Convergence and Empirical Processes
• Asymptotic Statistics
• Semiparametric Statistics (Ecole d'Ete St Flour 1999)
• Fundamental of Nonparametrics Bayesian Inference
• Limits of Experiments

Selected talks

• Kansrijk (Text), Kansrijk (Slides), Oratie Vrije Universiteit (Amsterdam, 2001) [67KB, 12MB]
• Algorithms for Smoothing array CGH data, (Amsterdam, 2003) [1.5 MB]
• Entropy methods in statistics, IXCLAPEM (Punta del Este, Uruquay, 2004) [48 KB, dvi files, viewed well with yap.exe]
• Bayesian adaptation, 4th Conference on Nonparametric Bayesian Statistics (Rome, 2004) [350 KB]
• Estimating a causal effect using observational data, Nederlandse Organisatie Sociaal-Wetenschappelijk Onderzoek (Utrecht, 2004) [870 KB]
• Higher order estimating equations, Joint Statistical Meeting (Minneapolis 2005) [285 KB]
• Some results in nonparametric Bayesian inference, including Gaussian process priors, Institut Henri Poincare (Paris, February 2006) [113 KB]
• Linkage analysis with censored data, Leiden University Medical Centre (Leiden, Spring 2007) [565 KB]
• Nonparametric inference with Gaussian process priors, Weierstrass Institute (Berlin, May 2007) [960 KB]
• Bayesian curve estimation using Gaussian process priors, (Universiteit Utrecht, May 2009).
• Entropy methods in statistics, Aio meeting (Hilversum, May 2009).
• Forum lectures 1, Forum lectures 2, European Meeting of Statisticians (Toulouse, July 2009).
• Le Cam lecture IMS, JSM (Washington, August 2009).
• Bayesian Regularization, Invited lecture, International Congress of Mathematicians (Hyderabad, August 2010).

This page was last updated in 2011.