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My research is in statistics and probability, both theory and applications.
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.
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. Information theory is still relevant, but must be combined
with approximation and bias-variance trade-off.
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 sparse models. Most recently we study
the validity (or not) of uncertainty quantification through posterior distributions.
Most of my applied work was 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.
I was also involved in medical
imaging and signal processing (PET and MEG), financial risk
management, and (historical) population dynamics. Occasionally
I am involved in commercial consultation.
List of publications
Several of my lecture notes also take the form of books (Time series, Stochastic Integration, Financial Stochastics, Statistical
Genetics, Statistical Learning). Some of these are in the public domain.
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, Uruguay, 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]
analysis with censored data, Leiden University Medical Centre (Leiden, Spring 2007) [565 KB]
inference with Gaussian process priors, Weierstrass Institute (Berlin, May
2007) [960 KB]
- Bayesian curve estimation using Gaussian process priors, (Universiteit Utrecht, May
- 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).
- Confidence in Nonparametric Credible Sets?
ISBA Foundational lecture, Kyoto, 2012.
- Bayesian Methods for Sparse Regression,
O'Bayes Conference, Duke University, December 2013.
- Semiparametric estimation in very high-dimensional models, ETH, Zurich, November 2015.
- Bayesian uncertainty quantification for sparsity models, Journees de Statistiques, Montpellier, May 2016.
- Statistical inference for some network models, CRM, Barcelona, June 2016.
- Causaliteit en statistiek, ICLON, Leiden September 2016.
- Responsible data science, Amsterdam, October 2016.
- Hotelling lecture 1, Hotelling lecture 2,
UNC, Chapel Hill, April 2017.
- Barrett lecture 1 (Bradley lecture), Barrett lecture 2 (Bradley lecture),
UT, Knoxville, May 2017.
This page was last updated in 2017.