Full Name
Aad van der Vaart
Job Title
Professor of Statistics
Company
Delft University of Technology
Speaker Bio
Aad van der Vaart studied mathematics, philosophy and psychology at the University of Leiden, and received a PhD in mathematics from this university in 1987. He held positions in College Station, Texas and Paris (not in Texas), held a Miller fellowship in Berkeley, and was visiting professor in Berkeley, Harvard and Seattle. Following a long connection to the Vrije Universiteit Amsterdam and a shorter one to Leiden University, he is now professor of statistics at TU Delft. He is a member of the Royal Netherlands Academy of Arts and Sciences and the Academiae Europaea. He received the C.J. Kok prize in 1988, the van Dantzig award in 2000, the NWO Spinoza Prize in 2015, and the DeGroot prize in 2019. He is fellow of the IM, fellow of ISBA, elected member of the ISI, and member of the circle of the IMU.
Aad van der Vaart's research has been funded by NWO, VU-USF, STW, CMSB, NDNS+, STAR, and by the European Research Council (ERC Advanced Grant, 2012).
Aad van der Vaart's research is in statistics and probability, as mathematical disciplines and in their applications to other sciences, with an emphasis on statistical models with large parameter spaces. He wrote books and lecture notes (on topics such as empirical processes, time series, stochastic integration, option pricing, statistical genetics, statistical learning, Bayesian nonparametrics), as well as research papers. See research page for more information.
Aad van der Vaart was associate editor of the Annals of Statistics, Statistica Neerlandica, Annales de l'Institut Henri Poincare, Probability Theory and Related Fields, Statistics and Decisions (co-editor), Indagationes Mathematicae, Journal of Statistical Planning and Inference and ALEA. He was program chair for the European Meeting of Statisticians 2006 in Oslo and BNP10 (2015) in Raleigh, and local chair of BNP9 and the European Meeting of Statisticians 2015. He was member of the programme committee of the International Congress of Mathematicians in Rio de Janeiro (2018) and the European Congress of Mathematics in Portoroz, Slovenia (2020, held virtually in 2021), and section chair for Statistics and Data Science for the International Congress of Mathematicians (2022, held virtually following the Russian invasion of Ukraine).
Keynote lectures include the Forum Lectures at the EMS 2009, the Le Cam lecture at the JSM 2009, invited address at the International Congress of Mathematicians in 2010, a foundational lecture at the world meeting of International Society for Bayesian Analysis in 2012, the Hotelling lectures in 2017, the Barrett lectures in 2017, the European Mathematical Society & Bernoulli Society lecture in 2019, and the Mordell lecture in 2023. Short courses and lecture series on semiparametric statistics, empirical processes and Bayesian inference, were delivered in, among others, Indonesia, France, the USA, Germany, China, Korea, Italy, Uruquay, Denmark, Mexico, Cyprus, Vietnam and the Netherlands.
Among former administrative functions are president of the Netherlands Society for Statistics and Operations Research (2003-07), head of the Department of Mathematics of VU University Amsterdam (2002-06), Scientific Director of the Mathematical Institute of Leiden University (2015-19), chair of the European Council of the Bernoulli Society, scientific chair of the Stieltjes Institute, chair of the mathematics board of the Lorentz Centre, board member of the NDNS+ and STAR clusters, and council member of the International Statistical Institute, the Institute of Mathematical Statistics, and the Bernoulli Society. He was a founding member of the masters programs in Stochastics and Financial Mathematics in Amsterdam and Statistics and Data Science in Leiden. In 2024 he is president of the International Society for Bayesian Analysis.
Aad van der Vaart's research has been funded by NWO, VU-USF, STW, CMSB, NDNS+, STAR, and by the European Research Council (ERC Advanced Grant, 2012).
Aad van der Vaart's research is in statistics and probability, as mathematical disciplines and in their applications to other sciences, with an emphasis on statistical models with large parameter spaces. He wrote books and lecture notes (on topics such as empirical processes, time series, stochastic integration, option pricing, statistical genetics, statistical learning, Bayesian nonparametrics), as well as research papers. See research page for more information.
Aad van der Vaart was associate editor of the Annals of Statistics, Statistica Neerlandica, Annales de l'Institut Henri Poincare, Probability Theory and Related Fields, Statistics and Decisions (co-editor), Indagationes Mathematicae, Journal of Statistical Planning and Inference and ALEA. He was program chair for the European Meeting of Statisticians 2006 in Oslo and BNP10 (2015) in Raleigh, and local chair of BNP9 and the European Meeting of Statisticians 2015. He was member of the programme committee of the International Congress of Mathematicians in Rio de Janeiro (2018) and the European Congress of Mathematics in Portoroz, Slovenia (2020, held virtually in 2021), and section chair for Statistics and Data Science for the International Congress of Mathematicians (2022, held virtually following the Russian invasion of Ukraine).
Keynote lectures include the Forum Lectures at the EMS 2009, the Le Cam lecture at the JSM 2009, invited address at the International Congress of Mathematicians in 2010, a foundational lecture at the world meeting of International Society for Bayesian Analysis in 2012, the Hotelling lectures in 2017, the Barrett lectures in 2017, the European Mathematical Society & Bernoulli Society lecture in 2019, and the Mordell lecture in 2023. Short courses and lecture series on semiparametric statistics, empirical processes and Bayesian inference, were delivered in, among others, Indonesia, France, the USA, Germany, China, Korea, Italy, Uruquay, Denmark, Mexico, Cyprus, Vietnam and the Netherlands.
Among former administrative functions are president of the Netherlands Society for Statistics and Operations Research (2003-07), head of the Department of Mathematics of VU University Amsterdam (2002-06), Scientific Director of the Mathematical Institute of Leiden University (2015-19), chair of the European Council of the Bernoulli Society, scientific chair of the Stieltjes Institute, chair of the mathematics board of the Lorentz Centre, board member of the NDNS+ and STAR clusters, and council member of the International Statistical Institute, the Institute of Mathematical Statistics, and the Bernoulli Society. He was a founding member of the masters programs in Stochastics and Financial Mathematics in Amsterdam and Statistics and Data Science in Leiden. In 2024 he is president of the International Society for Bayesian Analysis.
Speaking At
Abstract
We consider the recovery of an unknown function f from a noisy observation u_f of the solution to a partial differential equation that has f as a parameter or boundary function. The challenging, but realistic, case is that the forward map f -> u_f is nonlinear, making this into a nonlinear inverse problem. We follow a standard, nonparametric Bayesian approach, thus regularising the solution of the inverse problem through a prior and and basing further inference on the posterior distribution. To gain computational and theoretical strength, we reformulate the problem as a combination of an embedded Bayesian linear problem and an analytic nonlinear problem, thus making it possible to obtain the posterior distribution using known and computationally efficient approaches for linear inverse problems in combination with numerical methods to map back to the original nonlinear problem. We consider several examples, including the Schrödinger and Darcy equations, and Gaussian process priors. After reviewing results for linear problems, we present contraction rates for the posterior distribution and coverage of credible sets for the nonlinear problems. We also discuss distributed posteriors to further alleviate the computational burden. [Joint work with Geerten Koers (TU Delft) and Botond Szabó (Bocconi, Milano).]
