Bioskech
Richard Nickl is originally from Vienna, Austria, where he obtained his PhD in 2005 at the University of Vienna. After a postdoc with Evarist Gine in the US he moved to the UK, where he is currently Professor of Mathematical Statistics at the University of Cambridge. His research is on various aspects to high-dimensional and non-parametric statistics, and recently on Bayesian theory for PDE-constrained inverse problems. He is author of the book `Mathematical foundations of infinite-dimensional statistical models’ published in 2016 at Cambridge University Press, and recipient of the 2017 Ethel Newbold Prize of the Bernoulli Society, the 2017 PROSE Award of the American Association of Publishers, and an ERC Consolidator Grant (2015).
Research area
Bayes methods for inverse problems have become very popular in applied mathematics in the last decade. They provide reconstruction algorithms as well as in-built `uncertainty quantification’ methodology via Bayesian credible sets, and particularly for Gaussian priors can be efficiently implemented by MCMC algorithms. For linear inverse problems, they are closely related to classical penalised least squares methods and thus not fundamentally new, but for non-linear and non-convex problems, they give genuinely distinct and computable algorithmic alternatives that cannot be studied by variational analysis or convex optimisation techniques. Richard Nickl's recent research has employed mathematical tools from Bayesian Non-Parametric statistics to give the first rigorous statistical guarantees for posterior mean reconstructions in non-linear non-convex inverse problems arising in various PDE models.