October 2020
Bayesian inverse problems, Gaussian processes, and partial differential equations
Richard Nickl - University of Cambridge
Abstract: The Bayesian approach to inverse problems has become very popular in the last decade after seminal work by Andrew Stuart (2010) and collaborators. Particularly in non-linear applications with PDEs and when using Gaussian process priors, this can leverage powerful MCMC methodology to tackle difficult high-dimensional and non-convex inference problems. Little is known in terms of rigorous performance guarantees for such algorithms. After laying out the main ideas behind Bayesian inversion, we will discuss recent progress providing both statistical and…
Find out more »On Estimating the Mean of a Random Vector
Gábor Lugosi, Pompeu Fabra University
Abstract: One of the most basic problems in statistics is the estimation of the mean of a random vector, based on independent observations. This problem has received renewed attention in the last few years, both from statistical and computational points of view. In this talk we review some recent results on the statistical performance of mean estimators that allow heavy tails and adversarial contamination in the data. The basic punchline is that one can construct estimators that, under minimal conditions,…
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