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On the nonparametric Bernstein-von Mises phenomenon

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In this talk I will discuss some limiting shape results for Bayesian posterior distributions in canonical nonparametric settings (white noise, density estimation). In particular, we will see that it is possible to obtain nonparametric Bernstein-von Mises theorems by stating the convergence in well-chosen large enough multiscale spaces. I will discuss applications to Donsker-type theorems for the posterior distribution function, as well as to (confident) credible sets. Joint work with Richard Nickl.

This talk is part of the Probability Theory and Statistics in High and Infinite Dimensions series.

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