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Eindhoven Stochastics Seminar
May 23, 2018, 15:45 - May 23, 2020, 16:45
Bayesian nonparametric approach to log-concave density estimation
In the beginning of the talk I will give a (somewhat) lengthier introduction to Bayesian nonparametric methods. Then I will focus on estimating log-concave densities on R, which is a canonical problem in the area of shape-constrained nonparametric inference. We present a Bayesian nonparametric approach to this problem based on an exponentiated Dirichlet process mixture prior and show that the posterior distribution converges to the log-concave truth at the (near-) minimax rate in Hellinger distance.