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Adaptive posterior contraction

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We investigate the problem of deriving posterior contraction rates in nonparametric models under different loss functions (in particular sup-norm loss). We derive a lower bound on posterior coverages of shrinking neighbourhoods. This will have some implications on proof strategies to derive posterior contraction rates. In a second part, feasible priors are constructed that lead to adaptive rates of contraction under L^2 or sup-norm loss and that moreover achieve our lower bound. [Joint work with Marc Hoffmann and Judith Rousseau (both Paris Dauphine).]

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