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Adaptive nonparametric credible balls

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Credible sets are central sets in the support of a posterior probability distribution, of a prescribed posterior probability. They are widely used as means of uncertainty quantification in a Bayesian analysis. We investigate the frequentist coverage of such sets in a nonparametric Bayesian setup. We show by example that credible sets can be much too narrow and misleading, and next introduce a concept of `polished tail’ parameters for which credible sets are of the correct order. The latter concept can be seen as a generalisation of self-similar functions as considered in a recent paper by Giné. Joint work with Botond Szabó and Harry van Zanten.

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

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