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A0531
Title: On the non-i.i.d. misspecified Bernstein-Von Mises theorem Authors:  Geerten Koers - Leiden University (Netherlands) [presenting]
Abstract: The asymptotic behaviour of misspecified posterior distributions is considered in a non-i.i.d. parametric setting. It is shown that a misspecified Bernstein-Von Mises theorem holds, and conditions on the distribution of the data and the likelihood functions of the model are relaxed compared to earlier results. The asymptotic behaviour of the well-specified posterior distribution is compared to that of the misspecified posterior distribution in a non-Gaussian model approximated by Gaussian likelihoods. Under regularity conditions, the misspecified posterior distribution will concentrate on the true parameter in these models. Natural examples in PDE-theory of models that were not covered by existing literature are analysed. The numerical analysis shows that the misspecified posterior distribution has an incorrect uncertainty quantification. It is observed that the resulting credible sets over-cover compared to the credible sets coming from the well-specified posterior distribution.