# Maximum a posteriori estimators in $\ell^p$ are well-defined for diagonal Gaussian priors

@inproceedings{Klebanov2022MaximumAP, title={Maximum a posteriori estimators in \$\ell^p\$ are well-defined for diagonal Gaussian priors}, author={Ilja Klebanov and Philipp Wacker}, year={2022} }

We prove that maximum a posteriori estimators are well-deﬁned for diagonal Gaussian priors µ on (cid:96) p under common assumptions on the potential Φ . Further, we show connections to the Onsager–Machlup functional and provide a corrected and strongly simpliﬁed proof in the Hilbert space case p = 2, previously established by Dashti et al. (2013); Kretschmann (2019).

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