Maximum a posteriori estimators in ℓ^p are well-defined for diagonal Gaussian priors

07/01/2022

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by   Ilja Klebanov, et al.

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We prove that maximum a posteriori estimators are well-defined for diagonal Gaussian priors μ on ℓ^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) and Kretschmann (2019).