Maximum a posteriori estimators in ℓp are well-defined for diagonal Gaussian priors

Abstract

Abstract 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 Inverse Problems 29 095017); Kretschmann (2019 PhD Thesis). These corrections do not generalize to the setting 1 ⩽ p < ∞ , which requires a novel convexification result for the difference between the Cameron–Martin norm and the p-norm.