Maximum a posteriori estimators in $\ell^p$ are welldefined for diagonal Gaussian priors
Abstract
We prove that maximum a posteriori estimators are welldefined for diagonal Gaussian priors $\mu$ on $\ell^p$ under common assumptions on the potential $\Phi$. Further, we show connections to the OnsagerMachlup 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). These corrections do not generalize to the setting $1 \leq p < \infty$, which requires a novel convexification result for the difference between the CameronMartin norm and the $p$norm.
 Publication:

arXiv eprints
 Pub Date:
 July 2022
 arXiv:
 arXiv:2207.00640
 Bibcode:
 2022arXiv220700640K
 Keywords:

 Mathematics  Statistics Theory;
 Mathematics  Probability;
 62F15;
 62F99;
 60H99