We prove that maximum a posteriori estimators are well-defined for diagonal Gaussian priors $\mu$ on $\ell^p$ under common assumptions on the potential $\Phi$. 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). These corrections do not generalize to the setting $1 \leq p < \infty$, which requires a novel convexification result for the difference between the Cameron--Martin norm and the $p$-norm.

翻译：我们证明,根据对潜在美元的共同假设,对Dashti等人(2013年)和Kretschmann(2019年)先前确定的对数高斯的事后估计值的上限定义非常明确,根据对潜在美元的共同假设,其成本为$\ ell ⁇ p$ 。此外,我们展示了与Onsager-Machlup功能的连接,并在Hilbert空间案中提供了经过更正和大力简化的证明,即$p=2美元,此前由Dashti等人(2013年)和Kretschmann(2019年)确定,这些更正并不概括于设置的1美元leq p <\infty$,这需要对Cameron-Martin规范与美元规范之间的差别进行新颖的整合。