We show that a nonparametric Bayesian inverse problem with a Gaussian prior has a strong maximum a posteriori estimator in the sense of small-ball modes as introduced by Dashti et al. (2013). This result holds in any separable Banach space under mild conditions on the forward operator and extends existing results by significantly relaxing the conditions on the log-likelihood and on the space in which the inverse problem is set.

翻译：我们证明了在Dashti等人（2013）提出的小球模态意义下，具有高斯先验的非参数贝叶斯反问题存在强最大后验估计量。该结果在任意可分Banach空间中，在正演算子的温和条件下成立，并通过显著放宽对对数似然函数以及反问题所在空间的条件，扩展了现有结果。