This article shows that a large class of posterior measures that are absolutely continuous with respect to a Gaussian prior have strong maximum a posteriori estimators in the sense of Dashti et al. (2013). This result holds in any separable Banach space and applies in particular to nonparametric Bayesian inverse problems with additive noise. When applied to Bayesian inverse problems, this significantly extends existing results on maximum a posteriori estimators by relaxing the conditions on the log-likelihood and on the space in which the inverse problem is set.

翻译：本文证明，一大类关于高斯先验绝对连续的后验测度，在Dashti等人(2013)的意义上具有强最大后验估计量。该结论适用于任何可分Banach空间，并特别适用于加性噪声的非参数贝叶斯逆问题。当应用于贝叶斯逆问题时，通过放宽对对数似然函数以及逆问题所在空间的条件，该结果显著扩展了现有关于最大后验估计量的结论。