The Bayesian approach is effective for inverse problems. The posterior density distribution provides useful information of the unknowns. However, for problems with non-unique solutions, the classical estimators such as the maximum a posterior (MAP) and conditional mean (CM) are not enough. We introduce two new estimators, the local maximum a posterior (LMAP) and local conditional mean (LCM). Their applications are demonstrated by three inverse problems: an inverse spectral problem, an inverse source problem, and an inverse medium problem.

翻译：Bayesian 方法对反面问题有效。 后方密度分布为未知点提供了有用的信息。 但是,对于非独有解决方案的问题,传统的测算器,如后方最大值(MAP)和有条件平均值(CM)是不够的。 我们引入了两个新的测算器,即本地最高值(LMAP)和本地有条件平均值(LCM ) 。 其应用通过三个反面问题(反光谱问题、反源问题和反介质问题)来证明: 反光谱问题、反源问题和反介质问题。