In this note we solve a general statistical inverse problem under absence of knowledge of both the noise level and the noise distribution via application of the (modified) heuristic discrepancy principle. Hereby the unbounded (non-Gaussian) noise is controlled via introducing an auxiliary discretisation dimension and choosing it in an adaptive fashion. We first show convergence for completely arbitrary compact forward operator and ground solution. Then the uncertainty of reaching the optimal convergence rate is quantified in a specific Bayesian-like environment.

翻译：在本说明中,我们解决了一个一般性的统计逆向问题,因为我们不了解噪音水平和通过应用(经过修改的)超常差异原则的噪音分布。在此情况下,不受限制的(非高加索)噪音通过引入辅助分解维度来控制,并以适应性的方式选择。我们首先表现出完全任意的紧凑远端操作器和地面解决方案的趋同。然后,在特定贝叶斯式的环境中量化达到最佳趋同率的不确定性。