A crucial aspect of mass mapping, via weak lensing, is quantification of the uncertainty introduced during the reconstruction process. Properly accounting for these errors has been largely ignored to date. We present a new method to reconstruct maximum a posteriori (MAP) convergence maps by formulating an unconstrained Bayesian inference problem with Laplace-type l₁-norm sparsity-promoting priors, which we solve via convex optimization. Approaching mass mapping in this manner allows us to exploit recent developments in probability concentration theory to infer theoretically conservative uncertainties for our MAP reconstructions, without relying on assumptions of Gaussianity. For the first time, these methods allow us to perform hypothesis testing of structure, from which it is possible to distinguish between physical objects and artefacts of the reconstruction. Here, we present this new formalism, and demonstrate the method on simulations, before applying the developed formalism to two observational data sets of the Abell 520 cluster. Initial reconstructions of the Abell 520 catalogues reported the detection of an anomalous ‘dark core’ – an overdense region with no optical counterpart – which was taken to be evidence for self-interacting dark matter. In our Bayesian framework, it is found that neither Abell 520 data set can conclusively determine the physicality of such dark cores at |$99{{\ \rm per\ cent}}$| confidence. However, in both cases the recovered MAP estimators are consistent with both sets of data.

中文翻译：

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具有不确定性的稀疏贝叶斯质量映射：结构的假设检验

通过弱透镜进行质量映射的一个关键方面是量化重建过程中引入的不确定性。迄今为止，对这些错误的正确解释在很大程度上被忽略了。我们提出了一种通过用拉普拉斯型l ₁制定无约束贝叶斯推理问题来重建最大后验 (MAP) 收敛图的新方法-norm 稀疏促进先验，我们通过凸优化解决。以这种方式进行质量映射使我们能够利用概率集中理论的最新发展来推断 MAP 重建的理论上保守的不确定性，而无需依赖高斯假设。这些方法第一次允许我们对结构进行假设检验，从中可以区分物理对象和重建的人工制品。在这里，我们展示了这种新的形式主义，并在将开发的形式主义应用于 Abell 520 集群的两个观测数据集之前，演示了模拟方法。Abell 520 目录的初步重建报告发现了一个异常的“暗核”——一个没有光学对应物的高密度区域——这被认为是自相互作用暗物质的证据。在我们的贝叶斯框架中，发现 Abell 520 数据集都不能最终确定这种暗核在|$99{{\ \rm per\ cent}}$| 置信度。然而，在这两种情况下，恢复的 MAP 估计量与两组数据一致。