具有不确定性的稀疏贝叶斯质量映射：结构的假设检验
Sparse Bayesian mass-mapping with uncertainties: hypothesis testing of structure
摘要：
质量映射的一个关键方面，通过弱透镜，是量化重建过程中引入的不确定性。迄今为止，对这些错误的适当解释在很大程度上被忽视了。我们提出了一种新的方法来重建最大后验（MAP）收敛映射，制定了一个无约束的贝叶斯推断问题与拉普拉斯型l1-范数稀疏促进先验，我们通过凸优化解决。以这种方式接近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我们的MAP重建的理论保守的不确定性，而不依赖于高斯假设。第一次，这些方法使我们能够进行假设检验的结构，从它是可能的，以区分物理对象和文物的重建。在这里，我们提出了这种新的形式主义，模拟演示的方法，然后将开发的形式主义的阿贝尔-520集群的两个观测数据集。阿贝尔-520星表的最初重建报告了一个异常的“暗核”的检测-一个没有光学对应物的过密区域-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，我们发现阿贝尔-520数据集都不能以99%的置信度最终确定这种暗核的物理性。然而，在这两种情况下，恢复的MAP估计是一致的两组数据。
英文摘要：
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 artifacts of the reconstruction. Here we present this new formalism, demonstrate the method on simulations, before applying the developed formalism to two observational datasets of the Abel-520 cluster. Initial reconstructions of the Abel-520 catalogs reported the detection of an anomalous 'dark core' -- an over dense 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 Abel-520 dataset can conclusively determine the physicality of such dark cores at 99% confidence. However, in both cases the recovered MAP estimators are consistent with both sets of data.
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