Sparse Bayesian mass mapping with uncertainties: peak statistics and feature locations
Sparse Bayesian mass mapping with uncertainties: peak statistics and feature locations
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DOI：
10.1093/mnras/stz2373
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发表时间：
2018-12
影响因子：
4.8
通讯作者：
Matthew Alexander Price;Xiaohao Cai;J. McEwen;T. Kitching
中科院分区：
文献类型：
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作者：
Matthew Alexander Price;Xiaohao Cai;J. McEwen;T. Kitching
弱透镜收敛图（可以计算高阶统计数据）可以通过解决透镜逆问题从剪切场的观测中恢复。对于典型的调查，这个逆问题是不适定的（通常是严重的），导致恢复的收敛图存在很大的不确定性。在本文中，我们提出了量化恢复特征位置的贝叶斯不确定性和累积峰值统计量（峰值计数作为信噪比（SNR）的函数）的不确定性的新方法。我们采用先前工作中开发的稀疏分层贝叶斯质量映射框架，该框架提供了重构收敛图的稳健重建和原则性统计解释，而无需假设或强加高斯性。我们在 Bolshoi N 体（簇尺度）和 Buzzard V-1.6（大型结构）N 体模拟上展示了我们的不确定性量化技术。这种方法第一次允许人们在明确定义的置信水平下恢复累积峰值统计量的近似贝叶斯上限和下限。
Weak lensing convergence maps – upon which higher order statistics can be calculated – can be recovered from observations of the shear field by solving the lensing inverse problem. For typical surveys this inverse problem is ill-posed (often seriously) leading to substantial uncertainty on the recovered convergence maps. In this paper we propose novel methods for quantifying the Bayesian uncertainty in the location of recovered features and the uncertainty in the cumulative peak statistic – the peak count as a function of signal-to-noise ratio (SNR). We adopt the sparse hierarchical Bayesian mass-mapping framework developed in previous work, which provides robust reconstructions and principled statistical interpretation of reconstructed convergence maps without the need to assume or impose Gaussianity. We demonstrate our uncertainty quantification techniques on both Bolshoi N-body (cluster scale) and Buzzard V-1.6 (large-scale structure) N-body simulations. For the first time, this methodology allows one to recover approximate Bayesian upper and lower limits on the cumulative peak statistic at well-defined confidence levels.