Hierarchical cosmic shear power spectrum inference
Hierarchical cosmic shear power spectrum inference
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DOI：
10.1093/mnras/stv2501
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发表时间：
2015-05
影响因子：
4.8
通讯作者：
Justin Alsing;A. Heavens;A. Jaffe;A. Kiessling;Benjamin Dan Wandelt;Till Hoffmann
中科院分区：
文献类型：
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作者：
Justin Alsing;A. Heavens;A. Jaffe;A. Kiessling;Benjamin Dan Wandelt;Till Hoffmann
我们开发了一种贝叶斯分层建模方法，用于宇宙剪切功率谱推断，从宇宙剪切场及其（层析）功率谱的后验分布中联合采样。剪切功率谱的推断是宇宙剪切分析的一个强大的中间产品，因为它只需要很少的模型假设，并且可以用来在不丢失信息的情况下对大范围的宇宙模型进行后验推断。我们证明了关节后验的剪切图和功率谱可以通过吉布斯采样进行有效采样，迭代地从图和功率谱中提取样本，每个样本都是互为条件的。这种方法巧妙地规避了与复杂的测量几何形状和掩模相关的困难，这些困难困扰着频率主义的功率谱估计器，因为功率谱推断在每个采样步骤都提供了掩模区域的先验信息。我们证明了这种方法可以从一个具有许多重要特征的模拟星系剪切目录中推断出层析剪切e模、b模和eb交叉功率谱；星系分布在天空和红移中，具有光度红移不确定性，每个星系都有真实的随机椭圆噪声和复杂的测量掩模。得到的层析功率谱系数的后验分布恢复了E和b模式的底层模拟功率谱，其中b模式的恢复水平比椭圆噪声水平低1-2个数量级。
We develop a Bayesian hierarchical modelling approach for cosmic shear power spectrum inference, jointly sampling from the posterior distribution of the cosmic shear eld and its (tomographic) power spectra. Inference of the shear power spectrum is a powerful intermediate product for a cosmic shear analysis, since it requires very few model assumptions and can be used to perform inference on a wide range of cosmological models a posteriori without loss of information. We show that joint posterior for the shear map and power spectrum can be sampled eectively by Gibbs sampling, iteratively drawing samples from the map and power spectrum, each conditional on the other. This approach neatly circumvents diculties associated with complicated survey geometry and masks that plague frequentist power spectrum estimators, since the power spectrum inference provides prior information about the eld in masked regions at every sampling step. We demonstrate this approach for inference of tomographic shear E-mode, B-mode and EB-cross power spectra from a simulated galaxy shear catalogue with a number of important features; galaxies distributed on the sky and in redshift with photometric redshift uncertainties, realistic random ellipticity noise for every galaxy and a complicated survey mask. The obtained posterior distributions for the tomographic power spectrum coecients recover the underlying simulated power spectra for both E- and B-modes, where the latter are recovered at a level of 1-2 orders of magnitude below the ellipticity noise level.