Exact joint likelihood of pseudo-Cl estimates from correlated Gaussian cosmological fields
Exact joint likelihood of pseudo-Cl estimates from correlated Gaussian cosmological fields
复制标题
来自相关高斯宇宙场的伪 Cl 估计的精确联合似然
DOI：
10.1093/mnras/stz3225
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发表时间：
2020
影响因子：
4.8
通讯作者：
Upham R
中科院分区：
文献类型：
--
作者：
Upham R
我们给出了从任意数目的高斯宇宙场测量的伪C-ℓ功率谱估计的精确联合似然估计。我们的方法既适用于自旋0的场，也适用于自旋2的场，包括两者的混合物，并且与宇宙微波背景(CMB)、弱透镜和星系团分析有关。我们证明了高斯宇宙场与掩模混合的方式保持了它们的高斯性，并且在不对掩模几何作任何假设的情况下，导出了切空球谐系数协方差的精确表达式，即伪a-ℓms。然后，我们证明了每个自或交叉伪C-ℓ估计量都可以写成一个二次型，并且应用二次型的已知联合分布来获得在存在任意掩码的情况下一组伪C-ℓ估计的精确联合似然。我们证明了同样的形式可以用来获得二次最大似然功率谱估计的精确联合似然。以CMB的偏振为例，我们通过模拟表明，我们的似然估计恢复了EE、BB和EB伪Cℓ功率谱的完整、准确的多变量分布。在一个统计精度不断提高的时代，我们的方法提供了一条从未来的CMB和大规模结构调查中获得稳健的宇宙学约束的途径。
We present the exact joint likelihood of pseudo-Cℓpower spectrum estimates measured from an arbitrary number of Gaussian cosmological fields. Our method is applicable to both spin-0 fields and spin-2 fields, including a mixture of the two, and is relevant to cosmic microwave background (CMB), weak lensing, and galaxy clustering analyses. We show that Gaussian cosmological fields are mixed by a mask in such a way that retains their Gaussianity and derive exact expressions for the covariance of the cut-sky spherical harmonic coefficients, the pseudo-aℓms, without making any assumptions about the mask geometry. We then show that each auto or cross-pseudo-Cℓestimator can be written as a quadratic form, and apply the known joint distribution of quadratic forms to obtain the exact joint likelihood of a set of pseudo-Cℓestimates in the presence of an arbitrary mask. We show that the same formalism can be applied to obtain the exact joint likelihood of quadratic maximum likelihood power spectrum estimates. Considering the polarization of the CMB as an example, we show using simulations that our likelihood recovers the full, exact multivariate distribution ofEE,BB, andEBpseudo-Cℓpower spectra. Our method provides a route to robust cosmological constraints from future CMB and large-scale structure surveys in an era of ever-increasing statistical precision.