We extend the modal decomposition method, previously applied to compress the information in the real-space bispectrum, to the anisotropic redshift-space galaxy bispectrum. In the modal method approach, the bispectrum is expanded on a basis of smooth functions of triangles and their orientations, such that a set of modal expansion coefficients can capture the information in the bispectrum. We assume a reference survey and compute Fisher forecasts for the compressed modal bispectrum and two other basis decompositions of the redshift-space bispectrum in the literature, one based on (single) spherical harmonics and another based on tripolar spherical harmonics. In each case, we compare the forecasted constraints from the compressed statistic with forecasted constraints from the full, uncompressed bispectrum which includes all triangles and orientations. Our main result is that all three compression methods achieve good recovery of the full information content of the bispectrum, but the modal decomposition approach achieves this the most efficiently: only 14 (42) modal expansion coefficients are necessary to obtain constraints that are within 10% (2%) of the full bispectrum result. The next most efficient decomposition is the one based on tripolar spherical harmonics, while the spherical harmonic multipoles are the least efficient.
Geometrical compression: a new method to enhance the BOSS galaxy bispectrum monopole constraints
我们提出了一种新的方法来压缩星系聚类三点统计，并将其应用到红移空间星系双谱测量从BOSS DR 12 CMASS数据考虑$k$ -空间范围的$0.03-0.12\,h/\mathrm{Mpc}$。该方法包括在binning在一起的双谱评价在组的波数形成封闭的三角形具有类似的几何性质：面积，余弦的最大角度和馀下两个角度的余弦之间的比率。这使得我们能够增加双谱测量的数量，例如通过标准分箱（从使用的116到2734个三角形）的因子$23$，否则标准分箱受限于可用于估计导出参数约束所需的协方差矩阵的模拟目录的数量。因此，推断参数$\left(b_1,b_2,f,σ_8\right)$的$68\%$可信区间分别减少了$\left(-39\%,-49\%,-29\%,-22\%\right)$。我们发现非常好的协议与最近获得的替代最大压缩方法的后验。这种新的方法不需要先验计算的数据向量协方差矩阵，并有可能直接适用于其他三点统计（如glaxy聚类，弱引力透镜，21厘米发射线）从未来的调查，如DESI，欧几里德，PFS和SKA测量。
GEOMAX: beyond linear compression for 3pt galaxy clustering statistics
我们提出了GEOMAX算法及其Python实现的双谱测量的两步压缩。第一步组双谱的几何性质，他们的参数，第二步，然后最大化的Fisher信息相对于一组选定的模型参数在每个组。该算法只需要数据向量对参数的导数和少量的模拟数据，从而产生有效的非线性压缩。通过将GEOMAX应用于来自BOSS DR 12 CMASS红移空间星系团数据的双谱测量，我们在全数据向量上相对于标准MCMC将推断参数$\left(b_1,b_2,f,σ_8\right)$的$68\%$可信区间减小了$\left(50.4\%,56.1\%,33.2\%,38.3\%\right)$。我们对100多个星系模型的压缩方法进行了分析和比较，以测试改进的统计意义。平均而言，GEOMAX执行$\sim15\%$优于单独的几何或最大线性压缩，并且与无损一致。鉴于其灵活性，GEOMAX方法有可能最佳地利用各种宇宙学探测器的三点统计数据，如来自当前和未来宇宙学数据集（如DESI，Euclid，PFS和SKA）的弱透镜或线强度图。
Hierarchical summaries for primordial non-Gaussianities
Laboratoire d’Annecy de Physique Theorique (LAPTh), CNRS/USMB（拉普斯理论物理实验室）；CNRS & Sorbonne Université, Institut d’Astrophysique de Paris (IAP)（法国国家科学研究中心与索邦大学，巴黎天体物理学研究所）；Department of Physics and Astronomy, Johns Hopkins University（约翰霍普金斯大学物理与天文系）；Department of Applied Mathematics and Statistics, Johns Hopkins University（约翰霍普金斯大学应用数学与统计系）；Center for Computational Astrophysics, Flatiron Institute（平顿研究所计算天体物理学中心）
