Fewer mocks and less noise: Reducing the dimensionality of cosmological observables with subspace projections
Fewer mocks and less noise: Reducing the dimensionality of cosmological observables with subspace projections
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DOI：
10.1103/physrevd.103.043508
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发表时间：
2020-09
影响因子：
5
通讯作者：
O. Philcox;M. Ivanov;M. Zaldarriaga;M. Simonović;M. Schmittfull
中科院分区：
文献类型：
--
作者：
O. Philcox;M. Ivanov;M. Zaldarriaga;M. Simonović;M. Schmittfull
创建精确且低噪声的协方差矩阵是现代宇宙学中的一项艰巨挑战。我们提出了一种形式主义压缩任意可观的到一个小数目的箱投影到一个特定的模型子空间，最大限度地减少了先验平均对数似然误差。较低的维度导致协方差矩阵噪声的显著降低，从而显著减少了需要计算的模拟的数量。给定一个理论模型，一组先验和一个简单的协方差模型，我们的方法通过使用奇异值分解来构建一个接近欧几里德的可观测基础;通过限制到前几个基向量，我们可以在低维子空间中捕获几乎所有的约束力。与传统方法不同，该方法可以针对特定的分析进行定制，并捕获Fisher矩阵中不存在的非线性，确保可以重现全部可能性。该程序是验证与全形状分析的重子振荡光谱巡天（BOSS）DR 12模拟目录的功率谱，显示96仓功率谱可以被替换为12个子空间系数不偏输出宇宙学，这使得精确的参数推断只使用$\ensuremath{\sim}100$模拟。这样的分解有助于准确测试功率谱协方差;对于最大的BOSS数据块，我们发现：（a）分析协方差提供准确的模型（有或没有三谱项）;以及（B）使用来自MultiDark-Patchy模拟的样本协方差在${\mathrm{\ensuremath {\Omega}_{m}$中引起$\ensuremath {\sim}0.5\ensuremath {\sigma}$偏移，除非应用子空间投影。该方法很容易扩展到高阶统计量;$\ensuremath{\sim}2000$-bin双谱可以压缩到只有$\ensuremath{\sim}10$系数，允许精确的分析使用几个模拟，而不必增加bin大小。
Creating accurate and low-noise covariance matrices represents a formidable challenge in modern-day cosmology. We present a formalism to compress arbitrary observables into a small number of bins by projection into a model-specific subspace that minimizes the prior-averaged log-likelihood error. The lower dimensionality leads to a dramatic reduction in covariance matrix noise, significantly reducing the number of mocks that need to be computed. Given a theory model, a set of priors, and a simple model of the covariance, our method works by using singular value decompositions to construct a basis for the observable that is close to Euclidean; by restricting to the first few basis vectors, we can capture almost all the constraining power in a lower-dimensional subspace. Unlike conventional approaches, the method can be tailored for specific analyses and captures nonlinearities that are not present in the Fisher matrix, ensuring that the full likelihood can be reproduced. The procedure is validated with full-shape analyses of power spectra from Baryon Oscillation Spectroscopic Survey (BOSS) DR12 mock catalogs, showing that the 96-bin power spectra can be replaced by 12 subspace coefficients without biasing the output cosmology; this allows for accurate parameter inference using only $\ensuremath{\sim}100$ mocks. Such decompositions facilitate accurate testing of power spectrum covariances; for the largest BOSS data chunk, we find the following: (a) analytic covariances provide accurate models (with or without trispectrum terms); and (b) using the sample covariance from the MultiDark-Patchy mocks incurs a $\ensuremath{\sim}0.5\ensuremath{\sigma}$ shift in ${\mathrm{\ensuremath{\Omega}}}_{m}$, unless the subspace projection is applied. The method is easily extended to higher order statistics; the $\ensuremath{\sim}2000$-bin bispectrum can be compressed into only $\ensuremath{\sim}10$ coefficients, allowing for accurate analyses using few mocks and without having to increase the bin sizes.