Extreme data compression for the CMB
Extreme data compression for the CMB
复制标题
CMB 的极端数据压缩
DOI：
10.1103/physrevd.93.083525
复制
发表时间：
2015
影响因子：
5
通讯作者：
S. Dodelson
中科院分区：
文献类型：
--
作者：
A. Zablocki;S. Dodelson
我们将 Karhunen-Loeve 方法应用于宇宙微波背景（CMB）数据集，并表明我们可以在一分钟内恢复输入宇宙学并获得 Λ 冷暗物质宇宙学中的边缘化可能性，比马尔可夫链蒙特卡罗方法快得多。这是通过在每个多极点 l 处形成功率谱的线性组合，并求解联立方程组以使 Fisher 矩阵局部不变来实现的。我们不需要对整个参数空间进行完整的似然评估，而是只需要评估感兴趣的参数的似然，数据压缩有效地边缘化所有其他参数。加权向量包含有关参数对 CMB 各向异性功率谱 Cl 的物理影响的见解。这些矢量的形状和幅度可以直观地感受宇宙微波背景的物理性质、观测到的光谱对宇宙学参数的敏感性以及不同实验对宇宙学参数的相对敏感性。我们在精确理论 Cl 以及从基准宇宙学的随机实现生成的类似威尔金森微波各向异性探针 (WMAP) 的 CMB 数据集上测试了该方法，将压缩结果与使用 CosmoMC 的完全似然分析的结果进行比较。此外，在证明该方法有效后，我们将其应用于 WMAP 七年数据发布的温度功率谱，并讨论我们的方法应用于真实数据集的成功和局限性。 « less
We apply the Karhunen-Loeve methods to cosmic microwave background (CMB) data sets, and show that we can recover the input cosmology and obtain the marginalized likelihoods in Λ cold dark matter cosmologies in under a minute, much faster than Markov chain Monte Carlo methods. This is achieved by forming a linear combination of the power spectra at each multipole l, and solving a system of simultaneous equations such that the Fisher matrix is locally unchanged. Instead of carrying out a full likelihood evaluation over the whole parameter space, we need evaluate the likelihood only for the parameter of interest, with the data compression effectively marginalizing over all other parameters. The weighting vectors contain insight about the physical effects of the parameters on the CMB anisotropy power spectrum Cl. The shape and amplitude of these vectors give an intuitive feel for the physics of the CMB, the sensitivity of the observed spectrum to cosmological parameters, and the relative sensitivity of different experiments to cosmological parameters. We test this method on exact theory Cl as well as on a Wilkinson Microwave Anisotropy Probe (WMAP)-like CMB data set generated from a random realization of a fiducial cosmology, comparing the compression results to those frommore » a full likelihood analysis using CosmoMC. Furthermore, after showing that the method works, we apply it to the temperature power spectrum from the WMAP seven-year data release, and discuss the successes and limitations of our method as applied to a real data set.« less