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arXiv 1402.3593astro-ph.CO
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宇宙微波背景实验的信息增益

Information Gains from Cosmic Microwave Background Experiments

Sebastian Seehars, Adam Amara, Alexandre Refregier, Aseem Paranjape, Joël Akeret

备注：
Published version. 14 pages, 4 figures, 1 table
发表信息：
Phys. Rev. D 90, 023533 (2014)
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摘要：

为了阐明暗能量和暗物质所带来的基本问题，人们进行了大量的实验，并结合起来约束宇宙学模型。我们提出了一种新的方法来量化从一系列实验中更新参数约束所获得的信息，这些实验可以补充早期的测量或取代它们。为此，我们使用Kullback-Leibler散度或信息论中的相对熵来测量来自一对实验的模型参数空间中的后验分布的差异。我们应用这种形式主义的历史系列的宇宙微波背景实验，从回旋镖WMAP，SPT，普朗克。考虑到这些实验的不同组合，因此，我们估计以比特为单位的信息增益，并区分统计误差减少的贡献和对应于参数中心值显著偏移的“惊喜”。对于这个实验系列，我们发现个体相对熵增益范围从大约1到30比特。在某些情况下，例如，当比较WMAP和普朗克的结果，我们发现，收益主要是由惊喜，而不是统计精度的提高。我们讨论了这种技术如何提供了一个有用的工具，既可以量化宇宙学探测器的数据的约束力和检测实验之间的紧张关系。

英文摘要：

To shed light on the fundamental problems posed by Dark Energy and Dark Matter, a large number of experiments have been performed and combined to constrain cosmological models. We propose a novel way of quantifying the information gained by updates on the parameter constraints from a series of experiments which can either complement earlier measurements or replace them. For this purpose, we use the Kullback-Leibler divergence or relative entropy from information theory to measure differences in the posterior distributions in model parameter space from a pair of experiments. We apply this formalism to a historical series of Cosmic Microwave Background experiments ranging from Boomerang to WMAP, SPT, and Planck. Considering different combinations of these experiments, we thus estimate the information gain in units of bits and distinguish contributions from the reduction of statistical errors and the `surprise' corresponding to a significant shift of the parameters' central values. For this experiment series, we find individual relative entropy gains ranging from about 1 to 30 bits. In some cases, e.g. when comparing WMAP and Planck results, we find that the gains are dominated by the surprise rather than by improvements in statistical precision. We discuss how this technique provides a useful tool for both quantifying the constraining power of data from cosmological probes and detecting the tensions between experiments.

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