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arXiv 1202.4898astro-ph.CO
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宇宙微波背景实验中Fisher矩阵的快速计算

Fast calculation of the Fisher matrix for cosmic microwave background experiments

Franz Elsner, Benjamin D. Wandelt

摘要:

宇宙微波背景(CMB)辐射功率谱系数的Fisher信息矩阵是表征CMB实验信息量的一个基本量。在最一般的情况下,其精确计算与数据点N的数量的三次方成比例,因此对于最先进的调查来说,计算上是禁止的。适用于一个非常大的类别的CMB实验没有特殊的对称性,我们展示了如何计算Fisher矩阵在只有O(N^2 log N)的操作,只要逆噪声协方差矩阵可以应用到一个数据向量的时间O(l_max^3 log l_max)。这一假设是真实的一个很好的近似所有CMB数据集迄今为止。该方法考虑到常见的系统,如任意的天空覆盖和现实的噪声相关性。因此,最优二次功率谱估计也变得可行,在O(N^2 log N)的操作,这一大组的实验。我们讨论了我们的研究结果的相关性,宇宙学的其他领域,最佳功率谱估计发挥了作用。

英文摘要:

The Fisher information matrix of the cosmic microwave background (CMB) radiation power spectrum coefficients is a fundamental quantity that specifies the information content of a CMB experiment. In the most general case, its exact calculation scales with the third power of the number of data points N and is therefore computationally prohibitive for state-of-the-art surveys. Applicable to a very large class of CMB experiments without special symmetries, we show how to compute the Fisher matrix in only O(N^2 log N) operations as long as the inverse noise covariance matrix can be applied to a data vector in time O(l_max^3 log l_max). This assumption is true to a good approximation for all CMB data sets taken so far. The method takes into account common systematics such as arbitrary sky coverage and realistic noise correlations. As a consequence, optimal quadratic power spectrum estimation also becomes feasible in O(N^2 log N) operations for this large group of experiments. We discuss the relevance of our findings to other areas of cosmology where optimal power spectrum estimation plays a role.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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