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arXiv 0804.2645astro-ph
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CMB实验中参数分量分离的极大似然算法

Maximum Likelihood algorithm for parametric component separation in CMB experiments

R. Stompor, S. Leach, F. Stivoli, C. Baccigalupi

摘要:

本文讨论了一种从宇宙微波背景(CMB)各向异性数据中分离微波多频天图的方法。该算法基于Eriksen等人最近详细阐述的两步、参数化、基于可能性的技术,(2006),其中在实际分离成分之前估计前景光谱参数。与以前的方法相比,我们完成了前一项任务的帮助下,解析推导的似然函数的频谱参数,其中,我们表明,产生估计等于极大似然值的完整的多维数据问题。然后,我们使用这些估计,通过标准的,广义最小二乘类程序执行第二步。我们证明,所提出的方法是相当于一个直接的最大化的全部数据的可能性,这是重铸在一个计算上易于处理的形式。我们使用相应的曲率矩阵来表征恢复参数的统计特性。我们将在形式主义的CMB数据集的一些基本特征,如不均匀的像素域噪声,未知的地图偏移以及校准误差,并研究其后果的分离。我们发现,校准是可能有一个占主导地位的影响,一个现实的CMB实验的光谱参数测定的精度。我们将算法应用于模拟数据,并讨论结果。我们的重点是部分天空,总强度和偏振,CMB实验,如计划气球和地面的努力,然而,这里提出的技术也应该适用于全天空的数据,例如,由WMAP产生的和普朗克预期。

英文摘要:

We discuss an approach to the component separation of microwave, multi-frequency sky maps as those typically produced from Cosmic Microwave Background (CMB) Anisotropy data sets. The algorithm is based on the two step, parametric, likelihood-based technique recently elaborated on by Eriksen et al., (2006), where the foreground spectral parameters are estimated prior to the actual separation of the components. In contrast with the previous approaches, we accomplish the former task with help of an analytically-derived likelihood function for the spectral parameters, which, we show, yields estimates equal to the maximum likelihood values of the full multi-dimensional data problem. We then use these estimates to perform the second step via the standard, generalized-least-square-like procedure. We demonstrate that the proposed approach is equivalent to a direct maximization of the full data likelihood, which is recast in a computationally tractable form. We use the corresponding curvature matrices to characterize statistical properties of the recovered parameters. We incorporate in the formalism some of the essential features of the CMB data sets, such as inhomogeneous pixel domain noise, unknown map offsets as well as calibration errors and study their consequences for the separation. We find that the calibration is likely to have a dominant effect on the precision of the spectral parameter determination for a realistic CMB experiment. We apply the algorithm to simulated data and discuss the results. Our focus is on partial-sky, total-intensity and polarization, CMB experiments such as planned balloon-borne and ground-based efforts, however, the techniques presented here should be also applicable to the full-sky data as for instance, those produced by WMAP and anticipated from Planck.

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