A novel estimator of the polarization amplitude from normally distributed Stokes parameters
A novel estimator of the polarization amplitude from normally distributed Stokes parameters
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DOI：
10.1093/mnras/stu270
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发表时间：
2013-12
影响因子：
4.8
通讯作者：
S. Plaszczynski;L. Montier;L. Montier;F. Levrier;M. Tristram
中科院分区：
文献类型：
--
作者：
S. Plaszczynski;L. Montier;L. Montier;F. Levrier;M. Tristram
我们提出了一种新颖的极化幅度估计器，通过对其正态分布 $(Q,U)$ 斯托克斯分量的单次测量来估计。基于莱斯分布的特性并被称为“MAS”（改进的 ASymptotic），它满足几个理想的标准：（i）它的值位于整个正区域； (ii) 其分布是连续的； （iii）它的信噪比（SNR）从类瑞利形状平滑地转变为高斯形状； (iv) 它是无偏的，并且一旦 SNR 超过 2，就达到其分量方差； (v) 它是分析性的，因此可以用于大型数据集。我们还重新审视了其相关置信区间的构造，并展示了 Feldman-Cousins 处方如何有效地解决完全位于非物理负域中的经典区间问题。这样的间隔可用于识别统计上显着的偏振区域，并反过来为偏振数据构建掩模。然后，我们考虑一般 $[Q,U]$ 协方差矩阵的情况，并对估计器进行泛化，以保留其渐近性质。我们证明它的偏差不依赖于真实的偏振角，并提供了其方差的分析估计。估计值及其方差提供了真实极化幅度的强大点估计，该点估计遵循 SNR 低至 2 的无偏高斯分布。这些结果可应用于将任何正态分布随机变量从笛卡尔坐标转换为极坐标的更一般情况。
We propose a novel estimator of the polarization amplitude from a single measurement of its normally distributed $(Q,U)$ Stokes components. Based on the properties of the Rice distribution and dubbed "MAS" (Modified ASymptotic), it meets several desirable criteria:(i) its values lie in the whole positive region; (ii) its distribution is continuous; (iii) it transforms smoothly with the signal-to-noise ratio (SNR) from a Rayleigh-like shape to a Gaussian one ; (iv) it is unbiased and reaches its components variance as soon as the SNR exceeds 2; (v) it is analytic and can therefore be used on large data-sets. We also revisit the construction of its associated confidence intervals, and show how the Feldman-Cousins prescription efficiently solves the issue of classical intervals lying entirely in the unphysical negative domain. Such intervals can be used to identify statistically significant polarized regions and conversely build masks for polarization data. We then consider the case of a general $[Q,U]$ covariance matrix and perform a generalization of the estimator that preserves its asymptotic properties. We show that its bias does not depend on the true polarization angle, and provide an analytic estimate of its variance. The estimator value, together with its variance, provide a powerful point-estimate of the true polarization amplitude that follows an unbiased Gaussian distribution for an SNR as low as 2. These results can be applied to the much more general case of transforming any normally distributed random variable from Cartesian to polar coordinates.