偏振测量分析II。极化分量和角度的最佳估计
Polarization measurements analysis II. Best estimators of polarization fraction and angle
摘要：
随着普朗克卫星等高精度偏振测量数据的发布，评估偏振分量和角度估计器的性能变得至关重要。这两个物理量在存在测量噪声的情况下会受到众所周知的偏差的影响，正如本系列第一部分所描述的那样。在本文中，第二部分的系列，我们探讨在何种程度上，各种估计可能纠正的偏见。传统的频率估计的极化分数相比，最近的两个估计：一个灵感来自贝叶斯分析和第二个以下的渐近方法。我们调查这些估计的敏感性的协方差矩阵的不对称性，这可能会在大的数据集。我们提出了第一次之间的比较偏振角估计，并评估统计偏差的角度时，出现的协方差矩阵表现出有效的椭圆。我们还解决了极化分数和角度不确定性估计的准确性的问题。的方法链接到可信区间和方差估计进行了测试，对强大的置信区间方法。从这个估计器池中，我们构建了适应不同用例的配方：构建掩码，计算大型地图，以及处理低S/N数据。更一般地说，我们表明，传统的估计遭受不连续分布在低S/N，而渐近和贝叶斯方法没有。注意给出的估计的输出分布的形状，并与高斯。在这方面，新的渐近方法提出了最好的性能，而贝叶斯输出分布被证明是强烈的不对称，在低S/N的急剧削减。最后，我们提出了一个优化的估计来自贝叶斯分析使用适应先验。
英文摘要：
With the forthcoming release of high precision polarization measurements, such as from the Planck satellite, it becomes critical to evaluate the performance of estimators for the polarization fraction and angle. These two physical quantities suffer from a well-known bias in the presence of measurement noise, as has been described in part I of this series. In this paper, part II of the series, we explore the extent to which various estimators may correct the bias. Traditional frequentist estimators of the polarization fraction are compared with two recent estimators: one inspired by a Bayesian analysis and a second following an asymptotic method. We investigate the sensitivity of these estimators to the asymmetry of the covariance matrix which may vary over large datasets. We present for the first time a comparison among polarization angle estimators, and evaluate the statistical bias on the angle that appears when the covariance matrix exhibits effective ellipticity. We also address the question of the accuracy of the polarization fraction and angle uncertainty estimators. The methods linked to the credible intervals and to the variance estimates are tested against the robust confidence interval method. From this pool of estimators, we build recipes adapted to different use-cases: build a mask, compute large maps, and deal with low S/N data. More generally, we show that the traditional estimators suffer from discontinuous distributions at low S/N, while the asymptotic and Bayesian methods do not. Attention is given to the shape of the output distribution of the estimators, and is compared with a Gaussian. In this regard, the new asymptotic method presents the best performance, while the Bayesian output distribution is shown to be strongly asymmetric with a sharp cut at low S/N.Finally, we present an optimization of the estimator derived from the Bayesian analysis using adapted priors.
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