偏振度和偏振角的点估计和区间估计。贝叶斯方法
Point and Interval Estimation on the Degree and the Angle of Polarization. A Bayesian approach
摘要：
线性偏振测量提供了对两个量的访问，即偏振度（DOP）和偏振角（AOP）。这项工作的目的是给一个完整和简洁的概述如何分析偏振测量。我们审查区间估计的DOP与频率和贝叶斯方法。点估计的DOP和区间估计的AOP进一步调查与贝叶斯方法，以配合观测的需要。点估计和区间估计是为频率论和贝叶斯统计数值计算的。进行蒙特卡罗模拟以阐明计算的意义。在观测条件下，真实的DOP和AOP是未知的，因此基于真实值的经典统计考虑不能直接使用。相比之下，贝叶斯统计可以很好地处理未知的真值，并直接为DOP和AOP生成点和区间估计。使用贝叶斯方法，我们展示了如何选择DOP点估计的基础上测得的信噪比。经典方法和贝叶斯方法的DOP区间估计在低信噪比的极限上存在很大差异。首次提出了基于观测数据的AOP区间估计。所有的结果都可以通过绘图和参数拟合直接使用。
英文摘要：
Linear polarization measurements provide access to two quantities, the degree (DOP) and the angle of polarization (AOP). The aim of this work is to give a complete and concise overview of how to analyze polarimetric measurements. We review interval estimations for the DOP with a frequentist and a Bayesian approach. Point estimations for the DOP and interval estimations for the AOP are further investigated with a Bayesian approach to match observational needs. Point and interval estimations are calculated numerically for frequentist and Bayesian statistics. Monte Carlo simulations are performed to clarify the meaning of the calculations. Under observational conditions, the true DOP and AOP are unknown, so that classical statistical considerations - based on true values - are not directly usable. In contrast, Bayesian statistics handles unknown true values very well and produces point and interval estimations for DOP and AOP, directly. Using a Bayesian approach, we show how to choose DOP point estimations based on the measured signal-to-noise ratio. Interval estimations for the DOP show great differences in the limit of low signal-to-noise ratios between the classical and Bayesian approach. AOP interval estimations that are based on observational data are presented for the first time. All results are directly usable via plots and parametric fits.
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