Point and Interval Estimation on the Degree and the Angle of Polarization: A Bayesian Approach

Abstract

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.