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.Comment: 11 pages, 14 figures, 3 table
