Placing Confidence Limits on Polarization Measurements

The determination of the true source polarization given a set of measurements is complicated by the requirement that the polarization always be positive. This positive bias also hinders construction of upper limits, uncertainties, and confidence regions, especially at low signal-to-noise ratios (S/Ns). We take a Bayesian approach to creating confidence regions and upper limits by integrating over the likelihood function for polarization measurements. These regions are valid for both low- and high-S/N measurements.