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.