Bayesian analysis of polarization measurements

Context. A detailed and formal account of polarization measurements using Bayesian analysis is given based on the assumption of gaussian error for the Stokes parameters. This analysis is crucial for the measurement of the polarization degree and angle at low and high signal-to-noise. The treatment serves as a framework for customized analysis of data based on a particular prior suited to the experiment. Aims. The aim is to provide a rigorous and self-consistent Bayesian treatment of polarization measurements and their statistical error focused on the case of a single measurement. Methods. Bayes Theorem is used to derive a variety of posterior distributions for polarization measurements. Results. A framework that may be used to construct accurate polarization point estimates and confidence intervals based on Bayesian ideas is given. The results may be customized for a prior and loss function chosen for a particular experiment.