Estimation of Faraday Rotation Measures of the Near Galactic Sky Using Gaussian Process Models

Our primary goal is to obtain a smoothed summary estimate of the magnetic field generated in and near to the Milky Way by using Faraday rotation measures (RM's). Each RM in our data set provides an integrated measure of the effect of the magnetic field along the entire line of sight to an extragalactic radio source. The ability to estimate the magnetic field generated locally by our galaxy and its environs will help astronomers distinguish local versus distant properties of the universe. RM's can be considered analogous to geostatistical data on a sphere. In order to model such data, we employ a Bayesian process convolution approach which uses Markov chain Monte Carlo (MCMC) for estimation and prediction. Complications arise due to contamination in the RM measurements, and we resolve these by means of a mixture prior on the errors.