  We introduce a method to quantify the quality-of-fit between data and
observables depending on the large scale Galactic magnetic field. We combine
WMAP5 polarized synchrotron data and Rotation Measures of extragalactic sources
in a joint analysis to obtain best fit parameters and confidence levels for GMF
models common in the literature. None of the existing models provide a good fit
in both the disk and halo regions, and in many instances best-fit parameters
are quite different than the original values. We note that probing a very large
parameter space is necessary to avoid false likelihood maxima. The thermal and
relativistic electron densities are critical for determining the GMF from the
observables but they are not well constrained. We show that some
characteristics of the electron densities can already be constrained using our
method and with future data it may be possible to carry out a self-consistent
analysis in which models of the GMF and electron densities are simultaneously
optimized.
