  We apply a previously developed Gibbs sampling framework to the foreground
corrected 3-yr WMAP polarization data and compute the power spectrum and
residual foreground template amplitude posterior distributions. We first
analyze the co-added Q- and V-band data, and compare our results to the
likelihood code published by the WMAP team. We find good agreement, and thus
verify the numerics and data processing steps of both approaches. However, we
also analyze the Q- and V-bands separately, allowing for non-zero EB
cross-correlations and including two individual foreground template amplitudes
tracing synchrotron and dust emission. In these analyses, we find tentative
evidence of systematics: The foreground tracers correlate with each of the Q-
and V-band sky maps individually, although not with the co-added QV map; there
is a noticeable negative EB cross-correlation at l <~ 16 in the V-band map; and
finally, when relaxing the constraints on EB and BB, noticeable differences are
observed between the marginalized band powers in the Q- and V-bands. Further
studies of these features are imperative, given the importance of the low-l EE
spectrum on the optical depth of reionization tau and the spectral index of
scalar perturbations n_s.
