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.
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