  Using a Gibbs sampling algorithm for joint CMB estimation and component
separation, we compute the large-scale CMB and foreground posteriors of the
3-yr WMAP temperature data. Our parametric data model includes the cosmological
CMB signal and instrumental noise, a single power law foreground component with
free amplitude and spectral index for each pixel, a thermal dust template with
a single free overall amplitude, and free monopoles and dipoles at each
frequency. This simple model yields a surprisingly good fit to the data over
the full frequency range from 23 to 94 GHz. We obtain a new estimate of the CMB
sky signal and power spectrum, and a new foreground model, including a
measurement of the effective spectral index over the high-latitude sky. A
particularly significant result is the detection of a common spurious offset in
all frequency bands of ~ -13muK, as well as a dipole in the V-band data.
Correcting for these is essential when determining the effective spectral index
of the foregrounds. We find that our new foreground model is in good agreement
with template-based model presented by the WMAP team, but not with their MEM
reconstruction. We believe the latter may be at least partially compromised by
the residual offsets and dipoles in the data. Fortunately, the CMB power
spectrum is not significantly affected by these issues, as our new spectrum is
in excellent agreement with that published by the WMAP team. The corresponding
cosmological parameters are also virtually unchanged.
