Bayesian analysis of white noise levels in the 5-year WMAP data
  We develop a new Bayesian method for estimating white noise levels in CMB sky
maps, and apply this algorithm to the 5-year WMAP data. We assume that the
amplitude of the noise RMS is scaled by a constant value, alpha, relative to a
pre-specified noise level. We then derive the corresponding conditional
density, P(alpha | s, Cl, d), which is subsequently integrated into a general
CMB Gibbs sampler. We first verify our code by analyzing simulated data sets,
and then apply the framework to the WMAP data. For the foreground-reduced
5-year WMAP sky maps and the nominal noise levels initially provided in the
5-year data release, we find that the posterior means typically range between
alpha=1.005 +- 0.001 and alpha=1.010 +- 0.001 depending on differencing
assembly, indicating that the noise level of these maps are biased low by
0.5-1.0%. The same problem is not observed for the uncorrected WMAP sky maps.
After the preprint version of this letter appeared on astro-ph., the WMAP team
has corrected the values presented on their web page, noting that the initially
provided values were in fact estimates from the 3-year data release, not from
the 5-year estimates. However, internally in their 5-year analysis the correct
noise values were used, and no cosmological results are therefore compromised
by this error. Thus, our method has already been demonstrated in practice to be
both useful and accurate.
