Bayesian analysis of white noise levels in the 5-year WMAP data

TL;DR

This paper introduces a Bayesian method to accurately estimate white noise levels in CMB sky maps, applied to WMAP data, revealing slight biases in the initially provided noise estimates and confirming the method's practical utility.

Contribution

A new Bayesian framework for estimating white noise levels in CMB maps, integrated into a Gibbs sampler, validated on simulated data and applied to WMAP 5-year data.

Findings

Estimated noise bias of 0.5-1.0% in WMAP maps

Validated Bayesian method on simulated data

Confirmed correctness of WMAP's internal noise values

Abstract

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.