Bayesian Power Spectrum Analysis of the First-Year Wilkinson Microwave Anisotropy Probe Data

Abstract

We present the first results from a Bayesian analysis of the Wilkinson Microwave Anisotropy Probe (WMAP) first-year data using a Gibbs sampling technique. Using two independent, parallel supercomputer codes, we analyze the WMAP Q, V, and W bands. The analysis results in a full probabilistic description of the information the WMAP data set contains about the power spectrum and the all-sky map of the cosmic microwave background anisotropies. We present the complete probability distributions for each Cl, including any non-Gaussianities of the power spectrum likelihood. While we find good overall agreement with the previously published WMAP spectrum, our analysis uncovers discrepancies in the power spectrum estimates at low-l multipoles. For example, we claim that the best-fit ΛCDM model is consistent with the C2 inferred from our combined Q+V+W analysis, with a 10% probability of an even larger theoretical C2. Based on our exact analysis, we can therefore attribute the ``low-quadrupole issue'' to a statistical fluctuation.