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

We present the first results from a Bayesian analysis of the 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 the best-fit Lambda-CDM 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.