First‐YearWilkinson Microwave Anisotropy Probe(WMAP) Observations: Parameter Estimation Methodology

We describe our methodology for comparing the WMAP measurements of the cosmicmicrowave background (CMB) and other complementary data sets to theoreticalmodels. The unprecedented quality of the WMAP data, and the tight constraintson cosmological parameters that are derived, require a rigorous analysis sothat the approximations made in the modeling do not lead to significant biases.We describe our use of the likelihood function to characterize the statisticalproperties of the microwave background sky. We outline the use of the MonteCarlo Markov Chains to explore the likelihood of the data given a model todetermine the best fit cosmological parameters and their uncertainties. We addto the WMAP data the l>~700 CBI and ACBAR measurements of the CMB, the galaxypower spectrum at z~0 obtained from the 2dF galaxy redshift survey (2dFGRS),and the matter power spectrum at z~3 as measured with the Ly alpha forest.These last two data sets complement the CMB measurements by probing the matterpower spectrum of the nearby universe. Combining CMB and 2dFGRS requires thatwe include in our analysis a model for galaxy bias, redshift distortions, andthe non-linear growth of structure. We show how the statistical and systematicuncertainties in the model and the data are propagated through the fullanalysis.