First-year Wilkinson Microwave Anisotropy Probe (WMAP) observations:: Parameter estimation methodology

We describe our methodology for comparing the Wilkinson-Microwave Anisotropy Probe (WMAP) measurements of the cosmic microwave background (CMB) and other complementary data sets to theoretical models. The unprecedented quality of the WMAP data and the tight constraints on cosmological parameters that are derived require a rigorous analysis so that the approximations made in the modeling do not lead to significant biases. We describe our use of the likelihood function to characterize the statistical properties of the microwave background sky. We outline the use of the Monte Carlo Markov Chains to explore the likelihood of the data given a model to determine the best-fit cosmological parameters and their uncertainties. We add to the WMAP data the lgreater than or similar to700 Cosmic Background Imager (CBI) and Arcminute Cosmology Bolometer Array Receiver (ACBAR) measurements of the CMB, the galaxy power spectrum at zsimilar to0 obtained from the Two-Degree Field Galaxy Redshift Survey (2dFGRS), and the matter power spectrum at zsimilar to3 as measured with the Lyalpha forest. These last two data sets complement the CMB measurements by probing the matter power spectrum of the nearby universe. Combining CMB and 2dFGRS requires that we include in our analysis a model for galaxy bias, redshift distortions, and the nonlinear growth of structure. We show how the statistical and systematic uncertainties in the model and the data are propagated through the full analysis.