2006ApJ...641..665E

We propose a method for CMB component separation based on standard Bayesian parameter estimation techniques. We assume a parametric spectral model for each signal component and fit the corresponding parameters pixel by pixel in a two-stage process. First we fit for the full parameter set (e.g., component amplitudes and spectral indices) in low-resolution and high signal-to-noise ratio maps using MCMC, obtaining both best-fit values for each parameter and the associated uncertainty. The goodness of fit is approximated by a χ² statistic. Then we fix all nonlinear parameters at their low-resolution best-fit values and solve analytically for high-resolution component amplitude maps. This likelihood approach has many advantages: the fitted model may be chosen freely, and the method is therefore completely general; all assumptions are transparent; no restrictions on spatial variations of foreground properties are imposed; the results may be monitored by goodness-of-fit tests; and, most importantly, we obtain reliable error estimates on all estimated quantities. We apply the method to simulated Planck satellite and 6 year WMAP data based on realistic models and show that separation at the microkelvin level is indeed possible in these cases. We also outline how the foreground uncertainties may be rigorously propagated through to the CMB power spectrum and cosmological parameters using a Gibbs sampling technique.