We propose a solution to the CMB component separation problem based on
standard 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 evaluated by
a chi^2 statistic. Then we fix all non-linear 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 rigorously 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
and six-year WMAP data based on realistic models, and show that separation at
the muK 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.Comment: 20 pages, 10 figures, submitted to ApJ. For a high-resolution
version, see http://www.astro.uio.no/~hke/docs/eriksen_et_al_fgfit.p