CMB Power Spectrum Likelihood with ILC
  We extend the ILC method in harmonic space to include the error in its CMB
estimate. This allows parameter estimation routines to take into account the
effect of the foregrounds as well as the errors in their subtraction in
conjunction with the ILC method. Our method requires the use of a model of the
foregrounds which we do not develop here. The reduction of the foreground level
makes this method less sensitive to unaccounted for errors in the foreground
model. Simulations are used to validate the calculations and approximations
used in generating this likelihood function.
