A Foreground Model Independent Estimation of Joint Posterior of CMB E
  mode Polarization over Large Angular Scales
  Ever since Cosmic Microwave Background (CMB) signal is being measured by
various satellites based observations with increasing experimental accuracies
there has been a parallel increase in the demand for a CMB reconstruction
technique which can provide accurate estimates of CMB signal and the
theoretical angular power spectrum along with reliable statistical error
estimates associated with them. In this work, we estimate the joint posterior
of CMB E mode signal (S) and corresponding theoretical angular power spectrum
(C^E_l) over large angular scales given the simulated polarization observations
of future generation COrE satellite mission. To generate samples from the joint
distribution we employ the ILC technique with prior information of CMB E mode
covariance matrix augmented by a Gibbs sampling technique. We estimate the
marginalized densities of S and C^E_l using the samples from full-posterior.
The best fit cleaned E mode map and the corresponding angular power spectrum
agree well with the input E mode map and the sky power spectrum implying
accurate reconstruction using COrE like observations. Using the samples C^E_l
of all Gibbs chains we estimate the likelihood function P(C^E_l|D) of any
arbitrary C^E_l given simulated observed maps (D) of COrE mission following
Blackwell-Rao estimator. The likelihood function can be seamlessly integrated
to the cosmological parameter estimation method. Apart from producing an
accurate estimate of E mode signal over large angular scales our method also
builds a connection between the component reconstruction and reliable
cosmological parameter estimation using CMB E mode observations over large
angular scales. The entire method does not assume any explicit models for E
mode foreground components in order to remove them, which is an attractive
property since foreground modelling uncertainty does not pose as a challenge in
this case.
