An Estimation of Joint Posterior of CMB Over Large Angular Scales Using Gibbs ILC Method

Abstract

We present a detailed study of the Gibbs ILC method which provides a novel way to estimate the joint posterior density of Cosmic Microwave Background (CMB) signal (S) and its theoretical angular power spectrum ($\mathbf{C_\ell }$) given the observed data in a model-independent manner. In order to generate samples from the joint CMB posterior density, we employ the internal-linear-combination (ILC) technique incorporated with prior information of the theoretical CMB covariance matrix augmented by the Gibbs sampling technique. We implement the method on low-resolution CMB maps simulated at WMAP and Planck frequency channels, assuming that the detector noise is negligible at large angular scales of the sky. We estimate a best-fit CMB cleaned map and its theoretical angular power spectrum (hereafter APS) along with the respective confidence intervals.