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In this work, we formalize a new technique to investigate joint posteriordensity of Cosmic Microwave Background (CMB) signal and its theoretical angularpower spectrum given the observed data, using the globalinternal-linear-combination (ILC) method first proposed by Sudevan & Saha(2017). We implement the method on low resolution CMB maps observed by WMAP andPlanck satellite missions, using Gibbs sampling, assuming that the detectornoise is negligible on large angular scales of the sky. The main products ofour analysis are best fit CMB cleaned map and its theoretical angular powerspectrum along with their error estimates. We validate the methodology byperforming Monte Carlo simulations that includes realistic foreground modelsand noise levels consistent with WMAP and Planck observations. Our method hasan unique advantage that the posterior density is obtained without any need toexplicitly model foreground components. Secondly, the power spectrum resultswith the error estimates can be directly used for cosmological parameterestimations.

An Application of Global ILC Algorithm over Large Angular Scales to Estimate CMB Posterior Using Gibbs Sampling