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

Abstract

Abstract In this work, we formalize a new technique to investigate the joint posterior density of the cosmic microwave background (CMB) signal and its theoretical angular power spectrum given the observed data, using the global internal-linear-combination method first proposed in a paper by Sudevan & Saha in 2017. We implement the method on low-resolution CMB maps observed by the Wilkinson Microwave Anisotropy Probe (WMAP) and the Planck satellite missions, using Gibbs sampling, assuming that the detector noise is negligible on large angular scales of the sky. The main products of our analysis are a best-fit cleaned CMB map and its theoretical angular power spectrum, along with their error estimates. We validate the method by performing Monte Carlo simulations that include realistic foreground models and noise levels consistent with WMAP and Planck observations. Our method has a unique advantage: the posterior density is obtained without any need to explicitly model foreground components. Second, the power spectrum results with the error estimates can be directly used for cosmological parameter estimations.