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In this article we present a formalism to incorporate the partial-sky maps tothe Gibbs ILC algorithm to estimate the joint posterior density of the CosmicMicrowave Background (CMB) signal and the theoretical CMB angular powerspectrum given the observed CMB maps. In order to generate the partial-sky mapswe mask all the observed CMB maps provided by WMAP and Planck satellite missionusing a Gaussian smoothed mask formed on the basis of thermal dust emissions inPlanck 353 GHz map. The central galactic region from all the input maps isremoved after the application of the smoothed mask. While implementing theGibbs ILC method on the partial-sky maps, we convert the partial-sky cleanedangular power spectrum to the full-sky angular power spectrum using themode-mode coupling matrix estimated from the smoothed mask. The main productsof our analysis are partial-sky cleaned best-fit CMB map and an estimate of theunderlying full-sky theoretical CMB angular power spectrum along with theirerror estimates. We validate the methodology by performing detailed Monte Carlosimulations after using realistic models of foregrounds and detector noiseconsistent with the WMAP and Planck frequency channels used in our analysis. Wecan estimate the posterior density and full-sky theoretical CMB angular powerspectrum, without any need to explicitly model the foreground components, frompartial-sky maps using our method. Another important feature of this method isthat the power spectrum results along with the error estimates can be directlyused for cosmological parameter estimations.

A Partial-Sky Gibbs ILC Approach for the Estimation of CMB Posterior over Large Angular Scales of the Sky