Precision cosmology with the cosmic microwave background

The cosmic microwave background (CMB) is a cornerstone of modern cosmology; extracting cosmological information from it requires high accuracy instruments as well as a great deal of signal processing. This article highlights a critical step of the CMB data processing pipeline: the construction of a likelihood function for the statistical exploitation of CMB data. Since this task is based on a sky map of CMB anisotropies, it requires some understanding of spherical analysis. The aim of this article is to introduce the reader to some of the issues related to spherical analysis for the CMB. It opens with a short overview of the CMB and explain how to build a spherical likelihood for it, starting with an idealized case of perfect (fullsky, noise-free) CMB observations and then moving to the actual computations with imperfect data using specific tools for signal processing on the sphere.