Likelihood methods for CMB experiments
  A great deal of experimental effort is currently being devoted to the precise
measurements of the cosmic microwave background (CMB) sky in temperature and
polarisation. Satellites, balloon-borne, and ground-based experiments
scrutinize the CMB sky at multiple scales, and therefore enable to investigate
not only the evolution of the early Universe, but also its late-time physics
with unprecedented accuracy. The pipeline leading from time ordered data as
collected by the instrument to the final product is highly structured.
Moreover, it has also to provide accurate estimates of statistical and
systematic uncertainties connected to the specific experiment. In this paper,
we review likelihood approaches targeted to the analysis of the CMB signal at
different scales, and to the estimation of key cosmological parameters. We
consider methods that analyze the data in the spatial (i.e., pixel-based) or
harmonic domain. We highlight the most relevant aspects of each approach and
compare their performance.
