  We present a new blind formulation of the Cosmic Microwave Background (CMB)
inference problem. The approach relies on a phenomenological model of the
multi-frequency microwave sky without the need for physical models of the
individual components. For all-sky and high resolution data, it unifies parts
of the analysis that have previously been treated separately, such as component
separation and power spectrum inference. We describe an efficient sampling
scheme that fully explores the component separation uncertainties on the
inferred CMB products such as maps and/or power spectra. External information
about individual components can be incorporated as a prior giving a flexible
way to progressively and continuously introduce physical component separation
from a maximally blind approach. We connect our Bayesian formalism to existing
approaches such as Commander, SMICA and ILC, and discuss possible future
extensions.
