  Sparsity has been recently introduced in cosmology for weak-lensing and CMB
data analysis for different applications such as denoising, component
separation or inpainting (i.e. filling the missing data or the mask). Although
it gives very nice numerical results, CMB sparse inpainting has been severely
criticized by top researchers in cosmology, based on arguments derived from a
Bayesian perspective. Trying to understand their point of view, we realize that
interpreting a regularization penalty term as a prior in a Bayesian framework
can lead to erroneous conclusions. This paper is by no means against the
Bayesian approach, which has proven to be very useful for many applications,
but warns about a Bayesian-only interpretation in data analysis, which can be
misleading in some cases.
