  Nowadays in density estimation, posterior rates of convergence for location
and location-scale mixtures of Gaussians are only known under light-tail
assumptions; with better rates achieved by location mixtures. It is
conjectured, but not proved, that the situation should be reversed under heavy
tails assumptions. The conjecture is based on the feeling that there is no need
to achieve a good order of approximation in regions with few data (say, in the
tails), favoring location-scale mixtures which allow for spatially varying
order of approximation. Here we test the previous argument on the Gaussian
errors mean regression model with random design, for which the light tail
assumption is not required for proofs. Although we cannot invalidate the
conjecture due to the lack of lower bound, we find that even with heavy tails
assumptions, location-scale mixtures apparently perform always worst than
location mixtures. However, the proofs suggest to introduce hybrid
location-scale mixtures that are find to outperform both location and
location-scale mixtures, whatever the nature of the tails. Finally, we show
that all tails assumptions can be released at the price of making the prior
distribution covariate dependent.
