  In this paper, we consider the so-called Shape Invariant Model which stands
for the estimation of a function f0 submitted to a random translation of law g0
in a white noise model. We are interested in such a model when the law of the
deformations is unknown. We aim to recover the law of the process P(f0,g0). In
this perspective, we adopt a Bayesian point of view and find prior on f and g
such that the posterior distribution concentrates at a polynomial rate around
P(f0,g0) when n goes to infinity. We intensively use some Bayesian non
parametric tools coupled with mixture models and believe that some of our
results obtained on this mixture framework may be also of interest for
frequentist point of view.
