  This paper deals with the estimation of the unknown distribution of hidden
random variables from the observation of pairwise comparisons between these
variables. This problem is inspired by recent developments on Bradley-Terry
models in random environment since this framework happens to be relevant to
predict for instance the issue of a championship from the observation of a few
contests per team. This paper provides three contributions on a Bayesian
nonparametric approach to solve this problem. First, we establish contraction
rates of the posterior distribution. We also propose a Markov Chain Monte Carlo
algorithm to approximately sample from this posterior distribution inspired
from a recent Bayesian nonparametric method for hidden Markov models. Finally,
the performance of this algorithm are appreciated by comparing predictions on
the issue of a championship based on the actual values of the teams and those
obtained by sampling from the estimated posterior distribution.
