  In this paper, we describe a Bayesian nonparametric approach to make
inference for a bivariate spherically symmetric distribution. We consider a
Dirichlet invariant process prior on the set of all bivariate spherically
symmetric distributions and we derive the Dirichlet invariant process
posterior. Indeed, our approach is an extension of Dirichlet invariant process
for the symmetric distributions on the real line to a bivariate spherically
symmetric distribution where the underlying distribution is invariant under a
finite group of rotations. Moreover, we obtain the Dirichlet invariant process
posterior for the infinite transformation group and we prove that it approaches
to Dirichlet process.
