  Approximate Bayesian computation methods are useful for generative models
with intractable likelihoods. These methods are however sensitive to the
dimension of the parameter space, requiring exponentially increasing resources
as this dimension grows. To tackle this difficulty, we explore a Gibbs version
of the ABC approach that runs component-wise approximate Bayesian computation
steps aimed at the corresponding conditional posterior distributions, and based
on summary statistics of reduced dimensions. While lacking the standard
justifications for the Gibbs sampler, the resulting Markov chain is shown to
converge in distribution under some partial independence conditions. The
associated stationary distribution can further be shown to be close to the true
posterior distribution and some hierarchical versions of the proposed mechanism
enjoy a closed form limiting distribution. Experiments also demonstrate the
gain in efficiency brought by the Gibbs version over the standard solution.
