Christian Robert

ABC-Gibbs: componentwise approximate Bayesian computation

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. [Joint work with Grégoire Clarté, Robin Ryder and
Julien Stoehr, Paris Dauphine]

My slides will be close to

https://www.slideshare.net/xianblog/abcgibbs

and the paper is available as

https://arxiv.org/abs/1905.13599