Section: New Results

Convergence results for approximate Bayesian computation

Participants : Frédéric Cérou, Arnaud Guyader.

This is a collaboration with Gérard Biau (ENS and université Pierre et Marie Curie).

Approximate Bayesian computation (ABC for short) is a family of computational techniques which offer an almost automated solution in situations where evaluation of the posterior likelihood is computationally prohibitive, or whenever suitable likelihoods are not available. In [31] , we analyze the procedure from the point of view of k-nearest neighbor theory and explore the statistical properties of its outputs. We discuss in particular some asymptotic features of the genuine conditional density estimate associated with ABC, which is a new interesting hybrid between a k-nearest neighbor and a kernel method. These are among the very few results on the convergence of ABC, and our assumptions on the underlying probability distribution are minimal.