Improving ABC via large deviations theory

Sample degeneracy in Approximate Bayesian Computation (ABC) is caused by the difficulty of simulating pseudo-data matching the observed data. In order to mitigate the resulting waste of computational resources and/or bias in the posterior distribution approximation, we propose to weight each parameter proposal by treating the generation of matching pseudo-data, given a “poor” parameter proposal, as a rare event in the sense of Sanov’s Theorem. We experimentally evaluate our methodology through a proof-of-concept implementation.