Probably approximate Bayesian computation: nonasymptotic convergence of ABC under misspecification
This provides theoretical guarantees for ABC methods under misspecification, which is important for practitioners in Bayesian statistics dealing with complex models where likelihood computation is intractable.
The paper develops theoretical bounds for the distance between statistics in approximate Bayesian computation (ABC), showing that some versions are robust to misspecification with explicit dependence on parameter dimension and number of statistics, and proposes a sequential Monte Carlo sampler that improves upon state-of-the-art methods.
Approximate Bayesian computation (ABC) is a widely used inference method in Bayesian statistics to bypass the point-wise computation of the likelihood. In this paper we develop theoretical bounds for the distance between the statistics used in ABC. We show that some versions of ABC are inherently robust to misspecification. The bounds are given in the form of oracle inequalities for a finite sample size. The dependence on the dimension of the parameter space and the number of statistics is made explicit. The results are shown to be amenable to oracle inequalities in parameter space. We apply our theoretical results to given prior distributions and data generating processes, including a non-parametric regression model. In a second part of the paper, we propose a sequential Monte Carlo (SMC) to sample from the pseudo-posterior, improving upon the state of the art samplers.