Robustifying Approximate Bayesian Computation

Approximate Bayesian computation (ABC) is one of the most popular “likelihood-free” methods. These methods have been applied in a wide range of fields to provide inferences in settings where exact Bayesian approaches are either infeasible or computationally costly. However, the performance of ABC can be unreliable when dealing with model misspecification. To circumvent the poor behavior of ABC in these settings, we propose a novel ABC approach that is robust to model misspecification. This new method delivers more accurate statistical inference under model misspecification than alternatives and also enables the detection of summary statistics that are incompatible with the assumed data-generating process. We demonstrate the effectiveness of our approach through empirical and simulated examples, and show that this approach delivers more accurate estimates and uncertainty quantification over other approaches when the model is misspecified.