$γ$-ABC: Outlier-Robust Approximate Bayesian Computation based on Robust Divergence Estimator

Making a reliable inference in complex models is an essential issue in statistical modeling. However, approximate Bayesian computation (ABC) proposed for highly complex models that have uncomputable likelihood is greatly affected by the sensitivity of the data discrepancy to outliers. Even using a data discrepancy with robust functions such as the Huber function does not entirely bypass its negative effects. In this paper, we propose a novel divergence estimator based on robust divergence and to use it as a data discrepancy in the ABC framework. Furthermore, we show that our estimator has an effective robustness property, known as the redescending property. Our estimator also enjoys ideal properties such as asymptotic unbiasedness, almost sure convergence, and linear time complexity. In ABC experiments on several models, we confirm that our method obtains a value closer to the true parameters than that of other discrepancy measures.