Approximate Bayesian computation (ABC) is a likelihood-free inference method that has been employed in various applications. However, ABC can be sensitive to outliers if a data discrepancy measure is chosen inappropriately. In this paper, we propose to use a nearest-neighbor-based $\gamma$-divergence estimator as a data discrepancy measure. We show that our estimator possesses a suitable theoretical robustness property called the redescending property. In addition, our estimator enjoys various desirable properties such as high flexibility, asymptotic unbiasedness, almost sure convergence, and linear-time computational complexity. Through experiments, we demonstrate that our method achieves significantly higher robustness than existing discrepancy measures.

翻译：近似贝叶斯计算法(ABC)是各种应用中采用的一种无可能性的推论方法。 但是,如果不适当地选择数据差异计量方法,ABC可能会对异常值敏感。 在本文中,我们提议使用一个以近邻为基址的$\gma$-divegence 估测器作为数据差异计量方法。我们显示我们的估测器拥有一个适当的理论稳健性属性,称为再隐性属性。此外,我们的估测器享有各种可取的属性,如高度灵活性、无症状的公正性、几乎肯定的趋同性以及线性计算复杂性。我们通过实验表明,我们的方法比现有差异计量方法的稳健性要高得多。