Kernelized Stein discrepancy (KSD) is a score-based discrepancy widely used in goodness-of-fit tests. It can be applied even when the target distribution has an unknown normalising factor, such as in Bayesian analysis. We show theoretically and empirically that the KSD test can suffer from low power when the target and the alternative distribution have the same well-separated modes but differ in mixing proportions. We propose to perturb the observed sample via Markov transition kernels, with respect to which the target distribution is invariant. This allows us to then employ the KSD test on the perturbed sample. We provide numerical evidence that with suitably chosen kernels the proposed approach can lead to a substantially higher power than the KSD test.

翻译：核化斯坦因差异(KSD)是一种基于得分函数的差异度量，广泛应用于拟合优度检验。即便目标分布具有未知归一化因子（如贝叶斯分析中的情况），该方法仍可适用。我们从理论和实证两方面证明，当目标分布与备择分布具有相同且良好分离的模态但混合比例不同时，KSD检验的统计效能可能较低。为此，我们提出通过马尔可夫转移核对观测样本进行扰动——该转移核能保持目标分布的不变性——随后对扰动后的样本实施KSD检验。数值实验表明，在适当选取核函数的情况下，所提方法相较KSD检验可获得显著更高的统计检验力。