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

Using Perturbation to Improve Goodness-of-Fit Tests based on Kernelized Stein Discrepancy