Using Perturbation to Improve Goodness-of-Fit Tests based on Kernelized Stein Discrepancy
This addresses a specific bottleneck in statistical testing for researchers, though it is incremental as it builds on existing KSD methods.
The paper tackled the problem of low power in goodness-of-fit tests using Kernelized Stein Discrepancy (KSD) when distributions have similar modes but different mixing proportions, and showed that perturbing samples with Markov transition kernels can substantially increase test power, with numerical evidence supporting this improvement.
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 distributions 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 transition kernels the proposed approach can lead to substantially higher power than the KSD test.