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Non-parametric goodness-of-fit testing procedures based on kernel Stein discrepancies (KSD) are promising approaches to validate general unnormalised distributions in various scenarios. Existing works have focused on studying optimal kernel choices to boost test performances. However, the Stein operators are generally non-unique, while different choices of Stein operators can also have considerable effect on the test performances. In this work, we propose a unifying framework, the generalised kernel Stein discrepancy (GKSD), to theoretically compare and interpret different Stein operators in performing the KSD-based goodness-of-fit tests. We derive explicitly that how the proposed GKSD framework generalises existing Stein operators and their corresponding tests. In addition, we show thatGKSD framework can be used as a guide to develop kernel-based non-parametric goodness-of-fit tests for complex new data scenarios, e.g. truncated distributions or compositional data. Experimental results demonstrate that the proposed tests control type-I error well and achieve higher test power than existing approaches, including the test based on maximum-mean-discrepancy (MMD).
We propose and analyse a novel nonparametric goodness of fit testing procedure for exchangeable exponential random graph models (ERGMs) when a single network realisation is observed. The test determines how likely it is that the observation is genera
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Survival Analysis and Reliability Theory are concerned with the analysis of time-to-event data, in which observations correspond to waiting times until an event of interest such as death from a particular disease or failure of a component in a mechan