Output Assessment for Monte Carlo Simulations via the Score Statistic

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A Kernelized Stein Discrepancy for Goodness-of-fit Tests (2016, methodology): “…from the (unknown) p ( x ) , the form (3) also enables efﬁcient empirical estimation of S ( p, q ) via a U -statistic, (4) The distribution of ˆ S ( p, q ) can be well characterized using the theory of U -statistics (Hoeffding, 1948; Serﬂing, 2009), allowing us to reduce the testing of p = q to”
Measuring Sample Quality with Stein's Method (2015, background): “For example, for a N (0 , 1) target, the score statistic of [32] cannot distinguish two samples with equal ﬁrst and second moments.”
Measuring Sample Quality with Diffusions (2016, background): “For example, when P = N (0, 1), the score statistic [24] cannot differentiate two samples with the same means and”
Measuring Sample Quality with Kernels (2017, background): “The score statistic of Fan et al. (2006) and the Gibbs sampler convergence criteria of Zellner & Min (1995) detect certain forms of non-convergence but fail to detect others due to the ﬁnite number of test functions tested.”