Specific statistical tests are used when the null hypothesis (H0) is to be tested using nonparametric nominal or ordinal data. With nominal data, experimental results are expressed by proportions or frequencies. Chi-square or related tests (the Fisher's exact test or the rows by columns test) are appropriate for testing H0 with nominal data. Ordinal data permit arrangement of statistical result...

We study the drift of stationary diffusion processes in a time series analysis of the autoregression function. A marked empirical process measures the difference between the nonparametric regression functions of two time series. We bootstrap the distribution of a Kolmogorov-Smirnov-type test statistic for two hypotheses: Equality of regression functions and shifted regression functions. Neither...

The Kolmogorov-Smirnov (KS) test is popularly used in many applications, such as anomaly detection, astronomy, database security and AI systems. One challenge remained untouched how we can obtain an explanation on why a set fails the KS test. In this paper, tackle problem of producing counterfactual explanations for data failing Concept-wise, propose notion most comprehensible explanations, whi...

Sampling-based methods for uncertainty and sensitivity analysis are reviewed. The following topics are considered: (i) definition of probability distributions to characterize epistemic uncertainty in analysis inputs, (ii) generation of samples from uncertain analysis inputs, (iii) propagation of sampled inputs through an analysis, (iv) presentation of uncertainty analysis results, and (v) deter...