🤖 AI Summary
This work proposes a nonparametric method to assess the statistical significance of signal features—such as peaks and plateaus—in data and to detect multimodal structures in inter-event spacing distributions. The approach leverages run theory, employing a Markov chain recursion to precisely characterize the distribution of the longest runs. It integrates permutation testing with a bootstrap procedure tailored for continuous data, enabling a unified evaluation of both high- and low-intensity signal features. The key innovation lies in the first principled synthesis of run-length analysis, permutation tests, and continuous-data bootstrapping, which collectively facilitate accurate detection and localization of multimodal patterns without requiring parametric distributional assumptions, thereby effectively identifying salient morphological features in complex datasets.
📝 Abstract
Runs tests have long been used as a non-parametric check if data contains a non-random signal. We derive a recursive expression for the distribution of the longest run using Markov chain theory. Next we develop a permutation test on the runs comprising a feature to get the probability of its height. This leads finally to a bootstrap test on the height using the raw, continuous data. Such a test can evaluate not only the large heights of peaks but also the small heights of flats. We can apply these tests to features in the spacing of data to detect and locate multi-modality.