Data-Driven Methods for Analyzing Non-Gaussian Variability in Human Postural Sway

Abstract

Postural sway during quiet standing is often analyzed using diffusion- or Brownian-type models that implicitly assume near-Gaussian statistics. In practice, center-of-pressure (COP) trajectories can exhibit heavy tails, asymmetry, and intermittent excursions that may bias variance-only variability descriptors. This study presents a reproducible Python-based analysis pipeline for assessing non-Gaussian structure in COP increment series by rotating increment pairs into a PCA-decorrelated coordinate system. Using the Human Balance Evaluation Database (HBEDB) (1930 trials from 163 subjects; 60 s at 100 Hz under four standing conditions: eyes open/closed and rigid/unstable surface; three repetitions each), we compare empirical increment distributions with mean- and covariance-matched Gaussian surrogates and quantify departures using complementary diagnostics, including probability–probability comparisons, robust spread descriptors (IQR and range), and uni-/bivariate kernel density estimation. We further introduce a compact central ellipse fraction (CEF) descriptor that measures central concentration in the PCA plane and relates distributional findings to linear and nonlinear variability measures, including Poincaré-type descriptors and recurrence indices. Across the dataset, empirical increments deviate systematically from Gaussian surrogates: P–P plots show tail departures, and the 2-D density in the PCA plane is more centrally concentrated than the matched Gaussian model (CEF higher by approximately 0.08–0.10), consistent with leptokurtic (peaked and heavy-tailed) behavior. These results motivate distribution-aware preprocessing and descriptor selection for computer-based posturography and fall-risk assessment algorithms beyond variance-only summaries.