Quantifying non-Gaussian intermittent fluctuations in physiology: Multiscale probability density function analysis using the Savitzky-Golay detrending

When measuring physiological data, the central limit theorem typically implies a consistent variance, resulting in data that closely follow a Gaussian distribution. However, physiological measurements often deviate from this expectation, increasing variance due to nonlinear correlations across various scales. The challenge lies in testing these tails, which comprise only rare and extreme values. We introduce multiscale probability density function (PDF) analysis, a method that estimates this non-Gaussianity parameter for physiological fluctuations in each of multiple timescales. We gain valuable insights into the observed distributions with heavier tails and nonlinear correlations by exploring the relationship between non-Gaussianity and logarithmic scale. To maintain the fidelity of the original data, we incorporate an adaptive detrending filter into our multiscale PDF analysis. This filter effectively eliminates trends without distorting the distribution in a way that might risk artifactual signatures of non-Gaussianity. Additionally, we explain why multiscale PDF analysis is especially well suited for examining data that follow lognormal distributions. In the final stretch, we demonstrate how multiscale PDF analysis can provide fresh perspectives on heart rate variability and postural control. This innovative approach can facilitate diagnoses in health and disease while also deepening our comprehension of how constraints influence human physiological performance.