COMPUTATIONALLY EFFICIENT STATISTICAL METHODS IN IOT AND HUMAN GAIT ANALYSIS

Abstract

In the era of smart systems and wearable technologies, computational efficiency and interpretability are paramount in developing suitable statistical methodologies for real-world applications. This thesis, titled Computationally Efficient Statistical Methods in IoT and Human Gait Analysis, presents a trilogy of studies addressing these needs through developments in outlier detection and human gait assessment. The first part of this thesis focuses on enhancing anomaly detection in Internet of Things (IoT)-based systems, where outliers such as faults or intrusions can compromise data reliability and Quality of Service. We improve upon the widely used Recursive Principal Component Analysis (R-PCA) method by introducing a data-driven Satterthwaite-based approximation to model the distribution of squared prediction error (SPE) scores more accurately. This refinement corrects the theoretical ambiguities of the Gaussian assumptions in traditional R-PCA and provides a reproducible, real-time outlier detection algorithm with superior performance validated through simulations and graphical plots. The second part of the thesis explores the use of beta regression models to under- stand how demographic and gait-specific parameters influence the human Gait Index (GI). By analyzing data from healthy individuals, this study identifies key factors such as walking speed, stride length, knee angle, and stance-to-swing phase ratio as significant contributors to gait variability. Importantly, it also reveals notable interaction effects, including those between age and gait features, which underscore the complexity of gait dynamics. We also develop an unified Beta regression model by using the Gait Index to improve gait stability assessment and for a better understanding of the variability in gait stability. This methodological advancement provides valuable insights for clinical applications, enabling personalized rehabilitation strategies and more accurate evaluations of gait health. The third study applies an interpretable machine learning framework using Bayesian Additive Regression Trees (BART) to classify gait patterns into healthy, neurological, and orthopedic categories based on data from over 40,000 footsteps across 230 subjects. The developed approach not only demonstrates high predictive performance (in terms of improved AUC and F1 scores), but also identifies physiologically meaningful features—such as loading phase, walking speed, stride length, and asymmetry in single support time—as key discriminators. Through SHAP and permutation-based analyses, we further establish the interpretability and clinical relevance of the model, offering insight into the underlying mechanics of gait abnormalities. Together, these studies provide a cohesive body of work that advances the statistical and machine learning methodologies for outlier detection and human gait analysis—balancing computational efficiency with interpretability and real-world applicability in both engineering and biomedical domains.