Statistical Tools for Frequency Response Functions from Posture Control Experiments: Estimation of Probability of a Sample and Comparison Between Groups of Unpaired Samples

The frequency response function (FRF) is an established way to describe the outcome of experiments in posture control literature. The FRF is an empirical transfer function between an input stimulus and the induced body segment sway profile, represented as a vector of complex values associated with a vector of frequencies. Having obtained an FRF from a trial with a subject, it can be useful to quantify the likelihood it belongs to a certain population, e.g., to diagnose a condition or to evaluate the human likeliness of a humanoid robot or a wearable device. In this work, a recently proposed method for FRF statistics based on confidence bands computed with bootstrap will be summarized, and, on its basis, possible ways to quantify the likelihood of FRFs belonging to a given set will be proposed. Furthermore, a statistical test to compare groups of unpaired samples is presented.