A1247
Title: Smoothly-stochastic differential equations for biomechanics data
Authors: Giles Hooker - University of Pennsylvania (United States) [presenting]
Edward Gunning - University of Pennsylvania (United States)
Abstract: In functional data analysis, replicate observations of a smooth functional process and its derivatives offer a unique opportunity to flexibly estimate continuous-time ordinary differential equation models. To estimate a linear ordinary differential equation from functional data, a technique called Principal Differential Analysis was proposed a long time ago. We re-formulate PDA as a generative statistical model in which functional observations arise as solutions of a deterministic ODE that is forced by a smooth random error process. This viewpoint defines a flexible class of functional models based on differential equations and leads to an improved understanding and characterization of the sources of variability in Principal Differential Analysis. It does, however, result in parameter estimates that can be heavily biased under the standard estimation approach of PDA. Therefore, we introduce an iterative bias-reduction algorithm that can be applied to improve parameter estimates. We also examine the utility of our approach when the form of the deterministic part of the differential equation is unknown and possibly non-linear, where Principal Differential Analysis is treated as an approximate model based on time-varying linearization. We demonstrate our approach on simulated data from linear and non-linear differential equations and on real data from human movement biomechanics.
