B0589
Title: A new understanding of principal differential analysis
Authors: Giles Hooker - University of Pennsylvania (United States) [presenting]
Edward Gunning - University of Limerick (Ireland)
Abstract: One of the features unique to functional data analysis is in affording the ability to examine the rates of change of a complex process and hence relationships between the derivatives of that process. Prinicipal differential analysis (PDA), constructs a concurrent linear model of the m'th derivative as a response to lower-order derivatives. PDA was originally presented as a data-reduction operation. It is re-examined as being a generative model in which the data is the result of a time-varying linear ordinary differential equation that is forced by a smooth but random error process. This model can also be thought of as estimating the Jacobian of a nonlinear differential equation, hence providing insight into the stability properties of the system, and a justification for how to register such systems. However, under this model, PDA estimates of parameters can be substantially biased. An iterative bias correction algorithm is developed. Results are demonstrated on both simulated data and from a study of human locomotion.
