From Functional Data Analysis to Differential
Equation Models, With Applications 
James Ramsay , Ph.D.
University of British Columbia
April 9, 2008
ABSTRACT
Dynamical models explain how a system responds to a change in the system
itself or in its environment. They are usually expressed as a set of differential
equations that explicitly link change as defined by time derivatives to the state of
the system and its inputs. Nonlinear systems are especially interesting because
of their potential to capture complex system behavior by a seemingly simple set
of equations. A new method will be outlined which permits the estimation of
nonlinear system parameters from noisy data along with confidence regions and
other inferential methodology. The procedure will be illustrated with examples
drawn from chemical engineering, clinical medicine and ecology.
