Ordinary Meeting of the Royal Statistical Society organized by the
Research Section
Wednesday, May 9th, 2007 at 5pm (tea from 4:30pm)
Venue: Royal Statistical Society, 12 Errol St, London EC1Y 8LX
J. O. Ramsay, G. Hooker, D. Campbell and J. Cao (McGill University,
Montreal)
Parameter estimation for differential equations: a generalized
smoothing approach
We propose a new method for estimating parameters in models that are
defined by a system of non-linear differential equations. Such
equations represent changes in system outputs by linking the behaviour
of derivatives of a process to the behaviour of the process itself.
Current methods for estimating parameters in differential equations
from noisy data are computationally intensive and often poorly suited
to the realization of statistical objectives such as inference and
interval estimation. The paper describes a new method that uses noisy
measurements on a subset of variables to estimate the parameters
defining a system of non-linear differential equations. The approach
is based on a modification of data smoothing methods along with a
generalization of profiled estimation. We derive estimates and
confidence intervals, and show that these have low bias and good
coverage properties respectively for data that are simulated from
models in chemical engineering and neurobiology. The performance of
the method is demonstrated by using real world data from chemistry and
from the progress of the autoimmune disease lupus.
You can download/view a PDF copy of this paper at
http://www.rss.org.uk/main.asp?page=1836#1852
From this page you can also download the nylon data that are analysed
in the paper (along with associated analysis/output).
Trevor Sweeting
Chair, RSS Research Section Committee
|