Skip to main content

Parameter estimation for differential equations: a generalized smoothing approach

Buy Article:

$51.00 plus tax (Refund Policy)

Abstract:

Summary. 

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.

Keywords: Differential equation; Dynamic system; Estimating equation; Functional data analysis; Gauss; Newton method; Parameter cascade; Profiled estimation

Document Type: Research Article

DOI: http://dx.doi.org/10.1111/j.1467-9868.2007.00610.x

Affiliations: McGill University, Montreal, Canada

Publication date: November 1, 2007

bpl/rssb/2007/00000069/00000005/art00001
dcterms_title,dcterms_description,pub_keyword
6
5
20
40
5

Access Key

Free Content
Free content
New Content
New content
Open Access Content
Open access content
Subscribed Content
Subscribed content
Free Trial Content
Free trial content
Cookie Policy
X
Cookie Policy
Ingenta Connect website makes use of cookies so as to keep track of data that you have filled in. I am Happy with this Find out more