Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Modeling with Differential Equations01:25

Modeling with Differential Equations

Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...
One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation01:24

One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation

This lesson introduces two critical methods in pharmacokinetics, the Wagner-Nelson and Loo-Riegelman methods, used for estimating the absorption rate constant (ka) for drugs administered via non-intravenous routes. The Wagner-Nelson method relates ka to the plasma concentration derived from the slope of a semilog percent unabsorbed time plot. However, it is limited to drugs with one-compartment kinetics and can be impacted by factors like gastrointestinal motility or enzymatic degradation.
On...
Exponential Equations for Modeling Growth01:26

Exponential Equations for Modeling Growth

Exponential models are essential for describing rapid, multiplicative changes in natural systems, such as population growth. When a population doubles at regular intervals, the process can be modeled using a suitable base. For instance, a bacterial culture that doubles every three hours follows the model n(t)=n0⋅2t/3, where n(t) is the population at the time t.A more general model uses the natural base e, especially for continuous growth. This takes the form n(t)=n0⋅ert, where r is the relative...
Linear Differential Equations01:27

Linear Differential Equations

The integrating factor method provides a systematic way to solve first-order linear differential equations, especially those that cannot be handled by separation of variables. This method is particularly useful in modeling time-dependent physical systems influenced by both constant inputs and resistive forces. A common example is the motion of a car subjected to a constant engine force while experiencing air resistance proportional to its velocity.In such scenarios, Newton’s second law yields a...
Differential Equations: Problem Solving01:21

Differential Equations: Problem Solving

When analyzing the motion of falling objects, it is essential to consider not only the force of gravity but also the opposing force of air resistance. A practical example involves releasing a heavy test weight during a safety check on a ship. As the weight falls from rest, gravity accelerates it downward while air resistance exerts an upward force that increases with velocity. This dynamic interplay of forces is well described by differential equations, which provide a mathematical framework...
Mechanistic Models: Compartment Models in Individual and Population Analysis01:23

Mechanistic Models: Compartment Models in Individual and Population Analysis

Mechanistic models are utilized in individual analysis using single-source data, but imperfections arise due to data collection errors, preventing perfect prediction of observed data. The mathematical equation involves known values (Xi), observed concentrations (Ci), measurement errors (εi), model parameters (ϕj), and the related function (ƒi) for i number of values. Different least-squares metrics quantify differences between predicted and observed values. The ordinary least squares (OLS)...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

[Relationship between overweight/obesity and hypertension among adults in China: a prospective study].

Zhonghua liu xing bing xue za zhi = Zhonghua liuxingbingxue zazhi·2016
Same author

HbA<sub>1c</sub> measurements across- different platforms: exercising caution when making decisions regarding diagnosis.

Diabetic medicine : a journal of the British Diabetic Association·2016
Same author

GW150914: Implications for the Stochastic Gravitational-Wave Background from Binary Black Holes.

Physical review letters·2016
Same author

GW150914: The Advanced LIGO Detectors in the Era of First Discoveries.

Physical review letters·2016
Same author

Local proliferation initiates macrophage accumulation in adipose tissue during obesity.

Cell death & disease·2016
Same author

[Correlation between type D personality and cognitive fusion in 388 employees of state-owned enterprises].

Zhonghua lao dong wei sheng zhi ye bing za zhi = Zhonghua laodong weisheng zhiyebing zazhi = Chinese journal of industrial hygiene and occupational diseases·2016

Related Experiment Video

Updated: Jun 3, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

Robust estimation for ordinary differential equation models.

J Cao1, L Wang, J Xu

  • 1Department of Statistics & Actuarial Science, Simon Fraser University, Burnaby, British Columbia V5A1S6, Canada. jiguo cao@sfu.ca

Biometrics
|March 16, 2011
PubMed
Summary
This summary is machine-generated.

This study introduces a robust method for estimating parameters in ordinary differential equations (ODEs) from noisy data with outliers. The approach ensures accurate modeling of dynamic processes in science and engineering.

Related Experiment Videos

Last Updated: Jun 3, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

Area of Science:

  • * Mathematical modeling
  • * Computational science
  • * Applied mathematics

Background:

  • * Ordinary differential equations (ODEs) are crucial for modeling dynamic systems in various scientific fields.
  • * Estimating ODE parameters from noisy data, particularly with outliers, presents significant challenges.
  • * Existing methods may struggle with data integrity, impacting model accuracy.

Purpose of the Study:

  • * To develop a robust method for accurate ODE parameter estimation from noisy data containing outliers.
  • * To enhance the reliability of dynamic process modeling in biology, engineering, and medicine.
  • * To provide a computationally efficient and stable estimation technique.

Main Methods:

  • * A nonparametric function, represented as a basis function combination, models the dynamic process.
  • * A robust penalized smoothing method estimates the nonparametric function, incorporating ODE model fidelity.
  • * Nested optimization levels estimate basis coefficients and ODE parameters, utilizing the implicit function theorem for analytic gradients.

Main Results:

  • * Simulation studies demonstrate the robust method's ability to yield satisfactory ODE parameter estimates from noisy, outlier-containing data.
  • * The method effectively handles data imperfections, improving parameter estimation accuracy.
  • * Successful application to a real-world predator-prey ecological model validates its practical utility.

Conclusions:

  • * The proposed robust method offers a reliable solution for ODE parameter estimation in the presence of data noise and outliers.
  • * This technique enhances the accuracy and applicability of ODE models in complex scientific domains.
  • * The method provides a valuable tool for analyzing dynamic systems with imperfect real-world data.