Quantifying uncertainty, variability and likelihood for ordinary differential equation models
نویسندگان
چکیده
منابع مشابه
Robust estimation for ordinary differential equation models.
Applied scientists often like to use ordinary differential equations (ODEs) to model complex dynamic processes that arise in biology, engineering, medicine, and many other areas. It is interesting but challenging to estimate ODE parameters from noisy data, especially when the data have some outliers. We propose a robust method to address this problem. The dynamic process is represented with a n...
متن کاملEfficient Bayesian estimation and uncertainty quantification in ordinary differential equation models
Abstract: In engineering, physics, biomedical sciences and many other fields the regression function is known to satisfy a system of ordinary differential equations (ODEs). Our interest lies in the unknown parameters involved in the ODEs. When the analytical solution of the ODEs is not available, one approach is to use numerical methods to solve the system. A four stage Runge-Kutta (RK4) method...
متن کاملFast integration-based prediction bands for ordinary differential equation models
MOTIVATION To gain a deeper understanding of biological processes and their relevance in disease, mathematical models are built upon experimental data. Uncertainty in the data leads to uncertainties of the model's parameters and in turn to uncertainties of predictions. Mechanistic dynamic models of biochemical networks are frequently based on nonlinear differential equation systems and feature ...
متن کاملCause and cure of sloppiness in ordinary differential equation models.
Data-based mathematical modeling of biochemical reaction networks, e.g., by nonlinear ordinary differential equation (ODE) models, has been successfully applied. In this context, parameter estimation and uncertainty analysis is a major task in order to assess the quality of the description of the system by the model. Recently, a broadened eigenvalue spectrum of the Hessian matrix of the objecti...
متن کاملQuantifying Geoacoustic Uncertainty and Seabed Variability for Propagation Uncertainty
Propagation and reverberation of acoustic fields in shallow waters depend strongly on the spatial variability of seabed geoacoustic parameters, and lack of knowledge of seabed variability is often a limiting factor in acoustic modeling applications. However, direct sampling (e.g., coring) of vertical and lateral variability is expensive and laborious, and matched-field and other long-range inve...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: BMC Systems Biology
سال: 2010
ISSN: 1752-0509
DOI: 10.1186/1752-0509-4-144