Bayesian two-step estimation in differential equation models
نویسندگان
چکیده
منابع مشابه
Bayesian estimation in differential equation models
Ordinary differential equations (ODEs) are used to model dynamic systems appearing in engineering, physics, biomedical sciences and many other fields. These equations contain unknown parameters, say θ of physical significance which have to be estimated from the noisy data. Often there is no closed form analytic solution of the equations and hence we cannot use the usual non-linear least squares...
متن کاملParameter Estimation of Partial Differential Equation Models.
Partial differential equation (PDE) models are commonly used to model complex dynamic systems in applied sciences such as biology and finance. The forms of these PDE models are usually proposed by experts based on their prior knowledge and understanding of the dynamic system. Parameters in PDE models often have interesting scientific interpretations, but their values are often unknown, and need...
متن کاملRobust 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 کاملParameter estimation in differential equation models with constrained states
We introduce a method to estimate parameters and states from a differential equation model while enforcing interpretability constraints such as monotone or non-negative states. We motivate the methodology using a real data chemical engineering example and show that a variety of restrictive constraints from earlier analyses do not address the problem of interpretability. Our proposed method esti...
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: Electronic Journal of Statistics
سال: 2015
ISSN: 1935-7524
DOI: 10.1214/15-ejs1099