Regresar

Ensemble Kalman Filter and Extended Kalman Filter for State-Parameter Dual Estimation in Mixed Effects Models Defined by a Stochastic Differential Equation

Abstract:

The biological processes that occur in the real world have complex dynamics. Mathematical models that try to describe these phenomena have nonlinear structures, observations are made at discrete time points and include measurement errors, and are difficult to estimate. In particular, when modeling dynamics of repeated measurements on individuals or objects, they are analyzed by mixed-effects diffusion models. The standard estimation methods in these cases are: maximum likelihood, EM, SAEM, Newton Raphson, among others. In this paper we propose a specific inference methodology for models. Apply extended Kalman Filter (EKF) and the ensemble Kalman filter (EnKF) to the estimation of both states and parameters of nonlinear state-space models. To illustrate the methodology, the states and parameters of an Ornstein- Uhlembeck (O-U) mixed-effects model were estimated, obtaining precise estimates with small standard deviations. To measure the estimation quality of the algorithms was used as a measure of goodness-of-fit known as the square root of the mean quadratic error, obtaining very small errors.