Statistical Inference for Non-Linear Models Involving Ordinary Differential Equations

Abstract

In the context of nonlinear fixed effect modeling, it is common to describe the relationship between a response variable and a set of explanatory variables by a system of nonlinear ordinary differential equations (ODEs). More often such a system of ODEs does not have any analytical closed form solution, making parameter estimation for these models quite challenging and computationally very demanding. Two new methods based on Euler’s approximation are proposed to obtain an approximate likelihood that is analytically tractable and thus making parameter estimation computationally less demanding than other competing methods. These methods are illustrated using a data on growth colonies of paramecium aurelium and simulation studies are presented to compare the performances of these new methods to other established methods in the literature.