Dynamic Modeling, Parameter Estimation and Uncertainty Analysis in R

Abstract

In a wide variety of research elds, dynamic modeling is employed as an instrument to learn and understand complex systems. The differential equations involved in this process are usually non-linear and depend on many parameters whose values decide upon the characteristics of the emergent system. The inverse problem, i.e. the inference or estimation of parameter values from observed data, is of interest from two points of view. First, the existence point of view, dealing with the question whether the system is able to reproduce the observed dynamics for any parameter values. Second, the identi ability point of view, investigating invariance of the prediction under change of parameter values, as well as the quanti cation of parameter uncertainty.\n\nIn this paper, we present the R package dMod providing a framework for dealing with the inverse problem in dynamic systems. The particularity of the approach taken by dMod is to provide and propagate accurate derivatives computed from symbolic expres-sions wherever possible. This derivative information highly supports the convergence of optimization routines and enhances their numerical stability, a requirement for the appli-cability of so sticated uncertainty analysis methods. Computational efficiency is achieved by automatic generation and execution of C code. The framework is object oriented (S3) and provides a variety of functions to set up dynamic models, observation functions and parameter transformations for multi-conditional parameter estimation.\n\nThe key elements of the framework and the methodology implemented in dMod are highlighted by an application on a three-compartment transporter model.