Inverse Modelling, Sensitivity and Monte Carlo Analysis in R Using Package FME

Abstract

Mathematical simulation models are commonly applied to analyze experimental or environmental data and eventually to acquire predictive capabilities. Typically these models depend on poorly defined, unmeasurable parameters that need to be given a value. Fitting a model to data, so-called inverse modelling, is often the sole way of finding reasonable values for these parameters. There are many challenges involved in inverse model applications, e.g., the existence of non-identifiable parameters, the estimation of parameter uncertainties and the quantification of the implications of these uncertainties on model predictions.

The R package FME is a modeling package designed to confront a mathematical model with data. It includes algorithms for sensitivity and Monte Carlo analysis, parameter identifiability, model fitting and provides a Markov-chain based method to estimate parameter confidence intervals. Although its main focus is on mathematical systems that consist of differential equations, FME can deal with other types of models. In this paper, FME is applied to a model describing the dynamics of the HIV virus.