## Model-Data comparison

The R-package FME was developed by Karline Soetaert in cooperation with Thomas Petzoldt from the University of Dresden (Germany). It contains statistical and fitting functions to help with model-data comparison. This is a very complex package, but quite powerful.

Typically, fitting a complex model to data proceeds in several steps. We start by determining the parameters that *can* be fitted, based on parameter collinearity and identifiability analyses. After producing a best-fit set of the selected parameters, we then use a MCMC technique to quantify parameter uncertainty, and to produce sensitivity ranges around the modeled variables. The MCMC implemented in FME is especially adapted to models that are computationally demanding.

The package is documented in five (!) different vignettes, each detailing a particular type of application. There is enough material in there – if you cannot find it in one of the vignettes, then it is probably not possible!

In the gallery at the bottom of this page, you will find several figures illustrating the process; the figures are taken from the main vignette, so you can find the R-code to create these plots in there.

#### FME main paper

The main paper describing the FME package; it uses a dynamic model of the HIV virus.

#### Inverse Modelling, Sensitivity, Monte Carlo – Applied to a Dynamic Simulation Model

This vignette shows how to run sensitivity analysis, calibration, identifiability and an MCMC method on a dynamic simulation model, describing the coupled dynamics of bacteria growing on a substrate.

#### Inverse Modelling, Sensitivity, Monte Carlo – Applied to a Steady-State Model

This applies the FME tricks to a steady-state solution of a nonlinear model describing oxygen in the sediment.

#### Inverse Modelling, Sensitivity, Monte Carlo – Applied to a Nonlinear Model

This application uses FME to fit a simple monod equation against data.

#### Tests of the Markov Chain Monte Carlo Implementation

The MCMC method implemented contains a few tricks to improve the convergence of the chain. This vignette tests them.