Open Access

Clemens Kreutz, Andreas Raue, Jens Timmer

• Mathematical models of dynamic processes contain parameters which have to be estimated based on time-resolved experimental data. This task is often approached by optimization of a suitably chosen objective function. Maximization of the likelihood, i.e. maximum likelihood estimation, has several beneficial theoretical properties ensuring efficient and accurate statistical analyses and is therefore often performed for identification of model parameters. For nonlinear models, optimization is challenging and advanced numerical techniques have been established to approach this issue. However, the statistical methodology typically applied to interpret the optimization outcomes often still rely on linear approximations of the likelihood. In this review, we summarize the maximum likelihood methodology and focus on nonlinear models like ordinary differential equations. The profile likelihood methodology is utilized to derive confidence intervals and for performing identifiability andMathematical models of dynamic processes contain parameters which have to be estimated based on time-resolved experimental data. This task is often approached by optimization of a suitably chosen objective function. Maximization of the likelihood, i.e. maximum likelihood estimation, has several beneficial theoretical properties ensuring efficient and accurate statistical analyses and is therefore often performed for identification of model parameters. For nonlinear models, optimization is challenging and advanced numerical techniques have been established to approach this issue. However, the statistical methodology typically applied to interpret the optimization outcomes often still rely on linear approximations of the likelihood. In this review, we summarize the maximum likelihood methodology and focus on nonlinear models like ordinary differential equations. The profile likelihood methodology is utilized to derive confidence intervals and for performing identifiability and observability analyses.…