Chapter 5: Model Uncertainty Analysis

Uncertainty analysis of model parameters is critical in assessing the reliability and usefulness of a model’s predictions. In this chapter, we illustrate and discuss different uncertainty analysis methods. We present both frequentist and Bayesian approaches for uncertainty quantification. Frequentist approaches, such as the construction of individual confidence intervals or ellipsoids for parameter pairs, have been widely applied due to their intuitive nature and easy computation. However, in high dimensions this intuition might be misleading, and the nonlinear relationship between parameters is often ignored. Algorithms derived from Bayesian inference can sample the posterior distribution of model parameters and show better performance when the kinetic model is nonlinear with complex parameter distributions and correlations. This approach, however, can be intractable for large numbers of parameters. We introduce Bayesian sampling methods such as Markov chain Monte Carlo and show how the confidence region obtained by Bayesian methods can reveal the nonlinear relationship between kinetic parameters, at the expense of a higher computational cost.