Linking data to models: data regression

Mathematical modelling is an essential tool in systems biology. To ensure the accuracy of mathematical models, model parameters must be estimated using experimental data, a process called regression. Also, pre-regression and post-regression diagnostics must be employed to evaluate the model goodness-of-fit and the reliability of the estimated parameter values.Maximum likelihood estimation and least-squares fitting are the most common regression schemes, yielding parameter values and their variance–covariance matrix. They work under the assumption that the estimated parameters have a normal distribution. When this assumption is not valid, Bayesian inference can be used, yielding the full parameter distribution.Prior to regression, the structural identifiability of models must be assessed to determine whether model parameters can be uniquely determined and what data are required to achieve that.Post-regression diagnostics include testing a model's goodness-of-fit, determining which model among competing ones fits the data best, evaluating parameter determinability and evaluating parameter significance.Parameters in probabilistic models must be inferred by either indirect inference or by Bayesian methods. In indirect inference, model parameters are estimated by minimizing the differences between intermediate statistics that characterize simulated and experimental data.