Editing Mathematical model (section)

====Prediction of empirical data====

Usually, the easiest part of model evaluation is checking whether a model predicts experimental measurements or other empirical data not used in the model development.  In models with parameters, a common approach is to split the data into two disjoint subsets: training data and verification data. The training data are used to estimate the model parameters.  An accurate model will closely match the verification data even though these data were not used to set the model's parameters. This practice is referred to as [[cross-validation (statistics)|cross-validation]] in statistics.

Defining a [[Metric (mathematics)|metric]] to measure distances between observed and predicted data is a useful tool for assessing model fit.  In statistics, decision theory, and some [[economic model]]s, a [[loss function]] plays a similar role. While it is rather straightforward to test the appropriateness of parameters, it can be more difficult to test the validity of the general mathematical form of a model.  In general, more mathematical tools have been developed to test the fit of [[statistical model]]s than models involving [[differential equation]]s.  Tools from [[nonparametric statistics]] can sometimes be used to evaluate how well the data fit a known distribution or to come up with a general model that makes only minimal assumptions about the model's mathematical form.