Residuals preserve the signed difference between a model output and a reference value, so their pattern can expose systematic overprediction or underprediction. Absolute error removes the sign and emphasizes the size of each discrepancy. Relative error scales the discrepancy to the reference value, making comparisons across differently sized quantities more informative. Together, these measures support a more detailed error assessment.
Goodness-of-fit provides a summary of how closely model outputs match reference values, while residuals and error measures show the size and direction of individual discrepancies. Considering both levels helps distinguish an apparently close overall fit from systematic bias in particular comparisons. This combined view is useful when deciding whether a model is suitable for calibration, validation, or prediction.
Sensitivity analysis examines how model outputs respond when parameters change. A strong response identifies parameters that substantially influence results, whereas a weak response indicates less effect within the changes considered. This information helps explain model behavior, focus model improvement, and interpret whether predictions depend heavily on particular parameter choices.
Different criteria emphasize different aspects of agreement between outputs and reference values. Error measures quantify discrepancies, goodness-of-fit summarizes correspondence, and sensitivity examines dependence on parameter changes. Comparing these results rather than relying on one value can support model selection while also showing whether a candidate model has bias or fragile parameter dependence.
Begin by comparing model outputs with observed measurements or other reference values. Calculate suitable residual, absolute-error, relative-error, or goodness-of-fit quantities, then inspect the results for systematic bias. Next, vary parameters to assess sensitivity. Use the combined evidence to calibrate the model, validate its behavior, compare alternatives, and judge its reliability for prediction or decision-making.
They are used wherever mathematical models must represent systems or predict observed behavior. The overview identifies physics, engineering, biology, and economics as applications. In each area, the criteria can support calibration, validation, comparison, and model improvement by relating calculated outputs to measurements or reference values rather than treating the model structure alone as sufficient evidence.
Reliability judgments should consider more than whether outputs resemble reference values. Error patterns can reveal systematic bias, while sensitivity results show whether predictions change substantially with parameter choices. Together, these findings clarify the strengths and limitations of a model and help determine whether its results are appropriate for prediction or decision-making in the intended application.