Model comparison
Model comparison evaluates alternative mathematical descriptions of the same biological system.
Fit versus complexity
A more flexible model can fit observed data better simply because it has more parameters. Criteria such as Akaike's information criterion balance likelihood against parameter count:
\[\mathrm{AIC}=2k-2\log L_{\max},\]where \(k\) is the number of estimated parameters.
Predictive comparison
Out-of-sample prediction or cross-validation can compare how well models generalise beyond their calibration data.
Biological comparison
Statistical performance is not the only consideration. Interpretability, biological assumptions, identifiability and suitability for the scientific purpose also matter.
Key idea. The preferred model is not automatically the most complicated or the one with the smallest in-sample error.