FIG. 1.

Illustration of the signal to noise ratio and the effects of finite sampling for the independent model. The SNR is the (squared) ratio of$\chi to{\sigma }_E.$ For this plot a “reference” independent model was used to generate a “test” MSA and a “training” MSA of 1000 sequences each, and then a new independent model was parametrized using only the training MSA. E(S) was then computed for the sequences of each MSA with both models. Finite sampling effects cause both the mean-squared-error ${\sigma }_E^2,$ and an overfitting effect visible as a shift $\delta E$ of the estimated energies of the training MSA relative to those of the test MSA.