The Limitations of Model-Based Experimental Design and Parameter Estimation in Sloppy Systems
Fig 2
Model manifold widths define relevant and irrelevant parameters.
(Left) The set of all possible model outputs defines a manifold of predictions. The true model ideally corresponds to a point near the manifold (red dot). For typical sloppy models, the manifold is bounded by a hierarchy of widths that are approximately given by the square-roots of the FIM eigenvalues (when parameterized in natural units). Widths of the model manifold are measured in units of the standard-deviation of the data, so that widths much less than one are practically indistinguishable from noise. Widths larger than one, on the other hand, are distinguishable from noise and must be tuned to reproduce the observations. This suggests describing parameter combinations corresponding to large eigenvalues and large widths as relevant or important for the model. In contrast, those parameters corresponding to small eigenvalues and widths are irrelevant or unimportant. We describe widths comparable to the experimental noise as marginal.