MMP.11:1 - Problem frame

Use this pattern when part of a model is supported, but a function or other relation is still unknown. You may know which quantities interact, what must be conserved, or how a response begins and ends, while lacking its form between those conditions. You need candidate models that retain this knowledge while allowing the missing contribution to vary.

Begin by locating the unknown contribution in the relations needed for the question. Say what it takes as input, what it supplies and which properties its variation must preserve. Construct a family for that contribution, then put it back into the model. For a response that rises from zero to one, a family of curves constrained by those properties gives a different starting point from an unrestricted fitted curve.

The first useful result is a family of models, its remaining adjustable parts and the restrictions introduced by its construction. It may already give a sufficient bound. When observations are available, the same construction lets you ask which functions, parameters or consequences those observations can distinguish.

You need the subject grounds for the retained relations and enough mathematics to construct and use the family, or access to that mathematical contribution. A known adequate relation can be used directly. An unknown numerical parameter inside a suitable family normally needs its estimation method. Use this pattern when the family itself needs construction or revision. B.5.FM and B.5.TU help when the missing contribution is the subject account or theory from which a relation should come.