MMP.11:4.4 - Put the family into the model before using its fit

Substitute the adjustable contribution into the relations that consume it. Derive the resulting observable or answer condition with shared quantities kept shared. An error measured on an isolated contribution and an error in the coupled output are different fitting questions.

Choose the insertion point from what must remain meaningful. In a component model, inserting an unknown relation before algebraic elimination can retain a named component’s inputs, outputs and connections. Adding a correction after elimination can be simpler, but the correction then acts on the transformed relations. Recover how it affects the properties needed by the original question. A reduced model may use MMP.9 to derive the contribution its simplification leaves open.

Represent how observations are produced. MMP.7 derives a probability law for records when probability is needed; C.16.IR uses the supplied indication relation to obtain compatible cases or bounds. Fitting an unobserved internal term as if it were measured supplies an extra premise. If that premise is unavailable, fit or constrain through the observable relation instead.

For a dynamic or implicitly defined model, obtain the consequence through its coupled equations and conditions. A good component fit does not settle whether the resulting evolution, initialization or constraints are usable. Apply the mathematical and computational method appropriate to the stated consequence; C.29.2 helps formulate its obtaining operation.