MMP.9:1 - Problem frame

Use this pattern when a supplied model describes how a state changes, but predicting the quantities you need would be easier with less state, shorter memory or a simpler update. After removing detail, the proposed update still depends on something you removed. You need to derive what can replace that contribution while retaining a useful answer.

Start with the quantity you want to keep and compute its change from the supplied model. Circle the part that cannot be obtained from the proposed smaller state. For an average, this may be the variance of the underlying values. For one observed component, it may be the effect of unobserved components. That expression identifies the construction needed next.

The result can be a smaller evolution law, a history-dependent rule, an approximation with a stated error, or bounds sufficient for the question. Keep the initial information, inputs and time range on which it depends. A model that is already affordable and sufficient can be used directly. If the original change law is missing, recover or construct it in the subject practice before using this reduction method.

You need the mathematics used by the supplied law: substitution and recurrence for discrete changes; differentiation and integration for differential equations; expectations when reducing a probability distribution. A mathematical collaborator may perform those operations from your stated question and model. This is reduction within mathematical modeling. A.3.3.PI supplies the general test of which information a prediction needs; C.29.1 supplies the comparison that transfers the reduced result back to the source question.