MMP.17:4.1 - Select the response and the input region

Let (M) be the source model and let (Q) extract the required response. Write the target as

[ r(x)=Q(M(x)),\qquad x\in D, ]

where (x) contains the inputs and (D) is the intended region of use. The input may be a number, a vector, a history, a function or a discrete configuration. State enough of its meaning to distinguish materially different conditions. If the same listed input gives different deterministic responses because a regime or previous state was omitted, restore that input before fitting a function.

Choose (Q) from the receiving operation. A mean, a tail probability and an entire probability law are different targets. So are a field value, its spatial derivative and a quantity integrated over that field. For a random source output (Y_x), a mean surrogate targets (\mathbb E[Y_x]); reproducing individual draws or their distribution requires another construction.

Determine how response error affects the receiving result. For a comparison with a limit, the distance to the limit matters. For a ranking, the gap between alternatives matters. If the receiver will differentiate, iterate or invert the response, include the corresponding sensitivity or structural requirement. A low average value error does not select these requirements for the practitioner.