MMP.14:4.1 - Choose the prediction and the discrepancy together

State the receiving quantity and conditions: a response at specified inputs, a probability of exceeding a limit, a distribution of recorded counts, or a forecast for a given horizon and group. Name the relevant observational unit. A message, a batch of messages and a whole operating period support different comparisons.

Recover the model and its observation law. Retain units, inputs, initial conditions, exposure, recording rules and material dependence. Separate unknown parameters from assumptions such as constant response, independent errors or complete recording.

Choose a discrepancy (D) that responds to a failure relevant to this use. For example:

• Conditional bias can be exposed by mean residuals within relevant input ranges, rather than a mean over all inputs.
• A tail count (D(y)=\sum_i 1{y_i>u}) asks whether the model accounts for excursions beyond the consequential level (u).
• A run length or (D(r)=\sum_{i=2}^n r_i r_{i-1}), with residuals in their actual order, can expose dependence hidden by a histogram.
• A distribution of recorded categories can reveal that predictions concern unfiltered events while observations concern selected records.

A conditional plot, a few statistics or a direct bound can suffice. Explain which repair would change the feature. A statistic that fitting nearly forces to agree, such as the mean in a fitted constant-mean model, usually contributes little to detecting omitted structure.

The user needs the target, conditional distributions or bounds, and the comparison’s construction. Obtain a missing calculation from a mathematically qualified collaborator: for example, a record generator and a discrepancy’s reference distribution. A human or AI participant may supply it; recover the subject assumptions and interpretation before using its output.