MMP.13:1 - Problem frame

Use this pattern when a probability model describes how records arise, and the work needs an estimate, an interval or a probability about something not directly known. The wanted quantity may be a failure probability, a mean before measurement error, a response for a different mix of cases, or a future outcome.

Start by writing the sentence the result must support. “This procedure covers the fixed unknown in at least 95% of its modeled repetitions” differs from “the unknown lies here with 95% posterior probability under these assumptions.” A probability about the next observation is another question. Choose the inferential construction that supports the required sentence.

The result is an estimator or posterior and its consequence for the requested target, with an interpretable account of uncertainty. It exposes which assumptions make the conclusion possible and which change would require recalculation. Reporting a fitted coefficient and a number labeled “error” can otherwise leave the actual question unanswered.

This is statistical inference within mathematical modeling. MMP.7 supplies the law of the records; MMP.12 supplies unresolved recovery ambiguities and any regularization choices. The present method constructs what may be concluded under that law and additional inferential assumptions. Selecting an action also needs its consequences and preferences, supplied by a decision method such as MMP.8.

The reader needs conditional probability, expectations and quantiles; continuous models also use integration. A mathematically qualified collaborator can supply those operations when the practitioner can specify the observation process and interpret the target.

Use an existing sufficient inference directly. If a compatible range already settles the question, C.16.IR can end the work without a probability model. A missing observation law returns to MMP.7; constructing a numerical sampler for an already specified posterior belongs to CMP.9.