MMP.19:4.3 - Infer case conditions from the factual observations

Let e denote the available factual record. Use the model and recording procedure that produced it, including the actual action regime. MMP.7 constructs the recording law; MMP.13 supplies the needed conditioning.

For a finite supplied input law and record likelihood k(e given u), form

w(u given e) = k(e given u) p(u) / sum_v k(e given v) p(v).

The denominator must be positive. An exact deterministic record has a likelihood of one for compatible inputs and zero for incompatible ones. A noisy or selected record needs its actual likelihood. An individually observed continuous value uses the appropriate conditional distribution or density, not division by the probability of a zero-probability point.

This operation uses the factual mechanisms. Conditioning after replacing them can select a different set of cases. If the supplied account cannot produce the record, return the conflict; changing an assumed mechanism or observation model is a separate justified repair.

A probability law need not be invented when only possible inputs are supported. Retain the inputs compatible with the record and derive the range of responses they permit. If there is no factual conditioning in the query, use the selected population law or set directly.