MMP.16:4.2 - Construct the law of the obtainable records

Let d denote a feasible design: the selected inputs or cases, preparation, observing times and recording procedure. For each alternative derive either:

• a set R(h,theta,d) of possible records under its bounded uncertainties; or
• a probability law P(Y | h,theta,d) for the records Y.

The record includes what the procedure would actually retain. Compose the modeled response with the selection, measurement, censoring, rounding or aggregation operation. If an intervention changes the subject, derive its response under that intervention; an observational association alone supplies no such law.

Keep unknowns shared across readings shared. An unknown calibration offset cannot take one arbitrary value for the first reading and an unrelated value for the next if the same offset governs both. A repeated observation can reduce independent noise while leaving that common ambiguity intact.

A probabilistic comparison integrates unknowns only under a supplied probability law. Otherwise retain them as conditional possibilities or compare performance across their admitted range. Choosing a convenient nuisance value separately for each model can make a design look more discriminating than it is.

For an adaptive design, later observation choices are functions of records already available. Derive their joint law with that dependence. A sequence of fixed-design calculations does not by itself describe an outcome-dependent stopping or sampling rule.