MMP.19:4.5 - Determine what the available information fixes

A fully supplied model gives a consequence conditional on that model. Identification asks whether all admissible models agreeing with the available information give the same target. Use MMP.15’s distinction between a proof of ambiguity and an unfinished search on the counterfactual construction now specified.

Two compatible models with different target values prove non-identification under their shared assumptions and available laws. More samples from those same laws cannot distinguish them. A narrower quantity can nevertheless be identified.

For a finite response-type construction, assign a nonnegative mass to each admitted type, with total mass one. Express the known marginal, joint and regime laws as constraints on those masses. Add a structural restriction only when the causal account supports it. Minimize and maximize the target over the compatible masses; for a conditional probability retain its conditioning denominator. MMP.10 helps formulate the constraints and an appropriate computational method can solve them.

Call the resulting bounds tight only when the construction establishes that no smaller range follows and that its extremes are attainable, or specifies unattained limiting extremes. A numerical search that finds two values supplies witnesses, not necessarily the full range. Uncertainty from estimating an input law with finite data is another layer, handled by MMP.13; it is not the same as ambiguity remaining even when that law is known.