Noninferability

Noninferability is the property of a claim, attribute, or parameter that cannot be reliably inferred from available data or evidence within a given modeling framework. It denotes the opposite of inferability: even with access to data D and a specified model, the truth of a proposition H remains essentially unconstrained by D under the assumed assumptions.

In statistics and machine learning, noninferability arises when information about a parameter is vanishingly small or the model is non-identifiable. Causes include high noise levels, small sample sizes, collinearity, or structural ambiguities in the model that prevent unique recovery of parameter values. In such cases, estimators exhibit large variance and posterior beliefs about the parameter stay close to their priors, making reliable inference impractical.

In privacy and data publishing, noninferability characterizes the idea that released data should not allow reliable inference of sensitive attributes beyond what was already possible. Formal approaches such as differential privacy aim to ensure noninferability by bounding how much the output distribution can change when any single individual's data are modified, thereby limiting updates to beliefs about private attributes.

Formal notions often use Bayesian or likelihood-based criteria. For a binary proposition H, noninferability can be expressed as a Bayes factor close to one, or as the posterior P(H|D) remaining near the prior P(H) within a specified tolerance. Limitations include dependence on modeling choices and the fact that noninferability is relative to the assumed data-generating process and context. See also inferability, identifiability, and differential privacy.