Hossein Jorjani
First publication: 2026 – 07 – 19
Much of classical statistical inference derives its strength from repeated observations and probabilistic regularities. An equally important source of scientific knowledge, however, arises from structure. In many disciplines, inference succeeds not primarily because observations are numerous but because they are constrained by systematic relationships.
Such constraints take many forms. Genetic variants are related through linkage disequilibrium, linguistic reconstructions through grammatical and semantic regularities, causal inference through directed causal structures, and many statistical procedures through covariance relationships. In each case, the inferential power arises less from isolated observations than from the organization that binds them together.
This perspective suggests a broader conception of scientific inference. Dependence, rather than independence, often becomes the principal source of information. Unknown quantities are estimated not individually but through their position within a network of interconnected variables. The structure itself restricts the set of admissible explanations.
A further consequence follows. In structured inference, the relationship between model and observation becomes reciprocal. Classical statistical reasoning often treats observations as fixed while estimating unknown parameters. Under structural constraints, however, the model also evaluates the plausibility of the observations themselves. Apparent inconsistencies may indicate measurement error, recording error, sample mix-ups, or other defects rather than genuine departures from the underlying process.
Reconstruction constitutes one important application of structured inference, but the underlying principle is considerably broader. Whenever relationships among observations contain substantial information, scientific reasoning increasingly depends upon exploiting those relationships rather than treating each observation as an isolated datum.
This perspective does not replace statistical inference but complements it. Scientific knowledge frequently emerges through the interaction of probabilistic evidence and structural constraints. Appreciating this interaction may help clarify why many contemporary forms of inference differ fundamentally from the simpler observational models that shaped earlier philosophies of science.
Hossein Jorjani 