The Statistical Bridge: From Events to Spines, Data Work, and the Interpretation of Results

Abstract

The Statistical Bridge develops a Theory-of-Data architecture for the interface between operational data and formal statistical reasoning. The central problem is not usually inside the estimator or theorem itself, but in the passage by which operational occurrences, records, identities, measurements, and transformations become the governed objects supplied to statistical theory—and in the interpretation by which formal results become claims about the world. The paper distinguishes two scopes of the statistical bridge. Broadly, the bridge is the governed interface between application and formal theory. Narrowly, its structural center is a regime-local event–spine relation, E(r)⇄S(r), connecting realized event-side evidence to independently established spine-side targets. Event and spine provide the geometry of a possible crossing, but not its warrant: a valid bridge additionally requires compatible anchors, lawful attribution, a forward evidence-production account, a target relation, and assumptions adequate for the intended claim. The framework separates four recurring questions—data, generation, inference, and interpretation—without treating them as stages of a mandatory workflow. It distinguishes deterministic data transformation from statistical inference, generation of possible evidence from inference using realized evidence, and formal results from the world-facing claims they license. Five recurrent failures—anchor substitution, universe substitution, hidden passage, imaginary generative connection, and claim overreach—show how an analysis can remain computationally and mathematically correct while its connection between evidence and target is broken or unstated. The Statistical Bridge does not replace sampling theory, missing-data theory, point-process theory, regression, prediction, causal inference, or domain expertise. It provides a common data foundation through which their local evidence–target bridges can be made explicit, governed, reviewed, and interpreted.