Reading Statistical Rethinking Through the Statistical Bridge

Abstract

Reading Statistical Rethinking Through the Statistical Bridge examines Richard McElreath's Statistical Rethinking through the architecture of The Statistical Bridge and Regime Has a Contract, and places that reading beside an empirically oriented tradition represented by algorithmic machine learning. The paper argues that a central distinction across statistical and machine-learning practice is not simply theory versus data, explanation versus prediction, or statistics versus machine learning, but what is provisionally assumed and what is being inferred. McElreath's program is interpreted as claim-founded: the scientific meaning sought from an analysis reaches backward to constrain causal structure, generative assumptions, estimands, and statistical procedure. An empirical or algorithmic orientation can begin from the opposite side, provisionally accepting governed data and a task and inferring a model as a predictive, representational, or compressive account of empirical regularity. The paper argues that these orientations are not competing one-way doctrines. They are different entry points into a multidirectional statistical architecture. The Statistical Bridge distinguishes the governed data objects of an analysis, the generation of possible evidence, inference from realized evidence to formal targets, and interpretation of formal results as world-facing claims. Regime Has a Contract adds an orthogonal distinction between reasoning within a value-generation regime and reasoning across regimes. Assumption and inference are therefore treated as roles within passages rather than permanent properties of objects. The comparison also develops a broader account of the semantic role of statistical frameworks. A useful framework reduces the semantic cost of intellectual work by giving stable names to distinctions that otherwise have to be reconstructed repeatedly: data versus model, event versus spine, generation versus inference, observational evidence versus intervention claims, and formal result versus licensed interpretation. The paper concludes that neither data-first nor model-first practice should be identified with the Statistical Bridge. The bridge is an architecture of governed relationships that can be entered and traversed in different directions: the bridge has directions; inquiry need not have only one direction.