Hierarchical Evidence Calculus (HEC): A Meta-Statistical Framework Unifying Frequentist and Bayesian Paradigms

Mainstream statistics is fundamentally dichotomized into Frequentist and Bayesian paradigms, both of which suffer from epistemological and structural limitations by reducing all forms of uncertainty to a singular measure of “probability.”We propose the Hierarchical Evidence Calculus (HEC), a deductive overarching framework that subjugates probability as a mere projection of a higher-order measure called “Evidence.” By formalizing the logical support between data, models, and priors within a join-semilattice derived from Noncommutative Hyperoperator Analysis (NHA), HEC achieves a unified orthogonal decompositionof aleatory, epistemic, and structural uncertainties, simultaneously preserving Frequentist objective consistency and Bayesian conditional updating.