Title: Toward an Axiomatic Theory of Statistical Inference

Abstract: I explore four guiding principles for statistical inference, namely Validity, Universality, Minimality, and an optional Optimality principle, together with their proposed mathematical formulation as an axiom system grounded in auxiliary prediction. 

Validity requires calibrated auxiliary prediction linked to assertions about unknown quantities through observed compatibility. Universality requires a common data-generating auxiliary representation across the parameter space. Minimality seeks efficient reduction of the auxiliary prediction problem while preserving relevant information and validity. 

Optimality compares valid and reduced procedures for a declared scientific target and efficiency criterion. I also show that inferential models provide the motivation and a calculus for this framework. More ambitiously, the goal is to develop a scientifically meaningful inferential framework, with a view toward trustworthy statistical reasoning and its eventual automation for scientific discovery.