The Coherence Principle: A Falsifiable Prior for Model Selection from the Grammar of Theories

2026-06-16

AI Summary

Bayesian model selection is often hindered by overly strong prior dependence lacking clear justification, with existing approaches either neglecting established theoretical structures or relying on impractical criteria. This work proposes a “consistency principle” that explicitly translates the syntactic structure of physical theories—such as symmetries, conservation laws, locality, and Lorentz invariance—into testable and falsifiable Bayesian priors. By invoking the maximum entropy principle, a calibratable parameter α is introduced to quantify the penalty for deviations from theoretical syntax. Distinct from Occam’s factor and naturalness, this approach emphasizes consistency with theoretical form rather than fine-tuning of parameters. Applied across multiple cases in cosmology and particle physics, as well as four landmark historical theories—including general relativity and Pauli’s neutrino hypothesis—the method successfully recovers the correct model preferences, demonstrating its validity and falsifiability.

Abstract

Bayesian model selection in cosmology and particle physics is often performed where posterior odds inherit a strong, often unacknowledged dependence on the prior assigned to competing models. Standard responses -- reference priors, hierarchical priors, or appeals to naturalness -- ignore relevant theoretical knowledge or rely on criteria hard to define operationally. We propose the \emph{Coherence Principle}: a reproducible prescription for assigning model priors according to compatibility with the validated structure of an existing theory. This structure, or \emph{grammar}, includes symmetries, conservation laws, locality, Lorentz invariance, and universality patterns. Unmotivated violations of these rules incur a coherence cost, converted into a prior weight through a maximum-entropy exponential form controlled by one calibratable parameter $α$. The resulting prior is distinct from both the Bayesian Occam factor and naturalness: it penalizes not parameter volume or fine tuning, but departures from validated theoretical grammar. We illustrate the principle with examples from cosmology and fundamental physics: neutrino mass mechanisms, dark energy and modified gravity, inflation, beyond-Standard-Model sectors, and hierarchical astrophysical inference. We test it also on four historical cases -- general relativity, Pauli's neutrino, parity violation, and special relativity -- where evidential and theoretical contexts can be reconstructed. These examples show that it favors the historically successful choice when the proper grammar is defined in the correct domain and time. The Coherence Principle makes explicit a common but usually tacit part of physical reasoning: trust in validated structural rules. It turns this judgment into a transparent, testable, and overrulable component of Bayesian inference, leaving empirical likelihoods free to dominate when data are sufficiently constraining.

Problem

• Bayesian model selection
• prior dependence
• theoretical grammar
• coherence
• model comparison

Innovation

• Coherence Principle
• theoretical grammar
• Bayesian model selection
• maximum-entropy prior
• falsifiable prior