A Bayesian Model Comparison Framework for Extrapolative Scientic Hypotheses: Methodology and Application to Holography in Theoretical Physics

We develop a general Bayesian model comparison framework for evaluating universal ontological claims in science - hypotheses that extrapolate domain-specific laws to universal status without direct experimental verification. The methodology comprises: (i) sharp hypothesis specification distinguishing universal from scale-specific claims; (ii) historically informed prior assignment based on patterns of theory succession; (iii) systematic evidence decomposition with explicit likelihood elicitation; (iv) formal treatment of evidential dependence via correlation-adjusted composite likelihoods; and (v) comprehensive sensitivity analysis. As a detailed case study, we apply this framework to the holographic principle in theoretical physics, comparing universal holography (all physical degrees of freedom are boundary-encoded) against scale-specific holography (holographic descriptions are powerful within particular regimes but not constitutive of reality). Under explicit assumptions, we obtain a posterior probability of 6-8% for universal holography (range from sensitivity analysis), with a Bayes factor of approximately 0.29, indicating moderate evidence favoring the scale-specific interpretation. The framework provides a template for disciplined probabilistic assessment of foundational claims across scientific domains where direct testing is infeasible. Bayesian inference, model comparison, Bayes factors, prior specification, evidence synthesis, sensitivity analysis, foundational physics, holographic principle, extrapolation, theory succession