On the True Significance of the Hubble Tension: A Bayesian Error Decomposition Accounting for Information Loss

The Hubble tension, a persistent discrepancy between early and late Universe measurements of H0, poses a significant challenge to the standard cosmological model. In this work, we present a new Bayesian hierarchical framework designed to meticulously decompose this observed tension into its constituent parts: standard measurement errors, information loss arising from parameter-space projection, and genuine physical tension. Our approach, employing Fisher matrix analysis with MCMC-estimated loss coefficients and explicitly modeling information loss via variance inflation factors (λ), is particularly important in high-precision analysis where even seemingly small information losses can impact conclusions. We find that the real tension component (Treal) has a mean value of 5.94 km/s/Mpc (95% CI: 3.32, 8.64 km/s/Mpc). Quantitatively, approximately 78% of the observed tension variance is attributed to real tension, 13% to measurement error, and 9% to information loss. Despite this, our decomposition indicates that the observed ∼6.39σ discrepancy is predominantly a real physical phenomenon, with real tension contributing ∼5.64σ. Our findings strongly suggest that the Hubble tension is robust and probably points toward new physics beyond the ΛCDM model.