The Bayesian view of DESI DR2 with unimpeded: Evidence and tension in a combined analysis with CMB and supernovae across cosmological models

We apply the unimpeded framework to perform a fully Bayesian reanalysis of the DESI DR2 data, using nested sampling with PolyChord to compute evidences for ΛCDM and seven extensions across combinations of DESI DR1/DR2, Planck CMB, supernovae (Pantheon+, Union3, DES-SN5YR, DES-Dovekie), and DES-Y1 weak lensing. The Bayesian Ockham's razor penalises extended models, yielding weaker or opposite preferences compared to Δχ^2-based analyses. For DESI DR2 BAO combined with Planck CMB alone, the DESI collaboration's 3.1σ frequentist preference for w_0w_aCDM is eliminated entirely: we obtain {ln B = -0.57{scriptstylepm0.26}}, modestly favouring ΛCDM. Adding DES-Dovekie, the recalibration of DES-SN5YR, maintains this concordance ({ln B = -0.30{scriptstylepm0.19}}). However, when the earlier DES-SN5YR calibration is included instead, the DESI collaboration's 4.2σ result survives the Bayesian Ockham penalty as a 3.07{scriptstylepm0.10},σ preference ({ln B = +3.32{scriptstylepm0.27}}). That this signal persists despite the Ockham penalty makes the role of tension quantification essential: our analysis traced the preference to the earlier DES-SN5YR calibration, which introduced a 2.95{scriptstylepm 0.04},σ conflict with DESI DR2 within ΛCDM -- a tension that stands out from the grid -- reduced to 1.96{scriptstylepm 0.04},σ with the DES-Dovekie recalibration. With DES-Dovekie, the Bayesian evidence for dynamical dark energy vanishes.