A comparison of Bayesian and frequentist confidence intervals in the presence of a late Universe degeneracy

Hubble tension is a problem in one-dimensional (1D) posteriors, since local H₀ H 0 determinations are only sensitive to a single parameter. Projected 1D posteriors for Λ Λ CDM cosmological parameters become more non-Gaussian with increasing effective redshift when the model is fitted to redshift-binned data in the late Universe. We explain mathematically why this non-Gaussianity arises and show, using observational Hubble data (OHD), that Markov chain Monte Carlo (MCMC) marginalisation leads to 1D posteriors that fail to track the χ ² χ 2 minimum at $$68%$$ 68 % confidence level in high redshift bins. To gain a second perspective, we resort to profile likelihoods as a complementary technique. Doing so, we observe that z 1 z ≳ 1 cosmic chronometer (CC) data currently prefer a non-evolving (constant) Hubble parameter over a Planck- Λ Λ CDM cosmology at ~ 2 σ ∼ 2 σ . Within the Hubble tension debate, it is imperative that subsamples of data sets with differing redshifts yield similar H₀ H 0 values. In addition, we confirm that MCMC degeneracies observed in 2D posteriors are not due to curves of constant χ ² χ 2 . Finally, on the assumption that the Planck- Λ Λ CDM cosmological model is correct, using profile likelihoods we confirm a >2 σ > 2 σ discrepancy with Planck- Λ Λ CDM in a combination of CC and baryon acoustic oscillations (BAO) data beyond z ~ 1.5 z ∼ 1.5 . This confirms a discrepancy reported earlier with fresh methodology.