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

Understand

Hubble tension is a problem in one-dimensional (1D) posteriors, since local $H_0$ determinations are only sensitive to a single parameter.

• Projected 1D posteriors for $\Lambda$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 $\chi^2$ minimum at $68\%$ confidence level in high redshift bins.
• To gain a second perspective, we resort to profile likelihoods as a complementary technique.