Clarifying the Hubble constant tension with a Bayesian hierarchical model of the local distance ladder

Estimates of the Hubble constant, H-0, from the local distance ladder and from the cosmic microwave background (CMB) are discrepant at the similar to 3 sigma level, indicating a potential issue with the standard Lambda cold dark matter (Lambda CDM) cosmology. A probabilistic (i.e. Bayesian) interpretation of this tension requires a model comparison calculation, which in turn depends strongly on the tails of the H-0 likelihoods. Evaluating the tails of the local H-0 likelihood requires the use of non-Gaussian distributions to faithfully represent anchor likelihoods and outliers, and simultaneous fitting of the complete distance-ladder data set to ensure correct uncertainty propagation. We have hence developed a Bayesian hierarchical model of the full distance ladder that does not rely on Gaussian distributions and allows outliers to be modelled without arbitrary data cuts. Marginalizing over the full similar to 3000-parameter joint posterior distribution, we find H-0 =(72.72 +/- 1.67) km s(-1) Mpc(-1) when applied to the outlier-cleaned Riess et al. data, and (73.15 +/- 1.78) km s(-1) Mpc(-1) with supernova outliers reintroduced (the pre-cut Cepheid data set is not available). Using our precise evaluation of the tails of the H-0 likelihood, we apply Bayesian model comparison to assess the evidence for deviation from Lambda CDM given the distance-ladder and CMB data. The odds against Lambda CDM are at worst similar to 10:1 when considering the Planck 2015 XIII data, regardless of outlier treatment, considerably less dramatic than naively implied by the 2.8 sigma discrepancy. These odds become similar to 60:1 when an approximation to the more-discrepant Planck Intermediate XLVI likelihood is included.