`Hyper Parameters' Approach to Joint Estimation: Applications to Cepheid-Calibrated Distances and X-Ray Clusters

Abstract

We use a generalised procedure for the combined likelihood analysis of different cosmological probes, the `Hyper-Parameters' method, that allows freedom in the relative weights of the raw measurements. We perform a joint analysis of the cepheid-calibrated data from the Hubble Space Telescope Key Project and the baryon mass fraction in clusters to constrain the total matter density of the universe, Omega_m, and the Hubble parameter, h. We compare the results obtained using Hyper-Parameters method with the estimates from standard chi^2 analysis. We assume that the universe is spatially flat, with a cosmological constant. We adopt the Big-Bang nucleosynthesis constraint for the baryon density, assuming the uncertainty is Gaussian distributed. Using this and the cluster baryon fraction data, we find that the matter density and the Hubble constant are correlated, Omega_m h^0.5~0.25, with preference for a very high h. To break the degeneracy, we add in the cepheid-calibrated data and find the best fit values (Omega_m, h) = (0.26 (+0.06,-0.06),0.72 (+0.04,-0.02)) (68 per cent confindence limits) using the Hyper-Parameters approach. We use the derived Hyper-Parameters to `grade' the 6 different data sets we analyse. Although our analysis is free of assumptions about the power spectrum of fluctuations, our results are in agreement with the Lambda-Cold Dark Matter `concordance' parameters derived from the Cosmic Microwave Background anisotropies combined with Supernovae Ia, redshift surveys and other probes.