Median statistics, H(0), and the accelerating universe

We develop median statistics that provide powerful alternatives to chi-squared methods and require fewer assumptions about the data, namely they do not assume Gaussianity of the errors or that their magnitudes are known. Applying median statistics to Huchra's compilation of nearly all estimates of the Hubble constant, we find H_0 = 67 +/- 2 km/s/Mpc (95% range, statistical errors only). Median statistics only assume measurements are independent and free of systematic errors. The statistical precision of this result may lead a cautious person to examine carefully the question of systematic effects. This estimate of H_0 = 67 km/s/Mpc is arguably the best summary of current knowledge because it uses all available data and, unlike other estimates, makes no assumption about the distribution of measurement errors. A Bayesian median statistics treatment of high-z Type Ia supernovae data from Riess et al. yields a posterior probability that the cosmological constant Lambda > 0 of 70 or 89%, depending on prior information used. The posterior probability of a spatially-open universe is about 47%. Analysis of the Perlmutter et al. high-z SNe Ia data show the best-fit flat-Lambda model favored over the best-fit Lambda = 0 open model by posterior odds of 366:1; corresponding Reiss et al. odds are 3:1 (assuming prior odds of 1:1). Median statistics analyses of the SNe Ia data do not rule out a time-variable Lambda model, and may even favor it over a time-independent Lambda and a Lambda = 0 open model.

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