Median Statistics, H0, and the Accelerating Universe

By J. Richard Gott III, Michael S. E. Vogeley, Silviu Podariu, Bharat Ratra. 2000

184 citations recorded by the source corpus.

We develop median statistics that provide powerful alternatives to χ2 likelihood methods and require fewer assumptions about the data. Application to astronomical data demonstrates that median statistics lead to results that are quite similar and almost as constraining as χ2 likelihood methods but with somewhat more confidence since 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 a median value H0 = 67 km s-1 Mpc-1. Median statistics assume only that the measurements are independent and free of systematic errors. This estimate 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. The 95% range of purely statistical errors is ±2 km s-1 Mpc-1. The high degree of statistical accuracy of this result demonstrates the power of using only these two assumptions and leads us to analyze the range of possible systematic errors in the median, which we estimate to be roughly ±5 km s-1 Mpc-1 (95% limits), dominating over the statistical errors. Using a Bayesian median statistics treatment of high-redshift Type Ia supernovae (SNe Ia) apparent magnitude versus redshift data from Riess et al., we find the posterior probability that the cosmological constant Λ > 0 is 70% or 89%, depending on the prior information we include. We find the posterior probability of an open universe is about 47%, and the probability of a spatially flat universe is 51% or 38%. Our results generally support the observers' conclusions but indicate weaker evidence for Λ > 0 (less than 2 σ). Median statistics analysis of the Perlmutter et al. high-redshift SNe Ia data shows that the best-fit flat-Λ model is favored over the best-fit Λ = 0 open model by odds of 366 : 1; the corresponding Riess et al. odds are 3 : 1 (assuming in each case prior odds of 1 : 1). A scalar field with a potential energy with a "tail" behaves like a time-variable Λ. Median statistics analyses of the SNe Ia data do not rule out such a time-variable Λ and may even favor it over a time-independent Λ and a Λ = 0 open model.

Subfields: Applied Mathematics, Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/9c6ba3465ad900f70f87a1a17fbc233a931f2df0

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Eric Mamajek
2. C. Bell
3. Bharat Ratra

In Astronomy and Astrophysics

1. C. Bell
2. Nuno C. Santos
3. Eric Mamajek
4. F. Bouchy
5. G. Hébrard
6. Hai-Bo Yu
7. Fa-yin Wang
8. C. Moutou

Citations in the corpus

• On the age of the β Pictoris moving group (2014, methodology): “When we mention a “standard error”, we are actually using the average of (1) the error of the true median (Gott et al. 2001), and (2) the standard error of the Chauvenet clipped mean (Bevington & Robinson 1992).”
• HUBBLE PARAMETER MEASUREMENT CONSTRAINTS ON THE REDSHIFT OF THE DECELERATION–ACCELERATION TRANSITION, DYNAMICAL DARK ENERGY, AND SPACE CURVATURE (2016, methodology): “For discussions and applications of median statistics, see Gott et al. (2001), Chen & Ratra (2003), Hodge et al. (2009), Crandall & Ratra (2014), Crandall et al. (2015), Ding et al. (2015), Crandall & Ratra (2015), and Zheng et al. (2016).”
• Hubble Parameter and Baryon Acoustic Oscillation Measurement Constraints on the Hubble Constant, the Deviation from the Spatially Flat ΛCDM Model, the Deceleration–Acceleration Transition Redshift, and Spatial Curvature (2017, result): “These are consistent with the most recent median statistics estimate H0=68±2.8 km s −1Mpc−1 (Chen & Ratra 2011a), which is consistent with earlier median statistics estimates (Gott et al. 2001; Chen et al. 2003).”
• SOPHIE velocimetry of Kepler transit candidates XVII. The physical properties of giant exoplanets within 400 days of period (2015, background): “…(PI: Hébrard) ; TNG programme IDs: A28DD2 (PI: Santerne) 8 The values and errors reported in this paragraph correspond to the mean and its uncertainty computed as σ/ √ N − k f , with σ the standard deviation, N the number of points, and k f the number of free parameters (Gott et al. 2001).”