Chi-square versus median statistics in SNIa data analysis

TL;DR

This study compares chi-square and median likelihood methods for analyzing supernova data to determine cosmological constraints, finding chi-square tighter with supernovae alone but similar when combined with other data.

Contribution

It provides a comparative analysis of chi-square and median statistics in supernova cosmology, highlighting their relative effectiveness and robustness with additional cosmological data.

Findings

Chi-square yields tighter constraints with supernova data alone.

Both methods produce similar results when combined with CMB and BAO data.

Median statistic is robust and comparable to chi-square in combined analyses.

Abstract

In this paper we compare the performances of the chi-square and median likelihood analysis in the determination of cosmological constraints using type Ia supernovae data. We perform a statistical analysis using the 307 supernovae of the Union 2 compilation of the Supernova Cosmology Project and find that the chi-square statistical analysis yields tighter cosmological constraints than the median statistic if only supernovae data is taken into account. We also show that when additional measurements from the Cosmic Microwave Background and Baryonic Acoustic Oscillations are considered, the combined cosmological constraints are not strongly dependent on whether one applies the chi-square statistic or the median statistic to the supernovae data. This indicates that, when complementary information from other cosmological probes is taken into account, the performances of the chi-square and median statistics are very similar, demonstrating the robustness of the statistical analysis.