How unbiased statistical methods lead to biased scientific discoveries: A case study of the Efron-Petrosian statistic applied to the luminosity-redshift evolution of Gamma-Ray Bursts

Abstract

Statistical methods are frequently built upon assumptions that limit their applicability to certain problems and conditions. Failure to recognize these limitations can lead to conclusions that may be inaccurate or biased. An example of such methods is the non-parametric Efron-Petrosian test statistic used in the studies of truncated data. We argue and show how the inappropriate use of this statistical method can lead to biased conclusions when the assumptions under which the method is valid do not hold. We do so by reinvestigating the evidence recently provided by multiple independent reports on the evolution of the luminosity/energetics distribution of cosmological Long-duration Gamma-Ray Bursts (LGRBs) with redshift. We show that the effects of detection threshold has been likely significantly underestimated in the majority of previous studies. This underestimation of detection threshold leads to severely-incomplete LGRB samples that exhibit strong apparent luminosity-redshift or energetics-redshift correlations. We further confirm our findings by performing extensive Monte Carlo simulations of the cosmic rates and the luminosity/energy distributions of LGRBs and their detection process.

A Comparative Study of Luminosity Functions and Event Rate Densities of Long GRBs with Non-parametric Method

“…The power-law index of k for the sample II will be about 3.62 once the F lim,2 is applied. It demonstrates that the deduced k values depend more on the sample selection but less on the instrumental effect, which is somewhat different from what mentioned by Bryant et al (2020). The reason is that all bursts in our samples are located above the lower limits of luminosities.…”

“…Strangely, they did not find the excessive components compared with the SFRs at lower redshift. In addition, Bryant et al (2020) recently argued that an underestimation of detection threshold will also lead to severely-incomplete lGRB samples which eventually affects the inferred event rates.…”

“…Bloom et al 2003;). On the other hand, Bryant et al (2020) pointed out that the detection threshold effect will be underestimated in a sense and should be given a conservative estimation of F lim,2 = 1.0 × 10 −7 erg cm −2 s −1 . The difference between F lim,1 and F lim,2 could play an un-negligible role on 0 2 4 6 8 1 0 4 8 1 0 4 9 1 0 5 0 1 0 5 1 1 0 5 2 1 0 5 3 1 0 5 4 1 0 5 5 modeling the observed luminosity-redshift relation when a significant fraction of lGRBs reside below the L lim for a GRB sample.…”

Tracing dark energy history with gamma ray bursts

“…A first evident deviation from the above-discussed case arises at z 1.5, where departures from the ΛCDM case lies on 2.4-σ for the H 0 of P20 and on 4-σ for the H 0 of R19. Clearly, at z 1.5 a severe observational bias exists and we could indeed observe only the brightest GRBs (Bryant et al 2020) 13 .…”