Statistical Significance of Lorentz invariance violation from GRB 160625B

Recently Wei et al (arXiv:1612.09425) have found for a transition from positive time lags to negative time lags in the spectral lag data of GRB 160625B. They have fit these observed lags to a sum of two components: an intrinsic time lag due to astrophysical mechanisms and an energy-dependent speed of light due to violation of Lorentz invariance, which could be a signature of quantum gravity. Here, we examine the statistical significance of the for this claim using the same data by comparing it against the null hypothesis, viz. the time-lags are induced only by intrinsic delays. We use three different model comparison techniques: a frequentist test and two information based criteria (AIC and BIC). From the frequentist model comparison test, we find that for Lorentz violation is favoured at 3.05σ and 3.74σ for linear and quadratic models respectively and do not cross the 5σ discovery threshold. We find that ΔAIC and ΔBIC have values ≳ 10 for the quadratic Lorentz violating model pointing to decisive evidence against Lorentz invariance violation compared to only astrophysically induced intrinsic emission. Another concern however is that none of the three models (including the null hypothesis) provide a good fit to the data, which implies that there is additional physics or systematic errors, which are not accounted for while fitting the data to these models.