  Gamma-ray bursts (GRBs) are characterised by a strong correlation between the
instantaneous luminosity and the spectral peak energy within a burst. This
correlation, which is known as the hardness-intensity correlation or the
Golenetskii correlation, not only holds important clues to the physics of GRBs
but is thought to have the potential to determine redshifts of bursts. In this
paper, I use a hierarchical Bayesian model to study the universality of the
rest-frame Golenetskii correlation and in particular I assess its use as a
redshift estimator for GRBs. I find that, using a power-law prescription of the
correlation, the power-law indices cluster near a common value, but have a
broader variance than previously reported ($\sim 1-2$). Furthermore, I find
evidence that there is spread in intrinsic rest-frame correlation
normalizations for the GRBs in our sample ($\sim 10^{51}-10^{53}$ erg
s$^{-1}$). This points towards variable physical settings of the emission
(magnetic field strength, number of emitting electrons, photospheric radius,
viewing angle, etc.). Subsequently, these results eliminate the Golenetskii
correlation as a useful tool for redshift determination and hence a
cosmological probe. Nevertheless, the Bayesian method introduced in this paper
allows for a better determination of the rest frame properties of the
correlation, which in turn allows for more stringent limitations for physical
models of the emission to be set.
