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We apply Bayesian inference to determine the posterior likelihooddistribution for the parameters describing the initial condition of thesmall-$x$ Balitsky-Kovchegov evolution equation at leading logarithmicaccuracy. The HERA structure function data is found to constrain most of themodel parameters well. In particular, we find that the HERA data prefers ananomalous dimension $\gamma\approx 1$ unlike in previous fits where $\gamma>1$which led to e.g. the unintegrated gluon distribution and the quark-targetcross sections not being positive definite. The determined posteriordistribution can be used to propagate the uncertainties in the non-perturbativeinitial condition when calculating any other observable in the Color GlassCondensate framework. We demonstrate this explicitly for the inclusive quarkproduction cross section in proton-proton collisions and by calculatingpredictions for the nuclear modification factor for the $F_2$ structurefunction in the EIC and LHeC/FCC-he kinematics.

Inferring the initial condition for the Balitsky-Kovchegov equation