  We determine the likelihood distribution for the model parameters describing
the event-by-event fluctuating proton geometry at small $x$ by performing a
Bayesian analysis within the Color Glass Condensate framework. The exclusive
$\mathrm{J}/\psi$ production data from HERA is found to constrain the model
parameters well, and we demonstrate that complementary constraints can be
obtained from simulations of Pb+Pb collisions at the LHC.
