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Exploiting high-energy electron beams colliding into high-intensity laser pulses brings an opportunity to reach high values of the dimensionless rest-frame acceleration 
$\chi$ and thereby invoke processes described by strong-field quantum electrodynamics (SFQED). Measuring deviations from the results of Furry-picture perturbation theory in SFQED at high 
$\chi$ can be valuable for testing existing predictions, as well as for guiding further theoretical developments. Nevertheless, such experimental measurements are challenging due to the probabilistic nature of the interaction processes, dominating signals of low-
$\chi$ interactions and limited capabilities to control and measure the alignment and synchronization in such collision experiments. Here we elaborate a methodology of using approximate Bayesian computations for drawing statistical inferences based on the results of many repeated experiments despite partially unknown collision parameters that vary between experiments. As a proof-of-principle, we consider the problem of inferring the effective mass change due to coupling with the strong-field environment.
