  Bubble chambers using liquid xenon (and liquid argon) have been operated
(resp. planned) by the Scintillating Bubble Chamber (SBC) collaboration for
GeV-scale dark matter searches and CE$\nu$NS from reactors. This will require a
robust calibration program of the nucleation efficiency of low-energy nuclear
recoils in these target media. Such a program has been carried out by the PICO
collaboration, which aims to directly detect dark matter using $\mathrm{C_3
F_8}$ bubble chambers. Neutron calibration data from mono-energetic neutron
beam and Am-Be source has been collected and analyzed, leading to a global fit
of a generic nucleation efficiency model for carbon and fluorine recoils, at
thermodynamic thresholds of $2.45$ and $3.29\,\mathrm{keV}$. Fitting the
many-dimensional model to the data ($34$ free parameters) is a non-trivial
computational challenge, addressed with a custom Markov Chain Monte Carlo
approach, which will be presented. Parametric MC studies undertaken to validate
this methodology are also discussed. This fit paradigm demonstrated for the
PICO calibration will be applied to existing and future scintillating bubble
chamber calibration data.
