  Multijet events with heavy-flavors are of central importance at the LHC since
many relevant processes -- such as $t\bar t$, $hh$, $t\bar t h$ and others --
have a preferred branching ratio for this final state. Current techniques for
tackling these processes use hard-assignment selections through $b$-tagging
working points, and suffer from systematic uncertainties because of the
difficulties in Monte Carlo simulations. We develop a flexible Bayesian mixture
model approach to simultaneously infer $b$-tagging score distributions and the
flavor mixture composition in the dataset. We model multidimensional jet
events, and to enhance estimation efficiency, we design structured priors that
leverages the continuity and unimodality of the $b$-tagging score
distributions. Remarkably, our method eliminates the need for a parametric
assumption and is robust against model misspecification -- It works for
arbitrarily flexible continuous curves and is better if they are unimodal. We
have run a toy inferential process with signal $bbbb$ and backgrounds $bbcc$
and $cccc$, and we find that with a few hundred events we can recover the true
mixture fractions of the signal and backgrounds, as well as the true
$b$-tagging score distribution curves, despite their arbitrariness and
nonparametric shapes. We discuss prospects for taking these findings into a
realistic scenario in a physics analysis. The presented results could be a
starting point for a different and novel kind of analysis in multijet events,
with a scope competitive with current state-of-the-art analyses. We also
discuss the possibility of using these results in general cases of signals and
backgrounds with approximately known continuous distributions and/or expected
unimodality.
