Improvement and generalization of ABCD method with Bayesian inference
Ezequiel Alvarez Leandro Da Rold Manuel Szewc Alejandro Szynkman Santiago A. Tanco Tatiana Tarutina
To find New Physics or to refine our knowledge of the Standard Model at the
LHC is an enterprise that involves many factors. We focus on taking advantage
of available information and pour our effort in re-thinking the usual
data-driven ABCD method to improve it and to generalize it using Bayesian
Machine Learning tools. We propose that a dataset consisting of a signal and
many backgrounds is well described through a mixture model. Signal, backgrounds
and their relative fractions in the sample can be well extracted by exploiting
the prior knowledge and the dependence between the different observables at the
event-by-event level with Bayesian tools. We show how, in contrast to the ABCD
method, one can take advantage of understanding some properties of the
different backgrounds and of having more than two independent observables to
measure in each event. In addition, instead of regions defined through hard
cuts, the Bayesian framework uses the information of continuous distribution to
obtain soft-assignments of the events which are statistically more robust. To
compare both methods we use a toy problem inspired by $pp\to hh\to b\bar b b
\bar b$, selecting a reduced and simplified number of processes and analysing
the flavor of the four jets and the invariant mass of the jet-pairs, modeled
with simplified distributions. Taking advantage of all this information, and
starting from a combination of biased and agnostic priors, leads us to a very
good posterior once we use the Bayesian framework to exploit the data and the
mutual information of the observables at the event-by-event level. We show how,
in this simplified model, the Bayesian framework outperforms the ABCD method
sensitivity in obtaining the signal fraction in scenarios with $1\%$ and
$0.5\%$ true signal fractions in the dataset. We also show that the method is
robust against the absence of signal.