  Likelihood-based inference, central in modern particle physics data analysis
requires the extensive evaluation of a likelihood function that depends on set
of parameters defined by the statistical model under consideration. If an
analytical expression for the likelihood can be defined from first principles
the procedure is computationally straightforward. However, most experiments
require approximating the likelihood numerically using large statistical
samples of synthetic events generated using Monte Carlo methods. As a result,
the likelihood consists of a comparison of the expected versus the observed
event rates in a collection of histogram bins, defining binned likelihood
functions. When this occurs, evaluating the likelihood function involves, on
each occasion, recalculating the prediction in those bins, increasing the
computational load of these analysis drastically. In this text, I highlight the
importance of identifying which are the unique event configurations in the
binned likelihood definition and I provide an exact formula to update the event
rate predictions utilizing the minimum number of necessary calculations by
means of factorization. The aim of the discussion is to decrease the
computational load of widespread high-energy physics analyses, leading to
substantial speed improvements and reduced carbon footprints.
