Probabilistic treatment of the uncertainty from the finite size of weighted Monte Carlo data

Understand

Parameter estimation in HEP experiments often involves Monte-Carlo simulation to model the experimental response function.

• A typical application are forward-folding likelihood analyses with re-weighting, or time-consuming minimization schemes with a new simulation set for each parameter value.
• Problematically, the finite size of such Monte Carlo samples carries intrinsic uncertainty that can lead to a substantial bias in parameter estimation if it is neglected and the sample size is small.
• We introduce a probabilistic treatment of this problem by replacing the usual likelihood functions with novel generalized probability distributions that incorporate the finite statistics via suitable marginalization.