Comparison of experimental data to Monte Carlo simulation—Parameter estimation and goodness-of-fit testing with weighted events

Relations are derived that can be used to infer parameters in situations where theoretical predictions can be compared to experimental data only indirectly via Monte Carlo simulation. We consider least square and likelihood ratio fits. Parameter changes in the fitting procedures are performed by re-weighting Monte Carlo events. Formulas for goodness-of-fit tests based on the χ 2 and the likelihood ratio statistic are presented.