Fitting simulated random events to experimental histograms by means of parametric models

Classical chi-square quantities are appropriate tools for fitting analytical parameter-dependent models to (multidimensional) measured histograms. In contrast, this article proposes a family of special chi-squares suitable for fits with models which simulate experimental data by Monte Carlo methods, thus introducing additional randomness. We investigate the dependence of such chi-squares on the number of experimental and simulated events in each bin, and on the theoretical parameter-dependent weight linking the two kinds of events. We identify the unknown probability distributions of the weights and their inter-bin correlations as the main obstacle to a general performance analysis of the proposed chi-square quantities.