Weighting Background-Subtracted Events

Often a full maximum likelihood (ML) estimate is inconvenient for computational reasons (e.g., iteration over large data sets). If a variable x is a discriminating variable (s(x) 6= b(x)), a weight function can be found which allows estimation of the number of signal events with a variance approaching that of a ML estimate of the same quantity. We derive a formula and discuss it in the context of more general results on event weighting from earlier papers by Barlow and Tkachov, which also nd weighting out-performs cutting.