The unbinned maximum-likelihood method provides a very powerful tool for estimating the values of model parameters in fits to experimental data. The method defines a log likelihood function on the data as a sum over all events in the sample, whose maximum in terms of the model parameters provides a statistical estimator for the parameters and their errors. The LHCb collaboration has published results based in part on an extension to the standard unbinned ML method called sFit, which allows events in the sample to be assigned weights in order to cancel out background contributions. This paper examines the statistical basis for the expressions employed in sFit, and introduces modifications that lead to improved statistical properties and error estimation.
