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Least-squares fits are an important tool in many data analysis applications.In this paper, we review theoretical results, which are relevant for theirapplication to data from counting experiments. Using a simple example, weillustrate the well known fact that commonly used variants of the least-squaresfit applied to Poisson-distributed data produce biased estimates. The bias canbe overcome with an iterated weighted least-squares method, which producesresults identical to the maximum-likelihood method. For linear models, theiterated weighted least-squares method converges faster than the equivalentmaximum-likelihood method, and does not require problem-specific startingvalues, which may be a practical advantage. The equivalence of both methodsalso holds for binomially distributed data. We further show that the unbinnedmaximum-likelihood method can be derived as a limiting case of the iteratedleast-squares fit when the bin width goes to zero, which demonstrates a deepconnection between the two methods.

Application of the Iterated Weighted Least-Squares Fit to counting experiments