A Measure of the Goodness of Fit in Unbinned Likelihood Fits

Details A Measure of the Goodness of Fit in Unbinned Likelihood Fits A Measure of the Goodness of Fit in Unbinned Likelihood Fits

2002-07-22

arxiv.org/abs/physics/0207083v2

Physics

Data Analysis, Statistics and Probability

26 pages, 8 figures

Scientific paper

Maximum likelihood fits to data can be done using binned data (histograms) and unbinned data. With binned data, one gets not only the fitted parameters but also a measure of the goodness of fit. With unbinned data, currently, the fitted parameters are obtained but no measure of goodness of fit is available. This remains, to date, an unsolved problem in statistics. Using Bayes theorem and likelihood ratios, we provide a method by which both the fitted quantities and a measure of the goodness of fit are obtained for unbinned likelihood fits, as well as errors in the fitted quantities. We provide an ansatz for determining Bayesian a priori probabilities.

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