A Measure of the Goodness of Fit in Unbinned Likelihood Fits; End of Bayesianism?

摘要

Maximum likelihood fits to data can be done using binned data (histograms)and unbinned data. With binned data, one gets not only the fitted parametersbut also a measure of the goodness of fit. With unbinned data, currently, thefitted parameters are obtained but no measure of goodness of fit is available.This remains, to date, an unsolved problem in statistics. Using Bayes' theoremand likelihood ratios, we provide a method by which both the fitted quantitiesand a measure of the goodness of fit are obtained for unbinned likelihood fits,as well as errors in the fitted quantities. The quantity, conventionallyinterpreted as a Bayesian prior, is seen in this scheme to be a number not adistribution, that is determined from data.