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

英文摘要：

Maximum likelihood fits to data can be done using binned data (histograms) and unbinned data. With binned data, one gets not only the fitted 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. The quantity, conventionally interpreted as a Bayesian prior, is seen in this scheme to be a number not a distribution, that is determined from data.