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

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

2004-01-26

arxiv.org/abs/physics/0401133v2

ECONFC030908:MOCT003,2003

Physics

Data Analysis, Statistics and Probability

8 Pages, 6 Figures, Submitted to PHYSTAT2003, SLAC, Stanford, California, September 8-11,2003

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. 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.

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