无面元似然拟合的拟合优度度量
A Measure of the Goodness of Fit in Unbinned Likelihood Fits
摘要：
对数据的极大似然拟合可以使用分箱数据（直方图）和未分箱数据来完成。利用分箱数据，不仅可以得到拟合参数，还可以得到拟合的拟合优度。对于未分组的数据，目前获得了拟合参数，但没有可用的拟合优度测量。迄今为止，这仍然是统计学上一个未解决的问题。使用贝叶斯定理和似然比，我们提供了一种方法，通过该方法可以获得未分组似然拟合的拟合量和拟合优度拟合优度，以及拟合量中的误差。我们提供了一个用于确定贝叶斯先验概率的方法。
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. We provide an ansatz for determining Bayesian a priori probabilities.
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