A Measure of the Goodness of Fit in Unbinned Likelihood Fits; End of Bayesianism?
نویسنده
چکیده
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.
منابع مشابه
A Measure of the Goodness of Fit in Unbinned Likelihood Fits
Abstract 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 a...
متن کاملA General Theory of Goodness of Fit in Likelihood Fits
Maximum likelihood fits to data can be performed using binned data and unbinned data. The likelihood fits in either case produce only the fitted quantities but not the goodness of fit. With binned data, one can obtain a measure of the goodness of fit by using the χ2 method, after the maximum likelihood fitting is performed. With unbinned data, currently, the fitted parameters are obtained but n...
متن کاملEvaluating Quality of Fit in Unbinned Maximum Likelihood Fitting
Abstract The unbinned maximimum likelihood fitting method, used in many current analyses including Belle’s measurements of sin and lifetimes, maximizes the use of available information to obtain the shape of a distribution in the face of limited statistics. However, a significant difficulty is that there has been no method for evaluating goodness-of-fit for the result. We examine some issues su...
متن کاملGoodness of Fit — with a View towards Particle Physics
This article reviews aspects of significance testing. Problems of detection of a specific signal with background noise from observed Poisson counts of events is used as a basic example throughout. In particular we discuss issues of using alternative test-statistics, unbinned likelihood fits, and comparing unweighted and weighted histograms. We point at the possibility of adding simultaneous con...
متن کاملGoodness of Fit: What Do We Really Want to Know?
The goodness-of-fit problem has recently attracted attention from the particle physics community. In modern particle experiments, one often performs an unbinned likelihood fit to data. The experimenter then needs to estimate how accurately the fit function approximates the observed distribution. A number of methods have been used to solve this problem in the past [1], and a number of methods ha...
متن کامل