dorsal/arxiv
View SchemaA Measure of the Goodness of Fit in Unbinned Likelihood Fits
| Authors | Rajendran Raja |
|---|---|
| Categories | |
| ArXiv ID | physics/0207083 |
| URL | https://arxiv.org/abs/physics/0207083 |
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 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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"abstract": "Maximum likelihood fits to data can be done using binned data (histograms)\nand unbinned data. With binned data, one gets not only the fitted parameters\nbut also a measure of the goodness of fit. With unbinned data, currently, the\nfitted parameters are obtained but no measure of goodness of fit is available.\nThis remains, to date, an unsolved problem in statistics. Using Bayes theorem\nand likelihood ratios, we provide a method by which both the fitted quantities\nand a measure of the goodness of fit are obtained for unbinned likelihood fits,\nas well as errors in the fitted quantities. We provide an ansatz for\ndetermining Bayesian a priori probabilities.",
"arxiv_id": "physics/0207083",
"authors": [
"Rajendran Raja"
],
"categories": [
"physics.data-an",
"physics.gen-ph"
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"title": "A Measure of the Goodness of Fit in Unbinned Likelihood Fits",
"url": "https://arxiv.org/abs/physics/0207083"
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