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Open AccessArticle

Universal Sample Size Invariant Measures for Uncertainty Quantification in Density Estimation

1
Department of Physics and Optical Science, University of North Carolina at Charlotte, Charlotte, NC 28223, USA
2
Center for Biomedical Engineering and Science, University of North Carolina at Charlotte, Charlotte, NC 28223, USA
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Author to whom correspondence should be addressed.
Entropy 2019, 21(11), 1120; https://doi.org/10.3390/e21111120
Received: 7 October 2019 / Revised: 8 November 2019 / Accepted: 8 November 2019 / Published: 15 November 2019
(This article belongs to the Special Issue Data Science: Measuring Uncertainties)
Previously, we developed a high throughput non-parametric maximum entropy method (PLOS ONE, 13(5): e0196937, 2018) that employs a log-likelihood scoring function to characterize uncertainty in trial probability density estimates through a scaled quantile residual (SQR). The SQR for the true probability density has universal sample size invariant properties equivalent to sampled uniform random data (SURD). Alternative scoring functions are considered that include the Anderson-Darling test. Scoring function effectiveness is evaluated using receiver operator characteristics to quantify efficacy in discriminating SURD from decoy-SURD, and by comparing overall performance characteristics during density estimation across a diverse test set of known probability distributions. View Full-Text
Keywords: density estimation; distribution free; non-parametric statistical test; decoy distributions; size invariance; scaled quantile residual; maximum entropy method; scoring function; outlier detection; overfitting detection density estimation; distribution free; non-parametric statistical test; decoy distributions; size invariance; scaled quantile residual; maximum entropy method; scoring function; outlier detection; overfitting detection
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MDPI and ACS Style

Farmer, J.; Merino, Z.; Gray, A.; Jacobs, D. Universal Sample Size Invariant Measures for Uncertainty Quantification in Density Estimation. Entropy 2019, 21, 1120.

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