Quasar Identification Using Multivariate Probability Density Estimated from Nonparametric Conditional Probabilities

Farmer, Jenny; Allen, Eve; Jacobs, Donald J.

doi:10.3390/math11010155

Quasar Identification Using Multivariate Probability Density Estimated from Nonparametric Conditional Probabilities

Journal Article · Tue Dec 27 23:00:00 EST 2022 · Mathematics

DOI:https://doi.org/10.3390/math11010155· OSTI ID:2425264

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Univ. of North Carolina, Charlotte, NC (United States)

Nonparametric estimation for a probability density function that describes multivariate data has typically been addressed by kernel density estimation (KDE). A novel density estimator recently developed by Farmer and Jacobs offers an alternative high-throughput automated approach to univariate nonparametric density estimation based on maximum entropy and order statistics, improving accuracy over univariate KDE. This article presents an extension of the single variable case to multiple variables. The univariate estimator is used to recursively calculate a product array of one-dimensional conditional probabilities. In combination with interpolation methods, a complete joint probability density estimate is generated for multiple variables. Good accuracy and speed performance in synthetic data are demonstrated by a numerical study using known distributions over a range of sample sizes from 100 to 10⁶ for two to six variables. Performance in terms of speed and accuracy is compared to KDE. The multivariate density estimate developed here tends to perform better as the number of samples and/or variables increases. As an example application, measurements are analyzed over five filters of photometric data from the Sloan Digital Sky Survey Data Release 17. The multivariate estimation is used to form the basis for a binary classifier that distinguishes quasars from galaxies and stars with up to 94% accuracy.

View Accepted Manuscript (DOE)

Research Organization:: US Department of Energy (USDOE), Washington, DC (United States). Office of Science, Sloan Digital Sky Survey (SDSS)

Sponsoring Organization:: USDOE Office of Science (SC)

OSTI ID:: 2425264

Journal Information:: Mathematics, Journal Name: Mathematics Journal Issue: 1 Vol. 11; ISSN 2227-7390

Publisher:: MDPICopyright Statement

Country of Publication:: United States

Language:: English

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79 ASTRONOMY AND ASTROPHYSICS
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galaxies
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Quasar Identification Using Multivariate Probability Density Estimated from Nonparametric Conditional Probabilities

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