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New distance measures for classifying X-ray astronomy data into stellar classes

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Abstract

The classification of the X-ray sources into classes (such as extragalactic sources, background stars,...) is an essential task in astronomy. Typically, one of the classes corresponds to extragalactic radiation, whose photon emission behaviour is well characterized by a homogeneous Poisson process. We propose to use normalized versions of the Wasserstein and Zolotarev distances to quantify the deviation of the distribution of photon interarrival times from the exponential class. Our main motivation is the analysis of a massive dataset from X-ray astronomy obtained by the Chandra Orion Ultradeep Project (COUP). This project yielded a large catalog of 1616 X-ray cosmic sources in the Orion Nebula region, with their series of photon arrival times and associated energies. We consider the plug-in estimators of these metrics, determine their asymptotic distributions, and illustrate their finite-sample performance with a Monte Carlo study. We estimate these metrics for each COUP source from three different classes. We conclude that our proposal provides a striking amount of information on the nature of the photon emitting sources. Further, these variables have the ability to identify X-ray sources wrongly catalogued before. As an appealing conclusion, we show that some sources, previously classified as extragalactic emissions, have a much higher probability of being young stars in Orion Nebula.

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References

  • Araujo A, Giné E (1980) The central limit theorem for real and Banach valued random variables. Wiley, New York

    MATH  Google Scholar 

  • Ascher S (1990) A survey of tests for exponentiality. Commun Stat Theory Methods 19:1811–1825

    Article  MathSciNet  Google Scholar 

  • Baíllo A, Cárcamo J, Nieto S (2015) A test for convex dominance with respect to the exponential class based on an $L^1$ distance. IEEE Trans Reliab 64:71–82

    Article  Google Scholar 

  • Broos PS, Getman KV, Povich MS, Townsley LK (2011) A naive Bayes source classifier for X-ray sources. Astrophys J Suppl Ser. https://doi.org/10.1088/0067-0049/194/1/4

    Google Scholar 

  • Cárcamo J (2017) Integrated empirical processes in $L^p$ with applications to estimate probability metrics. Bernoulli 23:3412–3436

    Article  MathSciNet  MATH  Google Scholar 

  • del Barrio E, Giné E, Matrán C (1999) Central limit theorems for the Wasserstein distance between the empirical and the true distributions. Ann Probab 27:1009–1071

    Article  MathSciNet  MATH  Google Scholar 

  • Efron B, Tibshirani RJ (1993) An introduction to the bootstrap. Chapman and Hall, New York

    Book  MATH  Google Scholar 

  • Feigelson ED, Babu GJ (2012) Modern statistical methods for astronomy. With R applications. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Feigelson ED, Getman K, Townsley L, Garmire G, Preibisch T, Grosso N, Montmerle T, Muench A, McCaughrean M (2005) Global X-ray properties of the Orion Nebula region. Astrophys J Suppl Ser 160:379–389

    Article  Google Scholar 

  • García-Escudero LA, Gordaliza A, Mayo-Iscar A (2014) A constrained robust proposal for mixture modeling avoiding spurious solutions. Adv Data Anal Classif 8:27–43

    Article  MathSciNet  Google Scholar 

  • Getman K, Feigelson E, Grosso N, McCaughrean M, Micela G, Broos P, Garmire G, Townsley L (2005a) Membership of the Orion Nebula population from the Chandra Orion Ultradeep Project. Astrophys J Suppl Ser 160:353–378

    Article  Google Scholar 

  • Getman K, Flaccomio E, Broos P, Grosso N, Tsujimoto M, Townsley L, Garmire G, Kastner J, Li J, Harnden F, Wolk S, Murray S, Lada C, Muench A, McCaughrean M, Meeus G, Damiani F, Micela G, Sciortino S, Bally J, Hillenbrand L, Herbst W, Preibisch T, Feigelson E (2005b) Chandra Orion Ultradeep Project: observations and source lists. Astrophys J Suppl Ser 160:319–352

    Article  Google Scholar 

  • Getman KV, Feigelson ED, Broos PS, Micela G, Garmire GP (2008a) X-ray flares in Orion young stars. I. Flare characteristics. Astrophys J 688:418–436

    Article  Google Scholar 

  • Getman KV, Feigelson ED, Micela G, Jardine MM, Gregory SG, Garmire GP (2008b) X-ray flares in Orion young stars. II. Flares, magnetospheres, and protoplanetary disks. Astrophys J 688:437–455

    Article  Google Scholar 

  • Grafakos L (2014) Classical Fourier analysis, 3rd edn. Springer, New York

    MATH  Google Scholar 

  • Henze N, Meintanis SG (2005) Recent and classical tests for exponentiality: a partial review with comparisons. Metrika 61:29–45

    Article  MathSciNet  MATH  Google Scholar 

  • Hubert M, Rousseeuw P, Segaert P (2017) Multivariate and functional classification using depth and distance. Adv Data Anal Classif 11:445–466

    Article  MathSciNet  Google Scholar 

  • Kallenberg O (2002) Foundations of modern probability, 2nd edn. Springer, New York

    Book  MATH  Google Scholar 

  • Kuhn M (2008) Building predictive models in R using the caret package. J Stat Softw 28:1–26

    Article  Google Scholar 

  • Ledoux M, Talagrand M (2011) Probability in Banach spaces. Springer, Berlin

    MATH  Google Scholar 

  • Rachev ST, Stoyanov SV, Fabozzi FJ (2011) A probability metrics approach to financial risk measures. Wiley-Blackwell, Oxford

    Book  Google Scholar 

  • Rachev ST, Klebanov LB, Stoyanov SV, Fabozzi FJ (2013) The methods of distances in the theory of probability and statistics. Springer, New York

    Book  MATH  Google Scholar 

  • Schulz NS (2012) The formation and early evolution of stars. Springer, Berlin

    Book  MATH  Google Scholar 

  • Scrucca L, Fop M, Murphy TB, Raftery AE (2016) mclust 5: clustering, classification and density estimation using Gaussian finite mixture models. R J 8:289–317

    Article  Google Scholar 

  • Shaked M, Shanthikumar JG (2007) Stochastic orders. Springer, New York

    Book  MATH  Google Scholar 

  • van der Vaart AW (1998) Asymptotic statistics. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  • van der Vaart AW, Wellner JA (1996) Weak convergence and empirical processes. Springer, New York

    Book  MATH  Google Scholar 

  • Venables WN, Ripley BD (2002) Modern applied statistics with S. Springer, New York

    Book  MATH  Google Scholar 

  • Wolk SJ, Harnden FR, Flaccomio E, Micela G, Favata F, Shang H, Feigelson ED (2005) Stellar activity on the young suns of Orion: COUP observations of K5–7 pre-main-sequence stars. Astrophys J Suppl S 160:423–449

    Article  Google Scholar 

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Acknowledgements

The authors are grateful to three reviewers and the associate editor for their insightful comments which have improved the presentation of the paper.

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Authors and Affiliations

  1. Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049, Madrid, Spain

    Amparo Baíllo & Javier Cárcamo

  2. Department of Astronomy and Astrophysics, Pennsylvania State University, University Park, PA, 16802-6305, USA

    Konstantin Getman

Authors
  1. Amparo Baíllo
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  2. Javier Cárcamo
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  3. Konstantin Getman
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Corresponding author

Correspondence to Javier Cárcamo.

Additional information

Research by AB and JC was supported by the Spanish MEyC Grants MTM2013-44045-P and MTM2016-78751-P. KG acknowledges the support from the Chandra ACIS Team contract SV4-74018 (G. Garmire and L. Townsley, PIs), issued by the Chandra X-ray Center, which is operated by the Smithsonian Astrophysical Observatory on behalf of NASA under Contract NAS8-03060.

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Baíllo, A., Cárcamo, J. & Getman, K. New distance measures for classifying X-ray astronomy data into stellar classes. Adv Data Anal Classif 13, 531–557 (2019). https://doi.org/10.1007/s11634-018-0309-2

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  • DOI: https://doi.org/10.1007/s11634-018-0309-2

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