## The Annals of Applied Statistics

### Detecting abrupt changes in the spectra of high-energy astrophysical sources

#### Abstract

Variable-intensity astronomical sources are the result of complex and often extreme physical processes. Abrupt changes in source intensity are typically accompanied by equally sudden spectral shifts, that is, sudden changes in the wavelength distribution of the emission. This article develops a method for modeling photon counts collected from observation of such sources. We embed change points into a marked Poisson process, where photon wavelengths are regarded as marks and both the Poisson intensity parameter and the distribution of the marks are allowed to change. To the best of our knowledge, this is the first effort to embed change points into a marked Poisson process. Between the change points, the spectrum is modeled nonparametrically using a mixture of a smooth radial basis expansion and a number of local deviations from the smooth term representing spectral emission lines. Because the model is over-parameterized, we employ an $\ell_{1}$ penalty. The tuning parameter in the penalty and the number of change points are determined via the minimum description length principle. Our method is validated via a series of simulation studies and its practical utility is illustrated in the analysis of the ultra-fast rotating yellow giant star known as FK Com.

#### Article information

Source
Ann. Appl. Stat., Volume 10, Number 2 (2016), 1107-1134.

Dates
Revised: December 2015
First available in Project Euclid: 22 July 2016

https://projecteuclid.org/euclid.aoas/1469199907

Digital Object Identifier
doi:10.1214/16-AOAS933

Mathematical Reviews number (MathSciNet)
MR3528374

Zentralblatt MATH identifier
06625683

#### Citation

Wong, Raymond K. W.; Kashyap, Vinay L.; Lee, Thomas C. M.; van Dyk, David A. Detecting abrupt changes in the spectra of high-energy astrophysical sources. Ann. Appl. Stat. 10 (2016), no. 2, 1107--1134. doi:10.1214/16-AOAS933. https://projecteuclid.org/euclid.aoas/1469199907

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