Statistical Modelling 22 (3) (2022), 175–198
Bayesian mixture modelling of the high-energy
photon counts collected by the Fermi Large
Area Telescope
Denise Costantin,
Center for Astrophysics,
Guangzhou University &
Astronomy Science and Technology Research Laboratory of Education of Guangdong Province,
Guangzhou,
China;
Department of Statistical Sciences,
University of Padova,
Padova,
Italy.
e-mail: denise.costantin@gmail.com
Andrea Sottosanti,
Department of Statistical Sciences,
University of Padova,
Padova,
Italy.
Alessandra R. Brazzale,
Department of Statistical Sciences,
University of Padova,
Padova,
Italy.
Denis Bastieri,
Center for Astrophysics,
Guangzhou University,
Guangzhou,
China;
Department of Physics and Astronomy ”G. Galilei”,
University of Padova &
Padova Division,
National Institute for Nuclear Physics,
Padova,
Italy.
JunHui Fan,
Center for Astrophysics,
Guangzhou University &
Astronomy Science and Technology Research Laboratory of Education of Guangdong Province,
Guangzhou,
China.
Abstract:
Identifying as yet undetected high-energy sources in the $\gamma$-ray sky is one of the declared objectives of the \Fermi\ LAT Collaboration. We develop a Bayesian mixture model which is capable of disentangling the high-energy extra-galactic sources present in a given sky region from the pervasive background radiation.
We achieve this by combining two model components. The first component models the emission activity of the single sources and incorporates the instrument response function of the \Fermi\ $\gamma$-ray space telescope. The second component reliably reflects the current knowledge of the physical phenomena which underly the $\gamma$-ray background.
The model parameters are estimated using a reversible jump MCMC algorithm, which simultaneously returns the number of detected sources, their locations and relative intensities, and the background component. Our proposal is illustrated using a sample of the \Fermi\ LAT data. In the analyzed sky region, our model correctly identifies 116 sources out of the 132 present. The detection rate and the estimated directions and intensities of the identified sources are largely unaffected by the number of detected sources.
Keywords:
bivariate exponential distribution, γ-ray photon, instrument response function, mixture
model, reversible jump MCMC
Downloads:
Example data and code in
zipped archive; README ; Supplementary material .
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