Statistical treatment of searches for counterparts of positionally-uncertain astrophysical sources: from flux upper limits to detection

Abstract

Rapid growth of the multimessenger and multiwavelength astrophysics had led to an increasing number of observations of the same events with instruments with different point spread functions. In particular pointing instruments with good angular resolution are used to pin-point the source of poorly-localized alert. In case no clear detection of the source counterpart is reached, the interpretation of the results requires statistical analysis. We investigate two approaches using the probability density function of the alert: frequentist and Bayesian, as well as agnostic approach not using this information. We discuss the advantages and problems of all the methods, and compare their reliability and performance. We consider both a simple one-dimensional toy simulations and a realistic use case of full simulations of the follow-up of a gravitational wave event with gamma-ray telescopes. The performance of both frequentist and Bayesian approaches for weak signals is comparable and superior to the agnostic one.

arXiv comment13 pages, 15 figures, accepted for publication in JHEAP

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