Rare Event Statistics Applied to Fast Radio Bursts

Understand

Statistical interpretation of sparsely sampled event rates has become vital for new transient surveys, particularly those aimed at detecting fast radio bursts (FRBs).

• We provide an accessible reference for a number of simple, but critical, statistical questions relevant for current transient and FRB research and utilizing the negative binomial model for counts in which the count rate parameter is uncertain or randomly biased from one study to the next.
• We apply these methods to re-assess and update results from previous FRB surveys, finding as follows.
• 1) Thirteen FRBs detected across five high-Galactic-latitude (> 30$^\circ$) surveys are highly significant $(p = 5\times 10^{-5})$ evidence of a higher rate relative to the single FRB detected across four low-latitude (< 5$^\circ$) surveys, even after accounting for effects that dampen Galactic plane sensitivity.