Are The Four Gamma-Ray Bursts of 1996 October 27-29 Due to Repetition of a Single Source?

BATSE, Ulysses, and TGRS and KONUS on WIND detected four gamma-ray events within 1.8 days during 1996 October 27-29, consistent with coming from the same location on the sky. We assess the evidence that these events may be due to a series of bursts from a single source by calculating the probability that such a clustering in position and in time of occurrence might happen by chance. The calculation of this probability is afflicted by the usual problem of a posteriori statistics. We introduce a clustering statistic, which is formed from the "minimum circle radius" (i.e. the radius of the smallest circle that just encloses the positions of all the events) and the minimum time lapse (i.e. the time elapsed between the first and last event). We also introduce a second clustering statistic, which is formed from the "cluster likelihood function" and the minimum time lapse. We show that the use of these statistics largely eliminates the "a posteriori" nature of the problem. The two statistics yield significances of the clustering of $3.3\times 10^{-4}$ and $3.1\times 10^{-5}$, respectively, if we interpret the four events as four bursts, whereas the clustering is not significant if we interpret the four events as only three bursts. However, in the latter case one of the bursts is the longest ever observed by BATSE.