Likelihood analysis of GRB repetition

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Abstract
We develop a framework for computing the likelihoods for GRB repetition models. Our approach is capable of fully and consistently accounting for positional uncertainty, which is crucial to resolving the issue of GRB repetition. We apply the simplest model, which assumes that each site produces at most two bursts, to various burst samples constructed from the BATSE catalogue. The uneven exposure in the BATSE catalogue is taken into account. We find no conclusive evidence of repetition in the spatial distribution of bursts over the entire observation time span. If we divide the catalogue into two-week time intervals, we find one interval with 14 bursts yielding odds of 356 to 1 on 5 repeating sites over no repetition. However, the probability of finding one such interval in the entire catalogue is not small, ∼4.6%. Nevertheless, this supports the idea that the timescale for repetition may be significantly smaller than the entire duration of the data set.

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