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Paper: Heuristic Estimates of Weighted Binomial Statistics for Use in Detecting Rare Point Source Transients
Volume: 125, Astronomical Data Analysis Software and Systems VI
Page: 151
Authors: Theiler, James; Bloch, Jeff
Abstract: The \htmladdnormallinkfoot{ALEXIS}{ projects/alexis/} (Array of Low Energy X-ray Imaging Sensors) (Priedhorsky et al. 1989) satellite scans nearly half the sky every fifty seconds, and downlinks time-tagged photon data twice a day. The standard science quicklook processing produces over a dozen sky maps at each downlink, and these maps are automatically searched for potential transient point sources. We are interested only in highly significant point source detections, and, based on earlier Monte-Carlo studies (Roussel-Dupre et al. 1996), only consider p<10(-7) , which is about 5.2 ``sigmas.'' Our algorithms are therefore required to operate on the far tail of the distribution, where many traditional approximations break down. Although an exact solution is available for the case of unweighted counts (Lampton 1994), the problem is more difficult in the case of weighted counts. We have found that a heuristic modification of a formula derived by Li & Ma (1983) provides reasonably accurate estimates of p-values for point source detections even for very low p-value detections.
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