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R. Protassov, D. van Dyk (Dept. of Statistics, Harvard University), A. Connors (Eureka Scientific), V. Kashyap, A. Siemiginowska (Harvard-Smithsonian Center for Astrophysics)
We examine the x-ray spectrum of the afterglow of GRB~970508, analyzed for Fe line emission by Piro et al (1999, ApJL, 514, L73). This is a difficult and extremely important measurement: the detection of x-ray afterglows from \gamma-ray bursts is at best a tricky business, relying on near-real satellite time response to unpredictable events; and a great deal of luck in catching a burst bright enough for a useful spectral analysis. Detecting a clear atomic (or cyclotron) line in the generally smooth and featureless afterglow (or burst) emission not only gives one of the few very specific keys to the physics local to the emission region, but also provides clues or confirmation of its distance (via redshift). Unfortunately, neither the likelihood ratio test or the related F-statistic commonly used to detect spectral lines adhere to their nominal Chi square and F-distributions.
Thus we begin by calibrating the F-statistic used in Piro et al (1999, ApJL, 514, L73) via a simulation study. The simulation study relies on a completely specified source model, i.e. we do Monte Carlo simulations with all model parameters fixed (so--called ``parametric bootstrapping''). Second, we employ the method of posterior predictive p-values to calibrate a LRT statistic while accounting for the uncertainty in the parameters of the source model. Our analysis reveals evidence for the Fe~K line.