Statistical analysis of spectral line candidates in gamma-ray burst GRB 870303

The Ginga data for the gamma-ray burst GRB 870303 exhibit low-energy dips i n two temporally distinct spectra, denoted Si and S2. S1, spanning 4 s, exh ibits a single line candidate at approximate to 20 keV, while S2, spanning 9 s, exhibits apparently harmonically spaced line candidates at approximate to 20 and 40 keV. The centers of the time intervals corresponding to S1 an d S2 are separated by 22.5 s. We rigorously evaluate the statistical eviden ce for these lines, using phenomenological continuum and line models which in their details are independent of the distance scale to gamma-ray bursts. We employ the methodologies based on both frequentist and Bayesian statist ical inference that we develop in a forthcoming paper. These methodologies utilize the information present in the data to select the simplest model th at adequately describes the data from among a wide range of continuum and c ontinuum-plus-line(s) models. This ensures that the chosen model does not i nclude free parameters that the data deem unnecessary and that would act to reduce the frequentist significance and Bayesian odds of the continuum-plu s-line(s) model. We calculate the significance of the continuum-plus-line(s ) models using the chi(2) maximum likelihood ratio test. We describe a para meterization of the exponentiated Gaussian absorption line shape that makes the probability surface in parameter space better behaved, allowing us to estimate analytically the Bayesian odds. We find that the significance of t he continuum-plus-line model requested by the S1 data is 3.6 x 10(-5) with the odds favoring it being 114:1. The significance of the continuum-plus-li nes model requested by; the S2 data is 1.7 x 10(-4), with the odds favoring it being 7:1. We also apply our methodology to the combined (S1 + S2) data . The significance of the continuum-plus-lines model requested by the combi ned data is 4.2 x 10(-8), with the odds favoring it being 40,300:1.