We have compiled three Type I SNe samples. The first is a sample of 37 Type Ia SNe at low redshift (z < 0.1) from the CfA SN Search Team (Riess 1998, private communication). The second is a sample of 46 moderate redshift (0.1 < z < 0.830) Type Ia SNe from the Supernova Cosmology Project (Perlmutter 1998, private communication). The third sample consists of 20 Type Ib, Ib/c, and Ic SNe compiled from IAU Circulars and various SNe catalogs.
We compare three hypotheses: H1: The association between SNe and GRBs is real. If a SN is observed, there is a chance that BATSE sees the associated GRB, where is the average BATSE temporal exposure. While varies with Declination, the variation is modest and we neglect it. The probability density for the time of occurrence of the ith supernova is assumed uniform in the interval , so that all GRBs that occur in that interval have an equal prior probability of being associated with the SN. : The association is real, but only a fraction f of detectable SNe produce detectable GRB. H2: There is no association between SNe and GRBs.
We calculate the Bayesian Odds, favoring H1 over H2. The details of the calculation are presented in (Graziani et al. 1998). We separately compare to H2, denoting the odds favoring over H2 by .Finally, we calculate the posterior probability distribution for the parameter f in the model , and infer an upper limit on its value.
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