Likelihood Analysis of GRB Evolution with Redshift

Abstract

We present a likelihood approach to modeling multi-dimensional GRB Epeak--fluence--redshift data that naturally incorporates instrument detection thresholds. The treatment of instrument thresholds is essential for analyzing evidence for GRB evolution. The method described here compares the data to a uniform jet model, in which the jet parameters are allowed to vary with redshift. Data from different experiments may be modeled jointly. In addition, BATSE data (for which no redshift information is available) may be incorporated by ascribing to each event a likelihood derived from the full model by integrating the probability density over the unknown redshift. The loss of redshift information is mitigated by the large number of available bursts. We discuss the implementation of the method, and validation of it using simulated data.