We present constraints derived from a search of four years of IceCube data for a prompt neutrino flux from gamma-ray bursts (GRBs). A single low-significance neutrino was found in coincidence with one of the 506 observed bursts, consistent with the expectation from atmospheric backgrounds. Although GRBs have been proposed as candidate sources for ultra-high energy cosmic rays, our limits on the neutrino flux disfavor much of the parameter space for the latest models. We also find that no more than ~1% of the recently observed astrophysical neutrino flux consists of prompt emission from GRBs that are potentially observable by existing satellites. These results currently represent world-leading constraints on a prompt neutrino flux from GRBs.

In this thesis, we also introduce an original machine learning software package called pybdt. This implementation is now the de facto standard tool for machine-learning-based classification in IceCube analyses. Finally, we describe an extension of the unbinned likelihood method used in past searches to allow for the combination of data from different detector configurations with different background characteristics in the calculation of model constraints.