A framework for interpreting fast radio transients search experiments: Application to the V-FASTR experiment

We define a framework for determining constraints on the detection rate of fast transient events from a population of underlying sources, with a view to incorporate beam shape, frequency effects, scattering effects, and detection efficiency into the metric. We then demonstrate a method for combining independent data sets into a single event rate constraint diagram, using a probabilistic approach to the limits on parameter space. We apply this new framework to present the latest results from the V-FASTR experiment, a commensal fast transients search using the Very Long Baseline Array (VLBA). In the 20 cm band, V-FASTR now has the ability to probe the regions of parameter space of importance for the observed Lorimer and Keane fast radio transient candidates by combining the information from observations with differing bandwidths, and properly accounting for the source dispersion measure, VLBA antenna beam shape, experiment time sampling, and stochastic nature of events. We then apply the framework to combine the results of the V-FASTR and Allen Telescope Array Fly's Eye experiments, demonstrating their complementarity. Expectations for fast transients experiments for the SKA Phase I dish array are then computed, and the impact of large differential bandwidths is discussed.