We relate the underlying properties of a population of fast radio-emitting transient events to its expected detection rate in a survey of finite sensitivity .
The distribution of the distances of the detected events is determined in terms of the population luminosity distribution and survey parameters , for both extragalactic and Galactic populations .
The detection rate as a function of Galactic position is examined to identify regions that optimize survey efficiency in a survey whose field of view is limited .
The impact of temporal smearing caused by scattering in the Interstellar Medium has a large and direction-dependent bearing on the detection of impulsive signals , and we present a model for the effects of scattering on the detection rate .
We show the detection rate scales as \Omega S _ { 0 } ^ { -3 / 2 + \delta } , where \Omega is the field of view , and S _ { 0 } is the minimum detectable flux density , and 0 < \delta \leq 3 / 2 for a survey of Galactic transients in which interstellar scattering or the finite volume of the Galaxy is important .
We derive formal conditions on the optimal survey strategy to adopt under different circumstances for fast transients surveys on next generation large-element , widefield arrays , such as ASKAP , LOFAR , the MWA and the SKA , and show how interstellar scattering and the finite spatial extent of a Galactic population modify the choice of optimal strategy .