In recent years there has been a proliferation of predictions for stochastic gravitational wave signals from cosmological sources. While the inflationary signal is the most widely discussed, it also has a very small amplitude, relative to other potential stochastic backgrounds. The latter include explosive particle production associated with preheating and bubble collisions associated with first order phase transitions, and are potentially detectable by the next generation of gravitational wave observatories. However, if such stochastic background is observed, how will we know what sourced it? In this talk I will investigate the possibility that higher order statistics of these backgrounds can be used to distinguish different possible sources of stochastic gravitational waves, and assess the practical challenges associated with their measurement.