The rate at which supernova occur at large distances with high redshifts is hard to obtain. New data collection would require several hundred orbits on the Hubble Space Telescope (HST). However, there are enough HST images of sufficiently deep, extragalactic fields available in archives and the only challenge is locating and identifying the supernovae within them to add the statistical rate analysis. There is a wealth of information on the appearance of high redshift events in relation to their host galaxies that can be used to train artificial neural networks (ANNs) to identify unique magnitude, color, and separation parameter spaces.
Shahady, Kristin, "Locating Supernovae via Artificial Neural Networks" (2015). Aerospace, Physics, and Space Science Student Publications. 16.