  We report measurements that show extreme events in the statistics of resonant
radiation emitted from spatiotemporal light bullets. We trace the origin of
these extreme events back to instabilities leading to steep gradients in the
temporal profile of the intense light bullet that occur during the initial
collapse dynamics. Numerical simulations reproduce the extreme valued
statistics of the resonant radiation which are found to be intrinsically linked
to the simultaneous occurrence of both temporal and spatial self-focusing
dynamics. Small fluctuations in both the input energy and in the spatial phase
curvature explain the observed extreme behaviour.
