  We show that \emph{stochastic bursting} is observed in a ring of
unidirectional delay-coupled noisy excitable systems, thanks to the
combinational action of time-delayed coupling and noise. Under the
approximation of timescale separation, i.e., when the time delays in each
connection are much larger than the characteristic duration of the spikes, the
observed rather coherent spike pattern can be described by idealized coupled
point processes with a leader-follower relationship. We derive analytically the
statistics of the spikes in each unit, pairwise correlations between any two
units, and the spectrum of the total output from the network. Theory is in a
good agreement with the simulations with a network of theta-neurons.
