  We present a conditional space-time proper orthogonal decomposition (POD)
formulation that is tailored to the eduction of the average, rare or
intermittent event from an ensemble of realizations of a fluid process. By
construction, the resulting spatio-temporal modes are coherent in space and
over a pre-defined finite time horizon and optimally capture the variance, or
energy of the ensemble. For the example of intermittent acoustic radiation from
a turbulent jet, we introduce a conditional expectation operator that focuses
on the loudest events, as measured by a pressure probe in the far-field and
contained in the tail of the pressure signal's probability distribution.
Applied to high-fidelity simulation data, the method identifies a statistically
significant `prototype', or average acoustic burst event that is tracked over
time. Most notably, the burst event can be traced back to its precursor, which
opens up the possibility of prediction of an imminent burst. We furthermore
investigate the mechanism underlying the prototypical burst event using linear
stability theory and find that its structure and evolution is accurately
predicted by optimal transient growth theory. The jet-noise problem
demonstrates that the conditional space-time POD formulation applies even for
systems with probability distributions that are not heavy-tailed, i.e. for
systems in which events overlap and occur in rapid succession.
