  We present maximum-likelihood search methods for time-dependent fluxes from
point sources, such as flares or periodic emissions. We describe a method for
the case when the time dependence of the flux can be assumed a priori from
other observations, and we additionally describe a method to search for bursts
with an unknown time dependence. In the context of high energy neutrino
astronomy, we simulate one year of data from a cubic-kilometer scale neutrino
detector and characterize these methods and equivalent binned methods with
respect to the duration of neutrino emission. Compared to standard
time-integrated searches, we find that up to an order of magnitude fewer events
are needed to discover bursts with short durations, even when the burst time
and duration are not known a priori.
