  The On-Off problem, aka. Li-Ma problem, is a statistical problem where a
measured rate is the sum of two parts. The first is due to a signal and the
second due to a background, both of which are unknown. Mostly frequentist
solutions are being used that are only adequate for high count numbers. When
the events are rare such an approximation is not good enough. Indeed, in
high-energy astrophysics this is often the rule rather than the exception. I
will present a universal objective Bayesian solution that depends only on the
initial three parameters of the On-Off problem: the number of events in the
"on" region, the number of events in the "off" region, and their
ratio-of-exposure. With a two-step approach it is possible to infer the
signal's significance, strength, uncertainty or upper limit in a unified a way.
The approach is valid without restrictions for any count number including zero
and may be widely applied in particle physics, cosmic-ray physics and
high-energy astrophysics. I apply the method to Gamma Ray Burst data.
