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For decades researchers have studied the On/Off counting problem, where ameasured rate consists of two parts. One due to a signal process and anotherdue to a background process, of which both magnitudes are unknown. While mostfrequentist methods are adequate for large count numbers, they cannot beapplied to sparse data. Here I want to present a new objective Bayesiansolution that only depends on three parameters: the number of events in thesignal region, the number of events in the background region, and the ratio ofthe exposure for both regions. First, the probability of the hypothesis thatthe counts are due to background only is derived analytically. Second, themarginalized posterior for the signal parameter is also derived analytically.With this two-step approach it is easy to calculate the signal's significance,strength, uncertainty, or upper limit in a unified way. The approach is validwithout restrictions for any count number including zero and may be widelyapplied in particle physics, cosmic-ray physics and high-energy astrophysics.In order to demonstrate its performance I apply the method to gamma-ray burstdata.

Signal discovery, limits, and uncertainties with sparse On/Off measurements: an objective Bayesian analysis