A Test for the Presence of a Signal, with Multiple Channels and Marked Poisson

We describe a statistical hypothesis test for the presence of a signal based on the likelihood ratio statistic. We derive the test for a special case of interest. We study extensions of the test to cases where there are multiple channels and to marked Poisson distributions. We show the results of a number of performance studies which indicate that the test works very well, even far out in the tails of the distribution and with multiple channels and marked Poisson.