  Searches for statistically significant correlations between arrival
directions of ultra-high energy cosmic rays and classes of astrophysical
objects are common in astroparticle physics. We present a method to test
potential correlation signals of a priori unknown strength and evaluate their
statistical significance sequentially, i.e., after each incoming new event in a
running experiment. The method can be applied to data taken after the test has
concluded, allowing for further monitoring of the signal significance. It
adheres to the likelihood principle and rigorously accounts for our ignorance
of the signal strength.
