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.
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