As an application of Stein’s method for Poisson approximation, we prove rates of convergence for the tail probabilities of two scan statistics that have been suggested for detecting local signals in sequences of independent random variables subject to possible change-points. Our formulation deals simultaneously with ordinary and with large deviations.
"Poisson approximation for two scan statistics with rates of convergence." Ann. Appl. Probab. 26 (4) 2384 - 2418, August 2016. https://doi.org/10.1214/15-AAP1150