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We present an improved Bonferroni inequality which gives an upper bound for the probability of the union of an arbitrary sequence of events. The bound is constructed in terms of the joint probability of pairs of events, which are represented by edges on a graph. Examples of applications to periodicity, location shift detection, Kolmogorov-Smirnov tests and outlier detection are given.
Keith J. Worsley (Fri,) studied this question.