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The task of monitoring for a change in the mean of a sequence of Bernoullirandom variables has been widely studied. However most existing approaches makeat least one of the following assumptions, which may be violated in manyreal-world situations: 1) the pre-change value of the Bernoulli parameter isknown in advance, 2) computational efficiency is not paramount, and 3) enoughobservations occur between change points to allow asymptotic approximations tobe used. We develop a novel change detection method based on Fisher's ExactTest which does not make any of these assumptions. We show that our method canbe implemented in a computationally efficient manner, and is hence suited tosequential monitoring where new observations are constantly being received overtime. We assess our method's performance empirically via using simulated data,and find that it is comparable to the optimal CUSUM scheme which assumes bothpre- and post-change values of the parameter to be known.

Sequential Monitoring of a Bernoulli Sequence when the Pre-change Parameter is Unknown