Sequential monitoring of a Bernoulli sequence when the pre-change parameter is unknown

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