  We study the problem of quickest detection of a change in the mean of an
observation sequence, under the assumption that both the pre- and post-change
distributions have bounded support. We first study the case where the
pre-change distribution is known, and then study the extension where only the
mean and variance of the pre-change distribution are known. In both cases, no
knowledge of the post-change distribution is assumed other than that it has
bounded support. For the case where the pre-change distribution is known, we
derive a test that asymptotically minimizes the worst-case detection delay over
all post-change distributions, as the false alarm rate goes to zero. We then
study the limiting form of the optimal test as the gap between the pre- and
post-change means goes to zero, which we call the Mean-Change Test (MCT). We
show that the MCT can be designed with only knowledge of the mean and variance
of the pre-change distribution. We validate our analysis through numerical
results for detecting a change in the mean of a beta distribution. We also
demonstrate the use of the MCT for pandemic monitoring.
