  This paper considers the problem of sequentially detecting a change in the
joint distribution of multiple data sources under a sampling constraint.
Specifically, the channels or sources generate observations that are
independent over time, but not necessarily independent at any given time
instant. The sources follow an initial joint distribution, and at an unknown
time instant, the joint distribution of an unknown subset of sources changes.
Importantly, there is a hard constraint that only a fixed number of sources are
allowed to be sampled at each time instant. The goal is to sequentially observe
the sources according to the constraint, and stop sampling as quickly as
possible after the change while controlling the false alarm rate below a
user-specified level. The sources can be selected dynamically based on the
already collected data, and thus, a policy for this problem consists of a joint
sampling and change-detection rule. A non-randomized policy is studied, and an
upper bound is established on its worst-case conditional expected detection
delay with respect to both the change point and the observations from the
affected sources before the change.
