  Assume that there are multiple data streams (channels, sensors) and in each
stream the process of interest produces generally dependent and non-identically
distributed observations. When the process is in a normal mode (in-control),
the (pre-change) distribution is known, but when the process becomes abnormal
there is a parametric uncertainty, i.e., the post-change (out-of-control)
distribution is known only partially up to a parameter. Both the change point
and the post-change parameter are unknown. Moreover, the change affects an
unknown subset of streams, so that the number of affected streams and their
location are unknown in advance. A good changepoint detection procedure should
detect the change as soon as possible after its occurrence while controlling
for a risk of false alarms. We consider a Bayesian setup with a given prior
distribution of the change point and propose two sequential mixture-based
change detection rules, one mixes a Shiryaev-type statistic over both the
unknown subset of affected streams and the unknown post-change parameter and
another mixes a Shiryaev-Roberts-type statistic. These rules generalize the
mixture detection procedures studied by Tartakovsky (2018) in a single-stream
case. We provide sufficient conditions under which the proposed multistream
change detection procedures are first-order asymptotically optimal with respect
to moments of the delay to detection as the probability of false alarm
approaches zero.
