  In this paper, the problem of quickly detecting an abrupt change on a
stochastic process under Bayesian framework is considered. Different from the
classic Bayesian quickest change-point detection problem, this paper considers
the case where there is uncertainty about the post-change distribution.
Specifically, the observer only knows that the post-change distribution belongs
to a parametric distribution family but he does not know the true value of the
post-change parameter. In this scenario, we propose two multi-chart detection
procedures, termed as M-SR procedure and modified M-SR procedure respectively,
and show that these two procedures are asymptotically optimal when the
post-change parameter belongs to a finite set and are asymptotically
$\epsilon-$optimal when the post-change parameter belongs to a compact set with
finite measure. Both algorithms can be calculated efficiently as their
detection statistics can be updated recursively. We then extend the study to
consider the multi-source monitoring problem with unknown post-change
parameters. When those monitored sources are mutually independent, we propose a
window-based modified M-SR detection procedure and show that the proposed
detection method is first-order asymptotically optimal when post-change
parameters belong to finite sets. We show that both computation and space
complexities of the proposed algorithm increase only linearly with respect to
the number of sources.
