  The paper addresses a sequential changepoint detection problem for a general
stochastic model, assuming that the observed data may be non-i.i.d. (i.e.,
dependent and non-identically distributed) and the prior distribution of the
change point is arbitrary. Tartakovsky and Veeravalli (2005), Baron and
Tartakovsky (2006), and, more recently, Tartakovsky (2017) developed a general
asymptotic theory of changepoint detection for non-i.i.d.\ stochastic models,
assuming the certain stability of the log-likelihood ratio process, in the case
of simple hypotheses when both pre-change and post-change models are completely
specified. However, in most applications, the post-change distribution is not
completely known. In the present paper, we generalize previous results to the
case of parametric uncertainty, assuming the parameter of the post-change
distribution is unknown. We introduce two detection rules based on mixtures --
the Mixture Shiryaev rule and the Mixture Shiryaev--Roberts rule -- and study
their asymptotic properties in the Bayesian context. In particular, we provide
sufficient conditions under which these rules are first-order asymptotically
optimal, minimizing moments of the delay to detection as the probability of
false alarm approaches zero.
