Bayesian Quickest Detection with Observation-Changepoint Feedback

We study Bayesian quickest detection problems where the observations and the underlying change-point are coupled. This setup supersedes classical models that assume independence of the two. We develop several continuous-time formulations of this problem for the cases of Poissonian and Brownian sensors. Our approach to detection uses methods of nonlinear filtering and optimal stopping and lends itself to an efficient numerical scheme that combines particle filtering with Monte Carlo dynamic programming. The developed models and algorithms are illustrated with numerical examples.